Metrics for sin(x)cos(y) + cos(x)sin(y)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample1.6s (46.6%)

Memory

149.1MiB live, 801.5MiB allocated

Samples

886.0ms	8 245×	0	valid
8.0ms	4×	3	valid
1.0ms	3×	2	valid
1.0ms	4×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 670.0ms

ival-sin: 178.0ms (26.6% of total)

ival-<=: 162.0ms (24.2% of total)

ival-cos: 128.0ms (19.1% of total)

ival-mult: 105.0ms (15.7% of total)

ival-add: 56.0ms (8.4% of total)

ival-and: 24.0ms (3.6% of total)

exact: 13.0ms (1.9% of total)

ival-assert: 4.0ms (0.6% of total)

adjust: 1.0ms (0.1% of total)

Bogosity

explain300.0ms (9%)

Memory

-1.2MiB live, 168.6MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(sin.f64 y)`
-	-	`(*.f64 (cos.f64 x) (sin.f64 y))`
-	-	`(*.f64 (sin.f64 x) (cos.f64 y))`
-	-	`(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))`
-	-	`y`
-	-	`(cos.f64 x)`
-	-	`(cos.f64 y)`
-	-	`(sin.f64 x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

101.0ms

512×

valid

Compiler

Compiled 77 to 31 computations (59.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-mult: 67.0ms (79.2% of total)

ival-sin: 8.0ms (9.5% of total)

ival-cos: 7.0ms (8.3% of total)

ival-add: 2.0ms (2.4% of total)

ival-true: 1.0ms (1.2% of total)

ival-assert: 0.0ms (0% of total)

preprocess19.0ms (0.6%)

Memory

5.7MiB live, 5.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	59
1	52	59
2	107	55
3	208	55
4	391	55
5	457	55
6	485	55
7	489	55
0	9	11
0	16	11
1	19	11
0	19	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))

Outputs
(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))
(fma.f64 (sin.f64 y) (cos.f64 x) (*.f64 (cos.f64 y) (sin.f64 x)))

Symmetry

(sort x y)

Compiler

Compiled 11 to 9 computations (18.2% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify2.0ms (0.1%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 y)
cost-diff	0	(sin.f64 x)
cost-diff	0	(*.f64 (sin.f64 x) (cos.f64 y))
cost-diff	1	(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
0	16	31
1	19	31
0	19	30

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))
(*.f64 (sin.f64 x) (cos.f64 y))
(sin.f64 x)
x
(cos.f64 y)
y
(*.f64 (cos.f64 x) (sin.f64 y))
(cos.f64 x)
(sin.f64 y)

Outputs
(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))
(fma.f64 (sin.f64 y) (cos.f64 x) (*.f64 (cos.f64 y) (sin.f64 x)))
(*.f64 (sin.f64 x) (cos.f64 y))
(*.f64 (cos.f64 y) (sin.f64 x))
(sin.f64 x)
x
(cos.f64 y)
y
(*.f64 (cos.f64 x) (sin.f64 y))
(*.f64 (sin.f64 y) (cos.f64 x))
(cos.f64 x)
(sin.f64 y)

localize27.0ms (0.8%)

Memory

10.4MiB live, 10.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 y)
accuracy	0.0	(cos.f64 x)
accuracy	0.0078125	(*.f64 (sin.f64 x) (cos.f64 y))
accuracy	0.0078125	(*.f64 (cos.f64 x) (sin.f64 y))

Samples

20.0ms

256×

valid

Compiler

Compiled 33 to 11 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sin: 4.0ms (34.3% of total)

ival-cos: 3.0ms (25.7% of total)

ival-mult: 3.0ms (25.7% of total)

ival-add: 1.0ms (8.6% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series8.0ms (0.2%)

Memory

4.2MiB live, 4.2MiB allocated

Counts

6 → 38

Calls

Call 1

Inputs
(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))
(*.f64 (sin.f64 x) (cos.f64 y))
(sin.f64 x)
(cos.f64 y)
(*.f64 (cos.f64 x) (sin.f64 y))
(cos.f64 x)

Outputs
(sin y)
(+ (sin y) (* x (cos y)))
(+ (sin y) (* x (+ (cos y) (* -1/2 (* x (sin y))))))
(+ (sin y) (* x (+ (cos y) (* x (+ (* -1/2 (sin y)) (* -1/6 (* x (cos y))))))))
(* x (cos y))
(* x (+ (cos y) (* -1/6 (* (pow x 2) (cos y)))))
(* x (+ (cos y) (* (pow x 2) (+ (* -1/6 (cos y)) (* 1/120 (* (pow x 2) (cos y)))))))
(* x (+ (cos y) (* (pow x 2) (+ (* -1/6 (cos y)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos y))) (* 1/120 (cos y))))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ (sin y) (* -1/2 (* (pow x 2) (sin y))))
(+ (sin y) (* (pow x 2) (+ (* -1/2 (sin y)) (* 1/24 (* (pow x 2) (sin y))))))
(+ (sin y) (* (pow x 2) (+ (* -1/2 (sin y)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin y))) (* 1/24 (sin y)))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* (cos x) (sin y)) (* (cos y) (sin x)))
(* (cos y) (sin x))
(sin x)
(* (cos x) (sin y))
(cos x)
(+ (sin x) (* y (cos x)))
(+ (sin x) (* y (+ (cos x) (* -1/2 (* y (sin x))))))
(+ (sin x) (* y (+ (cos x) (* y (+ (* -1/2 (sin x)) (* -1/6 (* y (cos x))))))))
(+ (sin x) (* -1/2 (* (pow y 2) (sin x))))
(+ (sin x) (* (pow y 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow y 2) (sin x))))))
(+ (sin x) (* (pow y 2) (+ (* -1/2 (sin x)) (* (pow y 2) (+ (* -1/720 (* (pow y 2) (sin x))) (* 1/24 (sin x)))))))
(+ 1 (* -1/2 (pow y 2)))
(+ 1 (* (pow y 2) (- (* 1/24 (pow y 2)) 1/2)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/24 (* -1/720 (pow y 2)))) 1/2)))
(* y (cos x))
(* y (+ (cos x) (* -1/6 (* (pow y 2) (cos x)))))
(* y (+ (cos x) (* (pow y 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow y 2) (cos x)))))))
(* y (+ (cos x) (* (pow y 2) (+ (* -1/6 (cos x)) (* (pow y 2) (+ (* -1/5040 (* (pow y 2) (cos x))) (* 1/120 (cos x))))))))
(cos y)

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((+ (* (sin x) (cos y)) (* (cos x) (sin y))) (* (sin x) (cos y)) (sin x) (cos y) (* (cos x) (sin y)) (cos x))
1.0ms	x	@	0	((+ (* (sin x) (cos y)) (* (cos x) (sin y))) (* (sin x) (cos y)) (sin x) (cos y) (* (cos x) (sin y)) (cos x))
1.0ms	y	@	0	((+ (* (sin x) (cos y)) (* (cos x) (sin y))) (* (sin x) (cos y)) (sin x) (cos y) (* (cos x) (sin y)) (cos x))
1.0ms	y	@	inf	((+ (* (sin x) (cos y)) (* (cos x) (sin y))) (* (sin x) (cos y)) (sin x) (cos y) (* (cos x) (sin y)) (cos x))
1.0ms	x	@	-inf	((+ (* (sin x) (cos y)) (* (cos x) (sin y))) (* (sin x) (cos y)) (sin x) (cos y) (* (cos x) (sin y)) (cos x))

simplify187.0ms (5.6%)

Memory

43.1MiB live, 43.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	152	498
1	470	470
2	1377	458
3	2210	446
4	3642	446
5	4245	446
6	4672	446
7	5243	446
8	6288	446
0	8602	391

Stop Event

1×	iter limit
1×	node limit

Counts

38 → 37

Calls

Call 1

Inputs
(sin y)
(+ (sin y) (* x (cos y)))
(+ (sin y) (* x (+ (cos y) (* -1/2 (* x (sin y))))))
(+ (sin y) (* x (+ (cos y) (* x (+ (* -1/2 (sin y)) (* -1/6 (* x (cos y))))))))
(* x (cos y))
(* x (+ (cos y) (* -1/6 (* (pow x 2) (cos y)))))
(* x (+ (cos y) (* (pow x 2) (+ (* -1/6 (cos y)) (* 1/120 (* (pow x 2) (cos y)))))))
(* x (+ (cos y) (* (pow x 2) (+ (* -1/6 (cos y)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos y))) (* 1/120 (cos y))))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ (sin y) (* -1/2 (* (pow x 2) (sin y))))
(+ (sin y) (* (pow x 2) (+ (* -1/2 (sin y)) (* 1/24 (* (pow x 2) (sin y))))))
(+ (sin y) (* (pow x 2) (+ (* -1/2 (sin y)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin y))) (* 1/24 (sin y)))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* (cos x) (sin y)) (* (cos y) (sin x)))
(* (cos y) (sin x))
(sin x)
(* (cos x) (sin y))
(cos x)
(+ (sin x) (* y (cos x)))
(+ (sin x) (* y (+ (cos x) (* -1/2 (* y (sin x))))))
(+ (sin x) (* y (+ (cos x) (* y (+ (* -1/2 (sin x)) (* -1/6 (* y (cos x))))))))
(+ (sin x) (* -1/2 (* (pow y 2) (sin x))))
(+ (sin x) (* (pow y 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow y 2) (sin x))))))
(+ (sin x) (* (pow y 2) (+ (* -1/2 (sin x)) (* (pow y 2) (+ (* -1/720 (* (pow y 2) (sin x))) (* 1/24 (sin x)))))))
(+ 1 (* -1/2 (pow y 2)))
(+ 1 (* (pow y 2) (- (* 1/24 (pow y 2)) 1/2)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/24 (* -1/720 (pow y 2)))) 1/2)))
(* y (cos x))
(* y (+ (cos x) (* -1/6 (* (pow y 2) (cos x)))))
(* y (+ (cos x) (* (pow y 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow y 2) (cos x)))))))
(* y (+ (cos x) (* (pow y 2) (+ (* -1/6 (cos x)) (* (pow y 2) (+ (* -1/5040 (* (pow y 2) (cos x))) (* 1/120 (cos x))))))))
(cos y)

Outputs
(sin y)
(sin.f64 y)
(+ (sin y) (* x (cos y)))
(fma.f64 (cos.f64 y) x (sin.f64 y))
(+ (sin y) (* x (+ (cos y) (* -1/2 (* x (sin y))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 y)) x (cos.f64 y)) x (sin.f64 y))
(+ (sin y) (* x (+ (cos y) (* x (+ (* -1/2 (sin y)) (* -1/6 (* x (cos y))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 y) x) (.f64 #s(literal -1/2 binary64) (sin.f64 y))) x (cos.f64 y)) x (sin.f64 y))
(* x (cos y))
(*.f64 (cos.f64 y) x)
(* x (+ (cos y) (* -1/6 (* (pow x 2) (cos y)))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (cos.f64 y))
(* x (+ (cos y) (* (pow x 2) (+ (* -1/6 (cos y)) (* 1/120 (* (pow x 2) (cos y)))))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) (cos.f64 y)) x)
(* x (+ (cos y) (* (pow x 2) (+ (* -1/6 (cos y)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos y))) (* 1/120 (cos y))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (cos.f64 y) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64))) (.f64 (cos.f64 y) x))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(+ (sin y) (* -1/2 (* (pow x 2) (sin y))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 y))
(+ (sin y) (* (pow x 2) (+ (* -1/2 (sin y)) (* 1/24 (* (pow x 2) (sin y))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) (sin.f64 y))
(+ (sin y) (* (pow x 2) (+ (* -1/2 (sin y)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin y))) (* 1/24 (sin y)))))))
(fma.f64 (.f64 (sin.f64 y) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x x) (sin.f64 y))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ (* (cos x) (sin y)) (* (cos y) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 y) (*.f64 (cos.f64 x) (sin.f64 y)))
(* (cos y) (sin x))
(*.f64 (sin.f64 x) (cos.f64 y))
(sin x)
(sin.f64 x)
(* (cos x) (sin y))
(*.f64 (cos.f64 x) (sin.f64 y))
(cos x)
(cos.f64 x)
(+ (sin x) (* y (cos x)))
(fma.f64 (cos.f64 x) y (sin.f64 x))
(+ (sin x) (* y (+ (cos x) (* -1/2 (* y (sin x))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) y (cos.f64 x)) y (sin.f64 x))
(+ (sin x) (* y (+ (cos x) (* y (+ (* -1/2 (sin x)) (* -1/6 (* y (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) y) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) y (cos.f64 x)) y (sin.f64 x))
(+ (sin x) (* -1/2 (* (pow y 2) (sin x))))
(.f64 (fma.f64 (.f64 y y) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 x))
(+ (sin x) (* (pow y 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow y 2) (sin x))))))
(.f64 (fma.f64 (fma.f64 (.f64 y y) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 y y) #s(literal 1 binary64)) (sin.f64 x))
(+ (sin x) (* (pow y 2) (+ (* -1/2 (sin x)) (* (pow y 2) (+ (* -1/720 (* (pow y 2) (sin x))) (* 1/24 (sin x)))))))
(fma.f64 (.f64 (sin.f64 x) (fma.f64 (fma.f64 (.f64 y y) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 y y) #s(literal -1/2 binary64))) (.f64 y y) (sin.f64 x))
(+ 1 (* -1/2 (pow y 2)))
(fma.f64 (*.f64 y y) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 1/24 (pow y 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 y y) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/24 (* -1/720 (pow y 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 y y) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 y y) #s(literal -1/2 binary64)) (*.f64 y y) #s(literal 1 binary64))
(* y (cos x))
(*.f64 (cos.f64 x) y)
(* y (+ (cos x) (* -1/6 (* (pow y 2) (cos x)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) y) y #s(literal 1 binary64)) y) (cos.f64 x))
(* y (+ (cos x) (* (pow y 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow y 2) (cos x)))))))
(.f64 (.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 y y) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) y)
(* y (+ (cos x) (* (pow y 2) (+ (* -1/6 (cos x)) (* (pow y 2) (+ (* -1/5040 (* (pow y 2) (cos x))) (* 1/120 (cos x))))))))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (.f64 (cos.f64 x) (fma.f64 (.f64 y y) (fma.f64 (.f64 y y) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (.f64 (cos.f64 x) y))
(cos y)
(cos.f64 y)

rewrite196.0ms (5.9%)

Memory

-29.8MiB live, 49.9MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
0	16	27
1	39	20
2	264	20
3	3552	20
0	8232	20

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

6 → 174

Calls

Call 1

Inputs
(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))
(*.f64 (sin.f64 x) (cos.f64 y))
(sin.f64 x)
(cos.f64 y)
(*.f64 (cos.f64 x) (sin.f64 y))
(cos.f64 x)

Outputs
(.f64 (pow.f64 (/.f64 (sin.f64 (-.f64 x y)) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (sin.f64 (-.f64 x y)) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64))) (pow.f64 (.f64 (.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 9 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) (pow.f64 (.f64 (.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 x y))) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 (+.f64 y x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x))) #s(literal 2 binary64)))) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (sin.f64 (-.f64 y x)) (*.f64 (sin.f64 y) (cos.f64 x)))))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x))) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x))) (-.f64 (.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x))) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 x y))) (*.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 x y)))) (sin.f64 (+.f64 y x)))
(.f64 (.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 y x))) (pow.f64 (sin.f64 (-.f64 y x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 x y))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64)) (.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 x y))))
(.f64 (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 y x)))
(.f64 (.f64 (neg.f64 (sin.f64 (+.f64 y x))) (sin.f64 (-.f64 x y))) (pow.f64 (neg.f64 (sin.f64 (-.f64 x y))) #s(literal -1 binary64)))
(.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 x y))) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64)))
(.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (/.f64 (sin.f64 (+.f64 y x)) (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)))))
(.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (.f64 (sin.f64 (+.f64 y x)) (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (sin.f64 (+.f64 y x)) (/.f64 (sin.f64 (-.f64 x y)) (sin.f64 (-.f64 x y))))
(.f64 (sin.f64 (+.f64 y x)) (.f64 (sin.f64 (-.f64 x y)) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64))))
(pow.f64 (/.f64 (sin.f64 (-.f64 y x)) (*.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 y x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 y x)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (sin.f64 (+.f64 y x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64))) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64))) (pow.f64 (.f64 (.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 9 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 9 binary64))) (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) (pow.f64 (.f64 (.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) (/.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y)))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -3 binary64))) (.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -3 binary64)))) (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) (/.f64 (pow.f64 (*.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y)))))))
(/.f64 (neg.f64 (*.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 y x)))) (neg.f64 (sin.f64 (-.f64 y x))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 (+.f64 y x))) (sin.f64 (-.f64 x y)))) (neg.f64 (neg.f64 (sin.f64 (-.f64 x y)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (sin.f64 (-.f64 x y))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64))) (pow.f64 (.f64 (.f64 (*.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 2 binary64))) (sin.f64 (-.f64 x y))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 9 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) (pow.f64 (.f64 (.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 3 binary64))) (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) (.f64 (sin.f64 (-.f64 x y)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)))) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 y x)) (sin.f64 (+.f64 y x))) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal -1 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal -1 binary64))))
(/.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 y x)) (sin.f64 (+.f64 y x))) #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (+.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 x y)))))) #s(literal -4 binary64))
(/.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 y x)) (sin.f64 (+.f64 y x))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 x y))))) #s(literal 4 binary64))
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal -1 binary64)) (+.f64 (sin.f64 (-.f64 y x)) (sin.f64 (+.f64 y x))))) (.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 x y)))) #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (+.f64 (sin.f64 (-.f64 y x)) (sin.f64 (+.f64 y x))))) #s(literal -4 binary64))
(/.f64 (fma.f64 (+.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 x y))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 y x)) (sin.f64 (+.f64 y x))))) #s(literal 4 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sin.f64 (+.f64 y x)) #s(literal -1 binary64))))
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(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) (.f64 (sin.f64 (-.f64 x y)) (+.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64))) (pow.f64 (.f64 (.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 2 binary64)))))
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(/.f64 (*.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 y x))) (sin.f64 (-.f64 y x)))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 y x)) (*.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 (+.f64 y x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 (+.f64 y x)) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 9 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 9 binary64))) (.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) (pow.f64 (.f64 (.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 3 binary64)))))
(/.f64 (*.f64 (neg.f64 (sin.f64 (+.f64 y x))) (sin.f64 (-.f64 x y))) (neg.f64 (sin.f64 (-.f64 x y))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)))))
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(/.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 y x)) (sin.f64 (+.f64 y x)))) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 y x)) (sin.f64 (+.f64 y x)))))
(/.f64 (+.f64 (sin.f64 (-.f64 y x)) (sin.f64 (+.f64 y x))) #s(literal 2 binary64))
(exp.f64 (.f64 (log.f64 (.f64 (sin.f64 y) (cos.f64 x))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (*.f64 (sin.f64 y) (cos.f64 x))))
(cos.f64 x)

eval25.0ms (0.8%)

Memory: 19.4MiB live, 19.4MiB allocated
Compiler: Compiled 5 150 to 656 computations (87.3% saved)

prune3.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	210	2	212

Accuracy

100.0%

Counts

212 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sin.f64 (+.f64 y x))
▶	48.3%	#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify3.0ms (0.1%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 y x)
cost-diff	0	(sin.f64 (+.f64 y x))
cost-diff	0	(sin.f64 y)
cost-diff	0	#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
0	16	26
1	20	26
0	20	25

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))
(sin.f64 y)
y
(sin.f64 (+.f64 y x))
(+.f64 y x)
y
x

Outputs
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))
(sin.f64 y)
y
(sin.f64 (+.f64 y x))
(+.f64 y x)
y
x

localize36.0ms (1.1%)

Memory

-63.2MiB live, 14.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 y x)
accuracy	0.0	(sin.f64 (+.f64 y x))
accuracy	0.0	(sin.f64 y)
accuracy	33.08604562298268	#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))

Samples

29.0ms

256×

valid

Compiler

Compiled 25 to 13 computations (48% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-sin: 11.0ms (53.6% of total)

ival-cos: 3.0ms (14.6% of total)

ival-mult: 3.0ms (14.6% of total)

ival-add: 2.0ms (9.7% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

4 → 22

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))
(sin.f64 y)
(sin.f64 (+.f64 y x))
(+.f64 y x)

Outputs
(sin y)
(+ (sin y) (* x (cos y)))
(+ (sin y) (* x (+ (cos y) (* -1/2 (* x (sin y))))))
(+ (sin y) (* x (+ (cos y) (* x (+ (* -1/2 (sin y)) (* -1/6 (* x (cos y))))))))
y
(+ x y)
(+ (* (cos x) (sin y)) (* (cos y) (sin x)))
(sin (+ x y))
x
(* x (+ 1 (/ y x)))
(sin (- y (* -1 x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(sin x)
(+ (sin x) (* y (cos x)))
(+ (sin x) (* y (+ (cos x) (* -1/2 (* y (sin x))))))
(+ (sin x) (* y (+ (cos x) (* y (+ (* -1/2 (sin x)) (* -1/6 (* y (cos x))))))))
(* y (+ 1 (* -1/6 (pow y 2))))
(* y (+ 1 (* (pow y 2) (- (* 1/120 (pow y 2)) 1/6))))
(* y (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/120 (* -1/5040 (pow y 2)))) 1/6))))
(* y (+ 1 (/ x y)))
(sin (- x (* -1 y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin y) (sin (+ y x)) (+ y x))
1.0ms	x	@	-inf	((+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin y) (sin (+ y x)) (+ y x))
1.0ms	y	@	-inf	((+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin y) (sin (+ y x)) (+ y x))
1.0ms	y	@	inf	((+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin y) (sin (+ y x)) (+ y x))
0.0ms	y	@	0	((+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin y) (sin (+ y x)) (+ y x))

simplify140.0ms (4.2%)

Memory

36.1MiB live, 36.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	173
1	235	173
2	548	167
3	2071	167
4	7149	167
0	8383	148

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 20

Calls

Call 1

Inputs
(sin y)
(+ (sin y) (* x (cos y)))
(+ (sin y) (* x (+ (cos y) (* -1/2 (* x (sin y))))))
(+ (sin y) (* x (+ (cos y) (* x (+ (* -1/2 (sin y)) (* -1/6 (* x (cos y))))))))
y
(+ x y)
(+ (* (cos x) (sin y)) (* (cos y) (sin x)))
(sin (+ x y))
x
(* x (+ 1 (/ y x)))
(sin (- y (* -1 x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(sin x)
(+ (sin x) (* y (cos x)))
(+ (sin x) (* y (+ (cos x) (* -1/2 (* y (sin x))))))
(+ (sin x) (* y (+ (cos x) (* y (+ (* -1/2 (sin x)) (* -1/6 (* y (cos x))))))))
(* y (+ 1 (* -1/6 (pow y 2))))
(* y (+ 1 (* (pow y 2) (- (* 1/120 (pow y 2)) 1/6))))
(* y (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/120 (* -1/5040 (pow y 2)))) 1/6))))
(* y (+ 1 (/ x y)))
(sin (- x (* -1 y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))

Outputs
(sin y)
(sin.f64 y)
(+ (sin y) (* x (cos y)))
(fma.f64 (cos.f64 y) x (sin.f64 y))
(+ (sin y) (* x (+ (cos y) (* -1/2 (* x (sin y))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 y)) x (cos.f64 y)) x (sin.f64 y))
(+ (sin y) (* x (+ (cos y) (* x (+ (* -1/2 (sin y)) (* -1/6 (* x (cos y))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 y) x) (.f64 #s(literal -1/2 binary64) (sin.f64 y))) x (cos.f64 y)) x (sin.f64 y))
y
(+ x y)
(+.f64 y x)
(+ (* (cos x) (sin y)) (* (cos y) (sin x)))
(fma.f64 (sin.f64 y) (cos.f64 x) (*.f64 (cos.f64 y) (sin.f64 x)))
(sin (+ x y))
(sin.f64 (+.f64 y x))
x
(* x (+ 1 (/ y x)))
(+.f64 y x)
(sin (- y (* -1 x)))
(sin.f64 (+.f64 y x))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(sin x)
(sin.f64 x)
(+ (sin x) (* y (cos x)))
(fma.f64 (cos.f64 x) y (sin.f64 x))
(+ (sin x) (* y (+ (cos x) (* -1/2 (* y (sin x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) y (cos.f64 x)) y (sin.f64 x))
(+ (sin x) (* y (+ (cos x) (* y (+ (* -1/2 (sin x)) (* -1/6 (* y (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) y) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) y (cos.f64 x)) y (sin.f64 x))
(* y (+ 1 (* -1/6 (pow y 2))))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1/6 binary64) y)
(* y (+ 1 (* (pow y 2) (- (* 1/120 (pow y 2)) 1/6))))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 y y) #s(literal -1/6 binary64)) y)
(* y (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/120 (* -1/5040 (pow y 2)))) 1/6))))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 y y) #s(literal 1/120 binary64)) (.f64 y y) #s(literal -1/6 binary64)) y)
(* y (+ 1 (/ x y)))
(+.f64 y x)
(sin (- x (* -1 y)))
(sin.f64 (+.f64 y x))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)

rewrite293.0ms (8.8%)

Memory

-157.2MiB live, 45.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
0	16	16
1	53	16
2	372	16
3	4880	16
0	8508	16

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 163

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))
(sin.f64 y)
(sin.f64 (+.f64 y x))
(+.f64 y x)

Outputs
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))
(sin.f64 y)
(.f64 (/.f64 (.f64 (sin.f64 (-.f64 x y)) (sin.f64 (+.f64 y x))) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 (+.f64 y x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x))) #s(literal 2 binary64)))) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (sin.f64 (-.f64 y x)) (*.f64 (sin.f64 y) (cos.f64 x)))))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x))) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x))) (-.f64 (.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x))) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (sin.f64 (-.f64 x y)) (sin.f64 (+.f64 y x))) (*.f64 (sin.f64 (-.f64 x y)) (sin.f64 (+.f64 y x)))) (sin.f64 (+.f64 y x)))
(.f64 (.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 y x))) (pow.f64 (sin.f64 (-.f64 y x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64)) (.f64 (sin.f64 (-.f64 x y)) (sin.f64 (+.f64 y x))))
(.f64 (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 y x)))
(.f64 (.f64 (neg.f64 (sin.f64 (+.f64 y x))) (sin.f64 (-.f64 x y))) (pow.f64 (neg.f64 (sin.f64 (-.f64 x y))) #s(literal -1 binary64)))
(.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (.f64 (sin.f64 (-.f64 x y)) (sin.f64 (+.f64 y x))) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64)))
(.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (/.f64 (sin.f64 (+.f64 y x)) (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)))))
(.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (.f64 (sin.f64 (+.f64 y x)) (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (sin.f64 (+.f64 y x)) (/.f64 (sin.f64 (-.f64 x y)) (sin.f64 (-.f64 x y))))
(.f64 (sin.f64 (+.f64 y x)) (.f64 (sin.f64 (-.f64 x y)) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64))))
(pow.f64 (/.f64 (sin.f64 (-.f64 y x)) (*.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 y x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 y x)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (sin.f64 (+.f64 y x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64))) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64))) (pow.f64 (.f64 (.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 9 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 9 binary64))) (pow.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) (pow.f64 (.f64 (.f64 (.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) (/.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y)))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -3 binary64))) (.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 (-.f64 x y)) #s(literal -3 binary64)))) (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y))) (/.f64 (pow.f64 (*.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x y)))))))
(/.f64 (neg.f64 (*.f64 (sin.f64 (+.f64 y x)) (sin.f64 (-.f64 y x)))) (neg.f64 (sin.f64 (-.f64 y x))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 (+.f64 y x))) (sin.f64 (-.f64 x y)))) (neg.f64 (neg.f64 (sin.f64 (-.f64 x y)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (sin.f64 (-.f64 y x)) (.f64 (sin.f64 y) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 2 binary64))) (sin.f64 (-.f64 x y))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 y) (cos.f64 x)) #s(literal 4 binary64))) (pow.f64 (.f64 (.f64 (*.f64 (sin.f64 y) (cos.f64 x)) (sin.f64 x)) (cos.f64 y)) #s(literal 2 binary64))) (sin.f64 (-.f64 x y))))
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(pow.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) (fma.f64 y y (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (fma.f64 y y (*.f64 x x)) (pow.f64 y #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 x y) x (.f64 y y)))
(/.f64 (-.f64 (pow.f64 (.f64 y (/.f64 y (-.f64 y x))) #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 x (-.f64 y x))) #s(literal 2 binary64))) (fma.f64 y (/.f64 y (-.f64 y x)) (*.f64 x (/.f64 x (-.f64 y x)))))
(/.f64 (-.f64 (pow.f64 (.f64 y (/.f64 y (-.f64 y x))) #s(literal 3 binary64)) (pow.f64 (.f64 x (/.f64 x (-.f64 y x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 y (/.f64 y (-.f64 y x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 y x))) #s(literal 2 binary64)) (.f64 (.f64 y (/.f64 y (-.f64 y x))) (*.f64 x (/.f64 x (-.f64 y x)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x)))) (neg.f64 (neg.f64 (-.f64 y x))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 y y (*.f64 x x)) (-.f64 y x)))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (fma.f64 y y (.f64 x x)) (pow.f64 y #s(literal 4 binary64))) (-.f64 y x)))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x y) x (*.f64 y y))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (fma.f64 (-.f64 x y) x (.f64 y y))))
(/.f64 (-.f64 (.f64 (.f64 y y) (-.f64 y x)) (.f64 (-.f64 y x) (.f64 x x))) (pow.f64 (-.f64 y x) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (-.f64 y x) (fma.f64 y y (.f64 x x))))
(/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (-.f64 y x) (fma.f64 (.f64 x x) (fma.f64 y y (*.f64 x x)) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 x y))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (*.f64 (+.f64 y x) (-.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) (.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (-.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))
(/.f64 (*.f64 (-.f64 y x) (+.f64 y x)) (-.f64 y x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (-.f64 x y) x (*.f64 y y)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x))) (-.f64 y x)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (-.f64 x y) x (*.f64 y y))))
(neg.f64 (/.f64 (*.f64 (-.f64 y x) (+.f64 y x)) (neg.f64 (-.f64 y x))))
(neg.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(fma.f64 (/.f64 (.f64 y y) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 y (+.f64 y x) (.f64 x x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (/.f64 (.f64 y y) (.f64 (-.f64 y x) (+.f64 y x))) (+.f64 y x) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (.f64 y y) (pow.f64 (-.f64 y x) #s(literal -1 binary64)) (neg.f64 (.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 y (/.f64 y (-.f64 y x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))
(-.f64 (.f64 y (/.f64 y (-.f64 y x))) (.f64 x (/.f64 x (-.f64 y x))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 y (/.f64 y (-.f64 y x))) (neg.f64 (.f64 x (/.f64 x (-.f64 y x)))))
(+.f64 y x)
(+.f64 x y)

eval22.0ms (0.6%)

Memory: 16.3MiB live, 16.3MiB allocated
Compiler: Compiled 4 231 to 586 computations (86.1% saved)

prune4.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	175	3	178

Accuracy

100.0%

Counts

178 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sin.f64 (+.f64 y x))
✓	48.3%	#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))
	52.8%	#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 x))

Compiler

Compiled 75 to 46 computations (38.7% saved)

regimes5.0ms (0.2%)

Memory

5.4MiB live, 5.4MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 x))
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))
(sin.f64 (+.f64 y x))
(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))

Outputs
(sin.f64 (+.f64 y x))

Calls

3 calls:

2.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))
2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes4.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 x))
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))

Outputs
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 x))
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y))

Calls

3 calls:

1.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
80.6%	2	`x`
85.1%	2	`y`
96.1%	2	`(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes3.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 x))

Outputs
#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 x))

Calls

3 calls:

1.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))
1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
52.8%	1	`x`
52.8%	1	`y`
52.8%	1	`(+.f64 (.f64 (sin.f64 x) (cos.f64 y)) (.f64 (cos.f64 x) (sin.f64 y)))`

Compiler

Compiled 13 to 13 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.5968695111098505e-298	3.992153901636265e-300

Compiler

Compiled 14 to 14 computations (0% saved)

simplify10.0ms (0.3%)

Memory

6.6MiB live, 6.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	60
1	26	60

Stop Event

1×

saturated

Calls

Call 1

Inputs

(sin.f64 (+.f64 y x))

(if (<=.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 y)) (*.f64 (cos.f64 x) (sin.f64 y))) #s(literal -4712544691453469/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104 binary64)) #s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 x)) #s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y)))

#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 x))

Outputs

(sin.f64 (+.f64 y x))

(if (<=.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 y)) (*.f64 (cos.f64 x) (sin.f64 y))) #s(literal -4712544691453469/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104 binary64)) #s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 x)) #s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 y)))

#s(approx (+ (* (sin x) (cos y)) (* (cos x) (sin y))) (sin.f64 x))

soundness466.0ms (14%)

Memory

3.7MiB live, 3.7MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	83	173
1	235	173
2	548	167
3	2071	167
4	7149	167
0	8383	148
0	152	498
1	470	470
2	1377	458
3	2210	446
4	3642	446
5	4245	446
6	4672	446
7	5243	446
8	6288	446
0	8602	391
0	9	27
0	16	27
1	39	20
2	264	20
3	3552	20
0	8232	20

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 85 to 49 computations (42.4% saved)

preprocess23.0ms (0.7%)

Memory: 15.8MiB live, 15.8MiB allocated
Remove: (sort x y)
Compiler: Compiled 150 to 72 computations (52% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	23	59
1	52	59
2	107	55
3	208	55
4	391	55
5	457	55
6	485	55
7	489	55
0	9	11
0	16	11
1	19	11
0	19	10

Iter	Nodes	Cost
0	23	59
1	52	59
2	107	55
3	208	55
4	391	55
5	457	55
6	485	55
7	489	55
0	9	11
0	16	11
1	19	11
0	19	10

start0.0ms (0%)

analyze1.0ms (0%)

sample1.6s (46.6%)

explain300.0ms (9%)

preprocess19.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify2.0ms (0.1%)

localize27.0ms (0.8%)

series8.0ms (0.2%)

simplify187.0ms (5.6%)

rewrite196.0ms (5.9%)

eval25.0ms (0.8%)

prune3.0ms (0.1%)

simplify3.0ms (0.1%)

localize36.0ms (1.1%)

series5.0ms (0.2%)

simplify140.0ms (4.2%)

rewrite293.0ms (8.8%)

eval22.0ms (0.6%)

prune4.0ms (0.1%)

regimes5.0ms (0.2%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch1.0ms (0%)

simplify10.0ms (0.3%)

soundness466.0ms (14%)

preprocess23.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	23	59
1	52	59
2	107	55
3	208	55
4	391	55
5	457	55
6	485	55
7	489	55
0	9	11
0	16	11
1	19	11
0	19	10