Metrics for Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3

analyze0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample1.7s (46.4%)

Memory

26.1MiB live, 1 653.0MiB allocated

Samples

1.5s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 812.0ms

ival-cos: 445.0ms (54.8% of total)

ival-sin: 169.0ms (20.8% of total)

ival-mult: 124.0ms (15.3% of total)

ival-add: 64.0ms (7.9% of total)

ival-true: 6.0ms (0.7% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

preprocess48.0ms (1.3%)

Memory

-25.6MiB live, 57.0MiB allocated

Algorithm

2×	egg-herbie

Rules

168×	`associate-r`
164×	`unsub-neg`
142×	`associate-l`
132×	`distribute-lft-neg-in`
116×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	96
1	81	90
2	141	90
3	323	90
4	491	90
5	733	90
6	904	90
7	987	90
8	1066	90
9	1132	90
10	1146	90
11	1151	90
12	1153	90
0	8	9
1	11	9
0	11	8

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ (* x (cos y)) (* z (sin y)))

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

Call 2

Inputs
(+ (* x (cos y)) (* z (sin y)))
(+ (* (neg x) (cos y)) (* z (sin y)))
(+ (* x (cos (neg y))) (* z (sin (neg y))))
(+ (* x (cos y)) (* (neg z) (sin y)))
(neg (+ (* (neg x) (cos y)) (* z (sin y))))
(neg (+ (* x (cos (neg y))) (* z (sin (neg y)))))
(neg (+ (* x (cos y)) (* (neg z) (sin y))))
(+ (* y (cos x)) (* z (sin x)))
(+ (* z (cos y)) (* x (sin y)))
(+ (* x (cos z)) (* y (sin z)))

Outputs
(+ (* x (cos y)) (* z (sin y)))
(+ (* (neg x) (cos y)) (* z (sin y)))
(- (* z (sin y)) (* x (cos y)))
(+ (* x (cos (neg y))) (* z (sin (neg y))))
(- (* x (cos y)) (* z (sin y)))
(+ (* x (cos y)) (* (neg z) (sin y)))
(- (* x (cos y)) (* z (sin y)))
(neg (+ (* (neg x) (cos y)) (* z (sin y))))
(- (* x (cos y)) (* z (sin y)))
(neg (+ (* x (cos (neg y))) (* z (sin (neg y)))))
(- (* z (sin y)) (* x (cos y)))
(neg (+ (* x (cos y)) (* (neg z) (sin y))))
(- (* z (sin y)) (* x (cos y)))
(+ (* y (cos x)) (* z (sin x)))
(+ (* z (cos y)) (* x (sin y)))
(+ (* (cos y) z) (* x (sin y)))
(+ (* x (cos z)) (* y (sin z)))

explain101.0ms (2.7%)

Memory

5.5MiB live, 243.9MiB allocated

FPErrors

Click to see full error table

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

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

49.0ms

512×

valid

Compiler

Compiled 76 to 36 computations (52.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-cos: 11.0ms (34.6% of total)

ival-sin: 11.0ms (34.6% of total)

ival-mult: 6.0ms (18.9% of total)

ival-add: 2.0ms (6.3% of total)

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

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

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.1%)

Memory

14.1MiB live, 14.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 z (sin.f64 y))
✓	cost-diff	0	(cos.f64 y)
✓	cost-diff	0	(*.f64 x (cos.f64 y))
✓	cost-diff	128	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Rules

8×	`-lowering-.f32`
8×	`-lowering-.f64`
8×	`accelerator-lowering-fma.f32`
8×	`accelerator-lowering-fma.f64`
4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	11	24
0	11	23

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* x (cos y)) (* z (sin y)))
(* x (cos y))
x
(cos y)
y
(* z (sin y))
z
(sin y)

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

localize35.0ms (0.9%)

Memory

-20.5MiB live, 98.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 y)
✓	accuracy	100.0%	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
✓	accuracy	99.8%	(*.f64 z (sin.f64 y))
✓	accuracy	99.8%	(*.f64 x (cos.f64 y))

Samples

27.0ms

256×

valid

Compiler

Compiled 26 to 10 computations (61.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-cos: 7.0ms (37% of total)

ival-sin: 7.0ms (37% of total)

ival-mult: 3.0ms (15.9% of total)

ival-add: 1.0ms (5.3% of total)

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

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

series7.0ms (0.2%)

Memory

18.5MiB live, 18.5MiB allocated

Counts

4 → 96

Calls

Call 1

Inputs
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (* x (cos y))>
#<alt (cos y)>
#<alt (* z (sin y))>

Outputs
#<alt (* z (sin y))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (* x (cos y))>
#<alt (* x (+ (cos y) (/ (* z (sin y)) x)))>
#<alt (* x (+ (cos y) (/ (* z (sin y)) x)))>
#<alt (* x (+ (cos y) (/ (* z (sin y)) x)))>
#<alt (* x (cos y))>
#<alt (* -1 (* x (+ (* -1 (cos y)) (* -1 (/ (* z (sin y)) x)))))>
#<alt (* -1 (* x (+ (* -1 (cos y)) (* -1 (/ (* z (sin y)) x)))))>
#<alt (* -1 (* x (+ (* -1 (cos y)) (* -1 (/ (* z (sin y)) x)))))>
#<alt x>
#<alt (+ x (* y z))>
#<alt (+ x (* y (+ z (* -1/2 (* x y)))))>
#<alt (+ x (* y (+ z (* y (+ (* -1/2 x) (* -1/6 (* y z)))))))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (* x (cos y))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (+ (* x (cos y)) (* z (sin y)))>
#<alt (* z (sin y))>
#<alt (* z (+ (sin y) (/ (* x (cos y)) z)))>
#<alt (* z (+ (sin y) (/ (* x (cos y)) z)))>
#<alt (* z (+ (sin y) (/ (* x (cos y)) z)))>
#<alt (* z (sin y))>
#<alt (* -1 (* z (+ (* -1 (sin y)) (* -1 (/ (* x (cos y)) z)))))>
#<alt (* -1 (* z (+ (* -1 (sin y)) (* -1 (/ (* x (cos y)) z)))))>
#<alt (* -1 (* z (+ (* -1 (sin y)) (* -1 (/ (* x (cos y)) z)))))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt x>
#<alt (+ x (* -1/2 (* x (pow y 2))))>
#<alt (+ x (* (pow y 2) (+ (* -1/2 x) (* 1/24 (* x (pow y 2))))))>
#<alt (+ x (* (pow y 2) (+ (* -1/2 x) (* (pow y 2) (+ (* -1/720 (* x (pow y 2))) (* 1/24 x))))))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt (* x (cos y))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow y 2)))>
#<alt (+ 1 (* (pow y 2) (- (* 1/24 (pow y 2)) 1/2)))>
#<alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/24 (* -1/720 (pow y 2)))) 1/2)))>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (cos y)>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* y z)>
#<alt (* y (+ z (* -1/6 (* (pow y 2) z))))>
#<alt (* y (+ z (* (pow y 2) (+ (* -1/6 z) (* 1/120 (* (pow y 2) z))))))>
#<alt (* y (+ z (* (pow y 2) (+ (* -1/6 z) (* (pow y 2) (+ (* -1/5040 (* (pow y 2) z)) (* 1/120 z)))))))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>
#<alt (* z (sin y))>

Calls

24 calls:

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

rewrite584.0ms (15.6%)

Memory

-8.3MiB live, 921.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

11 480×	`accelerator-lowering-fma.f32`
11 480×	`accelerator-lowering-fma.f64`
4 168×	`-lowering-.f32`
4 168×	`-lowering-.f64`
4 068×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	24	19
2	180	19
3	1853	19
0	8395	18

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 176

Calls

Call 1

Inputs
(+ (* x (cos y)) (* z (sin y)))
(* x (cos y))
(cos y)
(* z (sin y))

Outputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (/.f64 (.f64 x x) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 z z) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))))))
(+.f64 (/.f64 (.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))) (neg.f64 (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z (sin.f64 y) (.f64 x (cos.f64 y))))) #s(literal -1 binary64)))
(-.f64 (.f64 x (cos.f64 y)) (.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y))))
(-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (/.f64 (.f64 x x) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))) (.f64 (.f64 z z) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))))
(-.f64 (/.f64 (.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 3 binary64)))) (fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))))) (/.f64 (/.f64 (pow.f64 (.f64 z (sin.f64 y)) #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 3 binary64)))) (fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 6 binary64)) (fma.f64 (.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (fma.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64)))) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (/.f64 (/.f64 (pow.f64 (.f64 z (sin.f64 y)) #s(literal 6 binary64)) (fma.f64 (.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (fma.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64)))) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64)) (fma.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))))) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (/.f64 (/.f64 (pow.f64 (.f64 z (sin.f64 y)) #s(literal 4 binary64)) (fma.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))))) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))))))) (-.f64 #s(literal 0 binary64) (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x (-.f64 #s(literal 0 binary64) (cos.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 #s(literal 0 binary64) (fma.f64 z (sin.f64 y) (.f64 x (cos.f64 y)))))
(-.f64 (/.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 6 binary64)) (.f64 (fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 3 binary64))))) (/.f64 (pow.f64 (.f64 z (sin.f64 y)) #s(literal 6 binary64)) (.f64 (fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 3 binary64))))))
(-.f64 (/.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 6 binary64)) (.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))) (fma.f64 (.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (fma.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64))))) (/.f64 (pow.f64 (.f64 z (sin.f64 y)) #s(literal 6 binary64)) (.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))) (fma.f64 (.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (fma.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64))))))
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(.f64 (/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 6 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 6 binary64))) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (fma.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64)))))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 4 binary64))) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))))))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))) (-.f64 (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))) #s(literal 2 binary64)))) (fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))))))
(.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (-.f64 #s(literal 0 binary64) (.f64 z z)) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 3 binary64)))) (fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 z (sin.f64 y)) (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y))))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))))) (+.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 9 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 z (sin.f64 y)) #s(literal 6 binary64)) (pow.f64 (.f64 (sin.f64 y) (.f64 (.f64 x (cos.f64 y)) z)) #s(literal 3 binary64))))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 6 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (*.f64 z (sin.f64 y)) #s(literal 3 binary64)))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 6 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (fma.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 4 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))))))
(exp.f64 (log.f64 (*.f64 x (cos.f64 y))))
(exp.f64 (.f64 (log.f64 (.f64 x (cos.f64 y))) #s(literal 1 binary64)))
(pow.f64 (*.f64 x (cos.f64 y)) #s(literal 1 binary64))
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 (cos.f64 y) #s(literal 1 binary64)))
(*.f64 (pow.f64 (cos.f64 y) #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (exp.f64 (log.f64 (cos.f64 y))) (exp.f64 (log.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 (cos.f64 y))))
(cos.f64 y)
(exp.f64 (log.f64 (*.f64 z (sin.f64 y))))
(exp.f64 (.f64 (log.f64 (.f64 z (sin.f64 y))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y))))
(neg.f64 (*.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y))))
(pow.f64 (*.f64 z (sin.f64 y)) #s(literal 1 binary64))
(*.f64 z (sin.f64 y))
(*.f64 (sin.f64 y) z)
(.f64 #s(literal -1 binary64) (.f64 z (-.f64 #s(literal 0 binary64) (sin.f64 y))))
(*.f64 (pow.f64 z #s(literal 1 binary64)) (pow.f64 (sin.f64 y) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sin.f64 y) #s(literal 1 binary64)) (pow.f64 z #s(literal 1 binary64)))
(*.f64 (exp.f64 (log.f64 (sin.f64 y))) (exp.f64 (log.f64 z)))
(*.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 (sin.f64 y))))

simplify745.0ms (19.9%)

Memory

-24.1MiB live, 492.3MiB allocated

Algorithm

1×	egg-herbie

Rules

14 080×	`accelerator-lowering-fma.f32`
14 080×	`accelerator-lowering-fma.f64`
3 812×	`-lowering-.f32`
3 812×	`-lowering-.f64`
2 968×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	620
1	295	616
2	892	610
3	2078	604
4	3746	604
5	6389	604
0	8805	554

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

Outputs
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (+ (cos y) (/ (* z (sin y)) x)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* x (+ (cos y) (/ (* z (sin y)) x)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* x (+ (cos y) (/ (* z (sin y)) x)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* -1 (* x (+ (* -1 (cos y)) (* -1 (/ (* z (sin y)) x)))))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* -1 (* x (+ (* -1 (cos y)) (* -1 (/ (* z (sin y)) x)))))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* -1 (* x (+ (* -1 (cos y)) (* -1 (/ (* z (sin y)) x)))))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
x
(+ x (* y z))
(fma.f64 z y x)
(+ x (* y (+ z (* -1/2 (* x y)))))
(fma.f64 y (fma.f64 y (*.f64 x #s(literal -1/2 binary64)) z) x)
(+ x (* y (+ z (* y (+ (* -1/2 x) (* -1/6 (* y z)))))))
(fma.f64 y (fma.f64 y (fma.f64 x #s(literal -1/2 binary64) (*.f64 (fma.f64 z y #s(literal 0 binary64)) #s(literal -1/6 binary64))) z) x)
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(+ (* x (cos y)) (* z (sin y)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (+ (sin y) (/ (* x (cos y)) z)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* z (+ (sin y) (/ (* x (cos y)) z)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* z (+ (sin y) (/ (* x (cos y)) z)))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* -1 (* z (+ (* -1 (sin y)) (* -1 (/ (* x (cos y)) z)))))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* -1 (* z (+ (* -1 (sin y)) (* -1 (/ (* x (cos y)) z)))))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* -1 (* z (+ (* -1 (sin y)) (* -1 (/ (* x (cos y)) z)))))
(fma.f64 x (cos.f64 y) (fma.f64 z (sin.f64 y) #s(literal 0 binary64)))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
x
(+ x (* -1/2 (* x (pow y 2))))
(.f64 x (fma.f64 y (.f64 y #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+ x (* (pow y 2) (+ (* -1/2 x) (* 1/24 (* x (pow y 2))))))
(.f64 x (fma.f64 (.f64 y y) (fma.f64 y (*.f64 y #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+ x (* (pow y 2) (+ (* -1/2 x) (* (pow y 2) (+ (* -1/720 (* x (pow y 2))) (* 1/24 x))))))
(fma.f64 (.f64 x (.f64 y y)) (fma.f64 y (.f64 y (fma.f64 (.f64 y y) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) x)
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow y 2)))
(fma.f64 y (*.f64 y #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 1/24 (pow y 2)) 1/2)))
(fma.f64 (.f64 y y) (fma.f64 y (.f64 y #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1/24 (* -1/720 (pow y 2)))) 1/2)))
(fma.f64 (.f64 y y) (fma.f64 y (.f64 y (fma.f64 (*.f64 y y) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(cos y)
(cos.f64 y)
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* y z)
(fma.f64 z y #s(literal 0 binary64))
(* y (+ z (* -1/6 (* (pow y 2) z))))
(fma.f64 y (.f64 z (fma.f64 y (.f64 y #s(literal -1/6 binary64)) #s(literal 1 binary64))) #s(literal 0 binary64))
(* y (+ z (* (pow y 2) (+ (* -1/6 z) (* 1/120 (* (pow y 2) z))))))
(.f64 z (.f64 y (fma.f64 (.f64 y y) (fma.f64 y (.f64 y #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(* y (+ z (* (pow y 2) (+ (* -1/6 z) (* (pow y 2) (+ (* -1/5040 (* (pow y 2) z)) (* 1/120 z)))))))
(.f64 y (fma.f64 (.f64 z (.f64 y y)) (fma.f64 y (.f64 y (fma.f64 y (*.f64 y #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) z))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
(* z (sin y))
(fma.f64 z (sin.f64 y) #s(literal 0 binary64))

eval35.0ms (0.9%)

Memory: 10.2MiB live, 47.6MiB allocated
Compiler: Compiled 10 138 to 554 computations (94.5% saved)

prune67.0ms (1.8%)

Memory

-5.9MiB live, 75.1MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	259	13	272
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	260	13	273

Accuracy

99.9%

Counts

273 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.3%	(fma.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (/.f64 x (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 z z) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))))
▶	99.8%	(fma.f64 (sin.f64 y) z (*.f64 x (cos.f64 y)))
	37.0%	(fma.f64 z (sin.f64 y) #s(literal 0 binary64))
	51.8%	(fma.f64 z y x)
▶	50.4%	(fma.f64 y (fma.f64 y (fma.f64 x #s(literal -1/2 binary64) (*.f64 (fma.f64 z y #s(literal 0 binary64)) #s(literal -1/6 binary64))) z) x)
	50.5%	(fma.f64 y (fma.f64 y (*.f64 x #s(literal -1/2 binary64)) z) x)
	64.4%	(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
	46.3%	(/.f64 (-.f64 (pow.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (/.f64 (.f64 x x) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 z z) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))) #s(literal 2 binary64))) (fma.f64 (.f64 x x) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (.f64 (.f64 z z) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))))
	48.6%	(/.f64 (-.f64 (.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))))
	42.8%	(/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) #s(literal 3 binary64)) (pow.f64 (.f64 z (sin.f64 y)) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))))))
▶	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))))
	48.6%	(.f64 (-.f64 (.f64 (.f64 z z) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 z (sin.f64 y)) (*.f64 x (cos.f64 y)))))
▶	40.2%	x

Compiler

Compiled 700 to 332 computations (52.6% saved)

simplify378.0ms (10.1%)

Memory

7.7MiB live, 555.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	192	(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))
✓	cost-diff	192	(-.f64 #s(literal 0 binary64) (.f64 (.f64 z z) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
✓	cost-diff	192	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))
✓	cost-diff	14720	(fma.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y))))) (/.f64 x (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 z z) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)))) (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))))
✓	cost-diff	0	(sin.f64 y)
✓	cost-diff	0	(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y))))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))))
✓	cost-diff	0	(fma.f64 z y #s(literal 0 binary64))
✓	cost-diff	0	(fma.f64 y (fma.f64 x #s(literal -1/2 binary64) (*.f64 (fma.f64 z y #s(literal 0 binary64)) #s(literal -1/6 binary64))) z)
✓	cost-diff	0	(fma.f64 y (fma.f64 y (fma.f64 x #s(literal -1/2 binary64) (*.f64 (fma.f64 z y #s(literal 0 binary64)) #s(literal -1/6 binary64))) z) x)
✓	cost-diff	64	(fma.f64 x #s(literal -1/2 binary64) (*.f64 (fma.f64 z y #s(literal 0 binary64)) #s(literal -1/6 binary64)))
✓	cost-diff	-64	(*.f64 x (cos.f64 y))
✓	cost-diff	0	(cos.f64 y)
✓	cost-diff	0	(sin.f64 y)
✓	cost-diff	0	(fma.f64 (sin.f64 y) z (*.f64 x (cos.f64 y)))

Rules

11 136×	`accelerator-lowering-fma.f32`
11 136×	`accelerator-lowering-fma.f64`
3 342×	`-lowering-.f32`
3 342×	`-lowering-.f64`
2 564×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	303
1	110	302
2	294	302
3	751	301
4	1957	301
5	4991	289
6	7403	289
0	8517	271

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (sin y) z) (* x (cos y)))
(sin y)
y
z
(* x (cos y))
x
(cos y)
x
(+ (* y (+ (* y (+ (* x -1/2) (* (+ (* z y) 0) -1/6))) z)) x)
y
(+ (* y (+ (* x -1/2) (* (+ (* z y) 0) -1/6))) z)
(+ (* x -1/2) (* (+ (* z y) 0) -1/6))
x
-1/2
(* (+ (* z y) 0) -1/6)
(+ (* z y) 0)
z
0
-1/6
(/ 1 (/ 1 (+ (* z (sin y)) (* x (cos y)))))
1
(/ 1 (+ (* z (sin y)) (* x (cos y))))
(+ (* z (sin y)) (* x (cos y)))
z
(sin y)
y
(* x (cos y))
x
(cos y)
(+ (* (* x (+ 1/2 (* 1/2 (cos (+ y y))))) (/ x (- (* x (cos y)) (* z (sin y))))) (- 0 (* (* z z) (/ (- 1/2 (* 1/2 (cos (+ y y)))) (- (* x (cos y)) (* z (sin y)))))))
(* x (+ 1/2 (* 1/2 (cos (+ y y)))))
x
(+ 1/2 (* 1/2 (cos (+ y y))))
1/2
(* 1/2 (cos (+ y y)))
(cos (+ y y))
(+ y y)
y
(/ x (- (* x (cos y)) (* z (sin y))))
(- (* x (cos y)) (* z (sin y)))
(* x (cos y))
(cos y)
(* z (sin y))
z
(sin y)
(- 0 (* (* z z) (/ (- 1/2 (* 1/2 (cos (+ y y)))) (- (* x (cos y)) (* z (sin y))))))
0
(* (* z z) (/ (- 1/2 (* 1/2 (cos (+ y y)))) (- (* x (cos y)) (* z (sin y)))))
(* z z)
(/ (- 1/2 (* 1/2 (cos (+ y y)))) (- (* x (cos y)) (* z (sin y))))
(- 1/2 (* 1/2 (cos (+ y y))))

Outputs
(+ (* (sin y) z) (* x (cos y)))
(fma.f64 (sin.f64 y) z (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
(sin y)
(sin.f64 y)
y
z
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
x
(cos y)
(cos.f64 y)
x
(+ (* y (+ (* y (+ (* x -1/2) (* (+ (* z y) 0) -1/6))) z)) x)
(fma.f64 y (fma.f64 y (fma.f64 y (*.f64 z #s(literal -1/6 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 0 binary64))) z) x)
y
(+ (* y (+ (* x -1/2) (* (+ (* z y) 0) -1/6))) z)
(fma.f64 y (fma.f64 y (*.f64 z #s(literal -1/6 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 0 binary64))) z)
(+ (* x -1/2) (* (+ (* z y) 0) -1/6))
(fma.f64 y (*.f64 z #s(literal -1/6 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 0 binary64)))
x
-1/2
#s(literal -1/2 binary64)
(* (+ (* z y) 0) -1/6)
(fma.f64 (fma.f64 y z #s(literal 0 binary64)) #s(literal -1/6 binary64) #s(literal 0 binary64))
(+ (* z y) 0)
(fma.f64 y z #s(literal 0 binary64))
z
0
#s(literal 0 binary64)
-1/6
#s(literal -1/6 binary64)
(/ 1 (/ 1 (+ (* z (sin y)) (* x (cos y)))))
(fma.f64 (sin.f64 y) z (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(/ 1 (+ (* z (sin y)) (* x (cos y))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 y) z (fma.f64 x (cos.f64 y) #s(literal 0 binary64))))
(+ (* z (sin y)) (* x (cos y)))
(fma.f64 (sin.f64 y) z (fma.f64 x (cos.f64 y) #s(literal 0 binary64)))
z
(sin y)
(sin.f64 y)
y
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
x
(cos y)
(cos.f64 y)
(+ (* (* x (+ 1/2 (* 1/2 (cos (+ y y))))) (/ x (- (* x (cos y)) (* z (sin y))))) (- 0 (* (* z z) (/ (- 1/2 (* 1/2 (cos (+ y y)))) (- (* x (cos y)) (* z (sin y)))))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 x (-.f64 #s(literal 0 binary64) (cos.f64 y)) (fma.f64 (sin.f64 y) z #s(literal 0 binary64)))) (fma.f64 z (*.f64 z (+.f64 (cos.f64 (+.f64 y y)) #s(literal -1 binary64))) (fma.f64 x (fma.f64 x (cos.f64 (+.f64 y y)) x) #s(literal 0 binary64))) #s(literal 0 binary64))
(* x (+ 1/2 (* 1/2 (cos (+ y y)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal 1/2 binary64)) #s(literal 0 binary64))
x
(+ 1/2 (* 1/2 (cos (+ y y))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* 1/2 (cos (+ y y)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal 0 binary64))
(cos (+ y y))
(cos.f64 (+.f64 y y))
(+ y y)
(+.f64 y y)
y
(/ x (- (* x (cos y)) (* z (sin y))))
(/.f64 x (-.f64 (fma.f64 x (cos.f64 y) #s(literal 0 binary64)) (fma.f64 (sin.f64 y) z #s(literal 0 binary64))))
(- (* x (cos y)) (* z (sin y)))
(-.f64 (fma.f64 x (cos.f64 y) #s(literal 0 binary64)) (fma.f64 (sin.f64 y) z #s(literal 0 binary64)))
(* x (cos y))
(fma.f64 x (cos.f64 y) #s(literal 0 binary64))
(cos y)
(cos.f64 y)
(* z (sin y))
(fma.f64 (sin.f64 y) z #s(literal 0 binary64))
z
(sin y)
(sin.f64 y)
(- 0 (* (* z z) (/ (- 1/2 (* 1/2 (cos (+ y y)))) (- (* x (cos y)) (* z (sin y))))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 x (-.f64 #s(literal 0 binary64) (cos.f64 y)) (fma.f64 (sin.f64 y) z #s(literal 0 binary64)))) #s(literal 0 binary64))
0
#s(literal 0 binary64)
(* (* z z) (/ (- 1/2 (* 1/2 (cos (+ y y)))) (- (* x (cos y)) (* z (sin y)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 z z #s(literal 0 binary64)) (fma.f64 x (-.f64 #s(literal 0 binary64) (cos.f64 y)) (fma.f64 (sin.f64 y) z #s(literal 0 binary64)))) #s(literal 0 binary64))
(* z z)
(fma.f64 z z #s(literal 0 binary64))
(/ (- 1/2 (* 1/2 (cos (+ y y)))) (- (* x (cos y)) (* z (sin y))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal 1/2 binary64)) (-.f64 (fma.f64 x (cos.f64 y) #s(literal 0 binary64)) (fma.f64 (sin.f64 y) z #s(literal 0 binary64))))
(- 1/2 (* 1/2 (cos (+ y y))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 y y)) #s(literal 1/2 binary64))

localize1.0ms (0%)

Memory: 1.8MiB live, 1.8MiB allocated
Compiler: Compiled 305 to 42 computations (86.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample1.7s (46.4%)

preprocess48.0ms (1.3%)

explain101.0ms (2.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize35.0ms (0.9%)

series7.0ms (0.2%)

rewrite584.0ms (15.6%)

simplify745.0ms (19.9%)

eval35.0ms (0.9%)

prune67.0ms (1.8%)

simplify378.0ms (10.1%)

localize1.0ms (0%)

end0.0ms (0%)

Profiling