Metrics for bug329 (missed optimization)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze12.0ms (1%)

Memory

-23.9MiB live, 14.8MiB allocated; 10ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
0%	0%	50%	50%	0%	0%	0%	1
50%	25%	25%	50%	0%	0%	0%	2
50%	25%	25%	50%	0%	0%	0%	3
75%	37.5%	12.5%	50%	0%	0%	0%	4
75%	37.5%	12.5%	50%	0%	0%	0%	5
87.5%	43.7%	6.2%	50%	0%	0%	0%	6
87.5%	43.7%	6.2%	50%	0%	0%	0%	7
93.8%	46.8%	3.1%	50%	0%	0%	0%	8
93.8%	46.8%	3.1%	50%	0%	0%	0%	9
96.9%	48.4%	1.6%	50%	0%	0%	0%	10
96.9%	48.4%	1.6%	50%	0%	0%	0%	11
98.4%	49.2%	0.8%	50%	0%	0%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample741.0ms (62.3%)

Memory

61.1MiB live, 563.6MiB allocated; 814ms collecting garbage

Samples

519.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 107.0ms

ival-atan: 53.0ms (49.7% of total)

ival-div!: 52.0ms (48.8% of total)

adjust: 2.0ms (1.9% of total)

Bogosity

preprocess89.0ms (7.5%)

Memory

-32.2MiB live, 62.0MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	33	26
2	86	26
3	162	26
4	427	26
5	2492	26

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(atan.f64 (/.f64 y x))

Symmetry

(negabs x)

(negabs y)

Compiler

Compiled 8 to 8 computations (0% saved)

series7.0ms (0.6%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22

Stop Event

1×	iter-limit

Counts

4 → 4

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))
(/.f64 y x)
y
x

Outputs
#s(approx (atan (/ y x)) (atan.f64 (/.f64 y x)))
#s(approx (/ y x) (/.f64 y x))
#s(approx x x)
#s(approx y y)

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((atan (/ y x)) (/ y x) y x)
1.0ms	x	@	-inf	((atan (/ y x)) (/ y x) y x)
1.0ms	y	@	inf	((atan (/ y x)) (/ y x) y x)
1.0ms	y	@	-inf	((atan (/ y x)) (/ y x) y x)
1.0ms	y	@	0	((atan (/ y x)) (/ y x) y x)

rewrite100.0ms (8.4%)

Memory

8.5MiB live, 97.9MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	6	9
1	14	9
2	46	9
3	184	9
0	930	9

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

4 → 164

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))
(/.f64 y x)
y
x

Outputs
(neg.f64 (atan.f64 (/.f64 (neg.f64 y) x)))
(atan.f64 (/.f64 y x))
(.f64 (.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 y))
(*.f64 (/.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(.f64 (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal -1 binary64) (neg.f64 y)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))))
(*.f64 (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (/.f64 (neg.f64 y) x) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 y) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(pow.f64 (exp.f64 (log.f64 (/.f64 x y))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 x y) (/.f64 x y)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 x y) #s(literal -1 binary64))
(pow.f64 (/.f64 y x) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (neg.f64 x))
(/.f64 (*.f64 (neg.f64 y) #s(literal -1 binary64)) x)
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 y)) x)
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) y)))
(/.f64 (.f64 #s(literal 2 binary64) (neg.f64 y)) (.f64 #s(literal 2 binary64) (neg.f64 x)))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) y) (.f64 #s(literal 2 binary64) x))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 2 binary64)))
(/.f64 (.f64 (neg.f64 y) #s(literal 2 binary64)) (.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 y #s(literal 2 binary64)) (.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (neg.f64 x) y)))
(/.f64 #s(literal -2 binary64) (*.f64 (/.f64 (neg.f64 x) y) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x y)))
(/.f64 #s(literal 2 binary64) (*.f64 (/.f64 x y) #s(literal 2 binary64)))
(/.f64 (/.f64 (neg.f64 y) x) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) y))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) y))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 (neg.f64 y) (*.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 y) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(/.f64 (neg.f64 y) (neg.f64 x))
(/.f64 (/.f64 y x) #s(literal 1 binary64))
(/.f64 y x)
(neg.f64 (/.f64 (neg.f64 y) x))
(fma.f64 (.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)) (.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 y) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 y) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 y) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal -1 binary64) x) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal -1 binary64) x) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (.f64 #s(literal -1 binary64) (neg.f64 y)) (/.f64 #s(literal 1 binary64) x) (.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal -1 binary64) (neg.f64 y)) (/.f64 #s(literal 1 binary64) x) (.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (*.f64 #s(literal -1 binary64) (neg.f64 y)) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (neg.f64 y) x) #s(literal -1 binary64) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (neg.f64 y) x) #s(literal -1 binary64) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (neg.f64 y) x) #s(literal -1 binary64) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) y)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) y)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 #s(literal -1 binary64) (/.f64 (neg.f64 y) x) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 (neg.f64 y) x) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 #s(literal -1 binary64) (/.f64 (neg.f64 y) x) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) y (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) y (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) y (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 #s(literal 1 binary64) (/.f64 y x) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 y x) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 #s(literal 1 binary64) (/.f64 y x) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 y x) #s(literal 1 binary64) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 y x) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 y x) #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 y (/.f64 #s(literal 1 binary64) x) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 y (/.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 y (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fabs.f64 (/.f64 y x))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64) #s(literal 0 binary64)))
(exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64)) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64))) (sinh.f64 (.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64))))
(+.f64 (/.f64 y x) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(+.f64 (/.f64 y x) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(+.f64 (/.f64 y x) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
y
x

eval14.0ms (1.2%)

Memory: 23.8MiB live, 23.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 035 to 401 computations (61.3% saved)

prune5.0ms (0.4%)

Memory

6.4MiB live, 6.4MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	162	3	165

Accuracy

100.0%

Counts

165 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(atan.f64 (/.f64 y x))
▶	99.4%	(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
▶	99.8%	(atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y))

Compiler

Compiled 16 to 16 computations (0% saved)

series22.0ms (1.9%)

Memory

-38.1MiB live, 8.3MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40

Stop Event

1×	iter-limit

Counts

9 → 6

Calls

Call 1

Inputs
(atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
y
(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 x y)

Outputs
#s(approx (atan (* (/ 1 x) y)) (atan.f64 (/.f64 y x)))
#s(approx (* (/ 1 x) y) (/.f64 y x))
#s(approx (/ 1 x) (/.f64 #s(literal 1 binary64) x))
#s(approx x x)
#s(approx (/ x y) (/.f64 x y))
#s(approx y y)

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	x	@	-inf	((atan (* (/ 1 x) y)) (* (/ 1 x) y) (/ 1 x) 1 x y (atan (/ 1 (/ x y))) (/ 1 (/ x y)) (/ x y))
1.0ms	y	@	-inf	((atan (* (/ 1 x) y)) (* (/ 1 x) y) (/ 1 x) 1 x y (atan (/ 1 (/ x y))) (/ 1 (/ x y)) (/ x y))
1.0ms	x	@	0	((atan (* (/ 1 x) y)) (* (/ 1 x) y) (/ 1 x) 1 x y (atan (/ 1 (/ x y))) (/ 1 (/ x y)) (/ x y))
1.0ms	x	@	inf	((atan (* (/ 1 x) y)) (* (/ 1 x) y) (/ 1 x) 1 x y (atan (/ 1 (/ x y))) (/ 1 (/ x y)) (/ x y))
1.0ms	y	@	inf	((atan (* (/ 1 x) y)) (* (/ 1 x) y) (/ 1 x) 1 x y (atan (/ 1 (/ x y))) (/ 1 (/ x y)) (/ x y))

rewrite130.0ms (10.9%)

Memory

26.0MiB live, 83.6MiB allocated; 61ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
0	15	23
1	41	23
2	147	23
0	886	23

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

9 → 503

Calls

Call 1

Inputs
(atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
y
(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 x y)

Outputs
(neg.f64 (atan.f64 (/.f64 (neg.f64 y) x)))
(atan.f64 (/.f64 y x))
(.f64 (.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 y))
(.f64 (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))))
(*.f64 (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (neg.f64 y) x) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
(.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 y) x))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(pow.f64 (exp.f64 (log.f64 (/.f64 x y))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 x y) (/.f64 x y)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 y x) #s(literal 1 binary64))
(pow.f64 (/.f64 x y) #s(literal -1 binary64))
(/.f64 (.f64 (neg.f64 y) #s(literal 2 binary64)) (.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 y #s(literal 2 binary64)) (.f64 x #s(literal 2 binary64)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal 2 binary64) (neg.f64 y)) (.f64 #s(literal 2 binary64) (neg.f64 x)))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) y) (.f64 #s(literal 2 binary64) x))
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) y)))
(/.f64 #s(literal -2 binary64) (*.f64 (/.f64 (neg.f64 x) y) #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (neg.f64 x) y)))
(/.f64 (/.f64 (neg.f64 y) x) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) y))
(/.f64 #s(literal 2 binary64) (*.f64 (/.f64 x y) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x y)))
(/.f64 (neg.f64 y) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(/.f64 (neg.f64 y) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) y))
(/.f64 (/.f64 y x) #s(literal 1 binary64))
(/.f64 y x)
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(neg.f64 (/.f64 (neg.f64 y) x))
(fma.f64 (.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)) (.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (*.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 y) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 y) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 y) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 (/.f64 y x) #s(literal 0 binary64)))
(fma.f64 (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 #s(literal 0 binary64) (/.f64 x y)))
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(/.f64 (.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (*.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (neg.f64 x)) (.f64 #s(literal 2 binary64) (neg.f64 y)))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (neg.f64 x) y)) #s(literal -2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) y))
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 x y)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 y))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (neg.f64 y) x)))
(/.f64 #s(literal -2 binary64) (*.f64 (/.f64 (neg.f64 y) x) #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 2 binary64) (*.f64 (/.f64 y x) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (/.f64 y x)))
(/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (neg.f64 x) y) #s(literal -1 binary64))
(/.f64 (neg.f64 x) (neg.f64 y))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 y) x))
(/.f64 (/.f64 x y) #s(literal 1 binary64))
(/.f64 x (*.f64 (neg.f64 y) #s(literal -1 binary64)))
(/.f64 x (*.f64 #s(literal -1 binary64) (neg.f64 y)))
(/.f64 x y)
(/.f64 #s(literal 1 binary64) (/.f64 y x))
(neg.f64 (/.f64 (neg.f64 x) y))
(fma.f64 (/.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 2 binary64) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (/.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 2 binary64) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 2 binary64) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 y x) #s(literal -1/2 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal 1/2 binary64)) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal 1/2 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal 1/2 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)) (neg.f64 x) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)) (neg.f64 x) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)) (neg.f64 x) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) y) (.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) y) (.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (*.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) y) (.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) y) (.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) y) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) y) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) x (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) x (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) x (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal -1 binary64) y) (neg.f64 x) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal -1 binary64) y) (neg.f64 x) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal -1 binary64) y) (neg.f64 x) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 #s(literal 1 binary64) y) x (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) y) x (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 #s(literal 1 binary64) y) x (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 (neg.f64 x) y) #s(literal -1 binary64) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (/.f64 (neg.f64 x) y) #s(literal -1 binary64) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 (neg.f64 x) y) #s(literal -1 binary64) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (neg.f64 x) (.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (neg.f64 x) (.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (neg.f64 x) (*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (neg.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (neg.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (neg.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (neg.f64 x) (/.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (neg.f64 x) (/.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (neg.f64 x) (/.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) y) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) y) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (neg.f64 x) y) #s(literal 1 binary64)) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (neg.f64 x) y) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (neg.f64 x) y) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) y) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) y) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) y) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 (/.f64 x y) #s(literal 1 binary64) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 (/.f64 x y) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 (/.f64 x y) #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 x (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 x (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 x (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 x (/.f64 #s(literal 1 binary64) y) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 x (/.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 x (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(fma.f64 #s(literal 1 binary64) (/.f64 x y) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 x y) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(fma.f64 #s(literal 1 binary64) (/.f64 x y) (/.f64 #s(literal 0 binary64) (/.f64 y x)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64))))
(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 y x)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) #s(literal 1 binary64)))
(+.f64 (/.f64 x y) (*.f64 (/.f64 x y) #s(literal 0 binary64)))
(+.f64 (/.f64 x y) (*.f64 #s(literal 0 binary64) (/.f64 x y)))
(+.f64 (/.f64 x y) (/.f64 #s(literal 0 binary64) (/.f64 y x)))

eval41.0ms (3.4%)

Memory: -18.4MiB live, 70.1MiB allocated; 11ms collecting garbage
Compiler: Compiled 2 319 to 1 041 computations (55.1% saved)

prune6.0ms (0.5%)

Memory

15.0MiB live, 15.0MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	356	0	356
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	356	3	359

Accuracy

100.0%

Counts

359 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(atan.f64 (/.f64 y x))
✓	99.4%	(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
✓	99.8%	(atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y))

Compiler

Compiled 27 to 27 computations (0% saved)

regimes6.0ms (0.5%)

Memory

13.3MiB live, 13.3MiB allocated; 0ms collecting garbage

Accuracy

Total -0.4b remaining (-5548%)

Threshold costs -0.4b (-5548%)

Counts

3 → 1

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))
(atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y))
(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))

Outputs
(atan.f64 (/.f64 y x))

Calls

4 calls:

1.0ms	y
1.0ms	x
1.0ms	(/.f64 y x)
1.0ms	(atan.f64 (/.f64 y x))

Results

Accuracy	Segments	Branch
100.0%	1	`(/.f64 y x)`
100.0%	1	`(atan.f64 (/.f64 y x))`
100.0%	1	`x`
100.0%	1	`y`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

derivations0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 4 to 4 computations (0% saved)

preprocess16.0ms (1.4%)

Memory

-17.0MiB live, 28.6MiB allocated; 4ms collecting garbage

Remove

(negabs y)

(negabs x)

Compiler

Compiled 24 to 24 computations (0% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze12.0ms (1%)

sample741.0ms (62.3%)

preprocess89.0ms (7.5%)

series7.0ms (0.6%)

rewrite100.0ms (8.4%)

eval14.0ms (1.2%)

prune5.0ms (0.4%)

series22.0ms (1.9%)

rewrite130.0ms (10.9%)

eval41.0ms (3.4%)

prune6.0ms (0.5%)

regimes6.0ms (0.5%)

derivations0.0ms (0%)

preprocess16.0ms (1.4%)

end0.0ms (0%)

Profiling