Metrics for Beckmann Sample, normalization factor

start0.0ms (0.0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze33.0ms (0.2%)

Memory

-26.5MiB live, 65.8MiB allocated; 20ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0.0%	0.0%	12.3%	87.7%	0.0%	0.0%	0.0%	0
0.0%	0.0%	12.3%	87.7%	0.0%	0.0%	0.0%	1
50.0%	6.2%	6.2%	87.7%	0.0%	0.0%	0.0%	2
50.0%	6.2%	6.2%	87.7%	0.0%	0.0%	0.0%	3
75.0%	9.2%	3.1%	87.7%	0.0%	0.0%	0.0%	4
75.0%	9.2%	3.1%	87.7%	0.0%	0.0%	0.0%	5
87.5%	10.8%	1.5%	87.7%	0.0%	0.0%	0.0%	6
87.5%	10.8%	1.5%	87.7%	0.0%	0.0%	0.0%	7
93.8%	11.5%	0.8%	87.7%	0.0%	0.0%	0.0%	8
93.8%	11.5%	0.8%	87.7%	0.0%	0.0%	0.0%	9
96.9%	11.9%	0.4%	87.7%	0.0%	0.0%	0.0%	10
96.9%	11.9%	0.4%	87.7%	0.0%	0.0%	0.0%	11
98.4%	12.1%	0.2%	87.7%	0.0%	0.0%	0.0%	12

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample4.3s (24.9%)

Memory

102.0MiB live, 2 816.6MiB allocated; 795ms collecting garbage

Samples

3.9s	8 255×	0	valid
9.0ms	56×	0	invalid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 2.9s

ival-add!: 1.2s (42.2% of total, 157.7 MiB)

ival-sqrt: 511.0ms (17.5% of total, 198.5 MiB)

ival-mult!: 491.0ms (16.8% of total, 301.3 MiB)

ival-exp: 394.0ms (13.5% of total, 209.3 MiB)

ival-div!: 139.0ms (4.8% of total, 217.2 MiB)

ival-sub!: 85.0ms (2.9% of total, 140.4 MiB)

ival-neg: 51.0ms (1.7% of total, 129.6 MiB)

adjust: 16.0ms (0.5% of total, 17.2 MiB)

ival-<: 1.0ms (0.0% of total, 1.7 MiB)

ival-pi: 0.0ms (0.0% of total, 0.0 MiB)

ival-assert: 0.0ms (0.0% of total, 0.5 MiB)

ival-and: 0.0ms (0.0% of total, 1.1 MiB)

Bogosity

preprocess611.0ms (3.5%)

Memory

-26.1MiB live, 70.7MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	152
1	391	138
2	2687	126
3	21472	126
4	40861	126

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Accuracy

Program

▶

98.1%

(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Compiler

Compiled 50 to 36 computations (28.0% saved)

sample0.0ms (0.0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Calls

Call 1

Inputs
1
(PI)
(sqrt (PI))
(/ 1 (sqrt (PI)))

Outputs
#s(literal 1 binary32)
#s(literal 13176795/4194304 binary32)
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)

Samples

0.0ms

1×

valid

Compiler

Compiled 10 to 6 computations (40.0% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total, 0.0 MiB)

series32.0ms (0.2%)

Memory

4.4MiB live, 92.6MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	540	5444

Stop Event

1×	iter-limit

Counts

18 → 12

Calls

Call 1

Inputs
#s(literal 1 binary32)
c
(+.f32 #s(literal 1 binary32) c)
(PI.f32)
(sqrt.f32 (PI.f32))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
cosTheta
(-.f32 #s(literal 1 binary32) cosTheta)
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(neg.f32 cosTheta)
(*.f32 (neg.f32 cosTheta) cosTheta)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs
#s(approx 1 #s(literal 0 binary32))
#s(approx cosTheta cosTheta)
#s(approx (- 1 cosTheta) #s(literal 1 binary32))
#s(approx (- 1 cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -1 binary32) cosTheta)))
#s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (-.f32 (.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1 binary32)))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (-.f32 (.f32 cosTheta (-.f32 (*.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1/2 binary32))) #s(literal 1 binary32)))))
#s(approx (neg cosTheta) (*.f32 #s(literal -1 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (- (- 1 cosTheta) cosTheta) (*.f32 #s(literal -2 binary32) cosTheta))
#s(approx c c)
#s(approx (+ 1 c) (+.f32 #s(literal 1 binary32) c))

Calls

6 calls:

Time	Variable	Point
4.0ms	cosTheta	-inf
4.0ms	cosTheta	inf
3.0ms	c	-inf
2.0ms	cosTheta	0
1.0ms	c	0

rewrite1.4s (8.0%)

Memory

4.4MiB live, 191.0MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	126
0	33	126
1	157	117
2	1019	110
3	11486	110
4	43632	110
0	50068	18

Stop Event

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

Counts

18 → 0

Calls

Call 1

Inputs
#s(literal 1 binary32)
c
(+.f32 #s(literal 1 binary32) c)
(PI.f32)
(sqrt.f32 (PI.f32))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
cosTheta
(-.f32 #s(literal 1 binary32) cosTheta)
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(neg.f32 cosTheta)
(*.f32 (neg.f32 cosTheta) cosTheta)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs

eval2.0ms (0.0%)

Memory: 5.6MiB live, 5.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 384 to 105 computations (72.7% saved)

prune2.0ms (0.0%)

Memory

8.0MiB live, 8.0MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	11	5	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	12	5	17

Accuracy

99.6%

Counts

17 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	93.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))

Compiler

Compiled 196 to 82 computations (58.2% saved)

sample0.0ms (0.0%)

Memory

1.3MiB live, 1.3MiB allocated; 0ms collecting garbage

Calls

Call 1

Inputs
1
(PI)
(sqrt (PI))
(/ 1 (sqrt (PI)))
14868421/8388608
9465531/16777216
-2
(/ 1 14868421/8388608)

Outputs
#s(literal 1 binary32)
#s(literal 13176795/4194304 binary32)
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)
#s(literal -2 binary32)
#s(literal 4732765/8388608 binary32)

Samples

0.0ms

1×

valid

Compiler

Compiled 16 to 10 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total, 0.0 MiB)

series1.2s (7.2%)

Memory

-297.2MiB live, 236.8MiB allocated; 1.9s collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1261	13199

Stop Event

1×	iter-limit

Counts

45 → 16

Calls

Call 1

Inputs
#s(literal 1 binary32)
c
(+.f32 #s(literal 1 binary32) c)
(PI.f32)
(sqrt.f32 (PI.f32))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
cosTheta
(-.f32 #s(literal 1 binary32) cosTheta)
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(neg.f32 cosTheta)
(*.f32 (neg.f32 cosTheta) cosTheta)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)
#s(approx (- 1 cosTheta) #s(literal 1 binary32))
#s(literal -2 binary32)
(*.f32 #s(literal -2 binary32) cosTheta)
(+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))
#s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32))
(*.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(*.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)
(sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta))
(/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))))
(/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)
(.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs
#s(approx 1 #s(literal 0 binary32))
#s(approx cosTheta cosTheta)
#s(approx (- 1 cosTheta) #s(literal 1 binary32))
#s(approx (- 1 cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -1 binary32) cosTheta)))
#s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (-.f32 (.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1 binary32)))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (-.f32 (.f32 cosTheta (-.f32 (*.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1/2 binary32))) #s(literal 1 binary32)))))
#s(approx (neg cosTheta) (*.f32 #s(literal -1 binary32) cosTheta))
#s(approx (* -2 cosTheta) (*.f32 #s(literal -2 binary32) cosTheta))
#s(approx (* cosTheta (sqrt (PI))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 14868421/8388608 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))))
#s(approx c c)
#s(approx (+ 1 c) (+.f32 #s(literal 1 binary32) c))

Calls

6 calls:

Time	Variable	Point
8.0ms	cosTheta	inf
4.0ms	cosTheta	-inf
3.0ms	cosTheta	0
2.0ms	c	0
1.0ms	c	inf

rewrite996.0ms (5.8%)

Memory

-3.4MiB live, 91.3MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	487
0	98	487
1	394	468
2	2670	446
3	21847	446
4	42547	446
0	50166	45

Stop Event

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

Counts

45 → 0

Calls

Call 1

Inputs
#s(literal 1 binary32)
c
(+.f32 #s(literal 1 binary32) c)
(PI.f32)
(sqrt.f32 (PI.f32))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
cosTheta
(-.f32 #s(literal 1 binary32) cosTheta)
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(neg.f32 cosTheta)
(*.f32 (neg.f32 cosTheta) cosTheta)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)
#s(approx (- 1 cosTheta) #s(literal 1 binary32))
#s(literal -2 binary32)
(*.f32 #s(literal -2 binary32) cosTheta)
(+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))
#s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32))
(*.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(*.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)
(sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta))
(/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))))
(/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)
(.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs

eval3.0ms (0.0%)

Memory: 13.0MiB live, 13.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 960 to 178 computations (81.5% saved)

prune4.0ms (0.0%)

Memory

15.4MiB live, 15.3MiB allocated; 0ms collecting garbage

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	39	8	47
Fresh	0	0	0
Picked	4	1	5
Done	0	0	0
Total	43	9	52

Accuracy

99.9%

Counts

52 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	92.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	93.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))
	96.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
▶	96.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))))
▶	92.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))

Compiler

Compiled 254 to 114 computations (55.1% saved)

sample1.0ms (0.0%)

Memory

1.9MiB live, 1.9MiB allocated; 0ms collecting garbage

Calls

Call 1

Inputs
1
14868421/8388608
9465531/16777216
-2
(/ 1 14868421/8388608)
16777216/9465531
-281474976710656/89596277111961
7311685/16777216

Outputs
#s(literal 1 binary32)
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)
#s(literal -2 binary32)
#s(literal 4732765/8388608 binary32)
#s(literal 3717105/2097152 binary32)
#s(literal -13176793/4194304 binary32)
#s(literal 7311685/16777216 binary32)

Samples

0.0ms

1×

valid

Compiler

Compiled 12 to 10 computations (16.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total, 0.0 MiB)

series895.0ms (5.2%)

Memory

-21.4MiB live, 214.5MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	970	9151

Stop Event

1×	iter-limit

Counts

43 → 30

Calls

Call 1

Inputs
#s(literal 1 binary32)
c
(+.f32 #s(literal 1 binary32) c)
cosTheta
(neg.f32 cosTheta)
(*.f32 (neg.f32 cosTheta) cosTheta)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)
#s(approx (- 1 cosTheta) #s(literal 1 binary32))
#s(literal -2 binary32)
(*.f32 #s(literal -2 binary32) cosTheta)
(+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))
#s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32))
(-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)
(sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta))
(/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)
(sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))))
(/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)
#s(literal 16777216/9465531 binary32)
(*.f32 #s(literal 16777216/9465531 binary32) cosTheta)
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))
#s(literal -281474976710656/89596277111961 binary32)
#s(literal 7311685/16777216 binary32)
(+.f32 #s(literal 7311685/16777216 binary32) c)
(*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))
(.f32 #s(literal -281474976710656/89596277111961 binary32) (.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c)))
(+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))
(.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))))
(.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(*.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta))
(.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta))
(.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs
#s(approx 1 #s(literal 0 binary32))
#s(approx cosTheta cosTheta)
#s(approx (neg cosTheta) (*.f32 #s(literal -1 binary32) cosTheta))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))
#s(approx (- 1 cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -1 binary32) cosTheta)))
#s(approx (* -2 cosTheta) (*.f32 #s(literal -2 binary32) cosTheta))
#s(approx (+ 1 (* -2 cosTheta)) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (-.f32 (.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1 binary32)))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (-.f32 (.f32 cosTheta (-.f32 (*.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1/2 binary32))) #s(literal 1 binary32)))))
#s(approx (* 16777216/9465531 cosTheta) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))))
#s(approx (* cosTheta (+ 7311685/16777216 c)) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c)))
#s(approx (* -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (.f32 #s(literal -281474976710656/89596277111961 binary32) (.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))
#s(approx (+ 16777216/9465531 (* -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c)))) #s(literal 16777216/9465531 binary32))
#s(approx (+ 16777216/9465531 (* -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c)))) (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 14868421/8388608 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
#s(approx c c)
#s(approx (+ 1 c) (+.f32 #s(literal 1 binary32) c))
#s(approx (+ 7311685/16777216 c) #s(literal 7311685/16777216 binary32))
#s(approx (+ 7311685/16777216 c) (+.f32 #s(literal 7311685/16777216 binary32) c))
#s(approx (* cosTheta (+ 7311685/16777216 c)) (*.f32 #s(literal 7311685/16777216 binary32) cosTheta))
#s(approx (* cosTheta (+ 7311685/16777216 c)) (fma.f32 #s(literal 7311685/16777216 binary32) cosTheta (*.f32 c cosTheta)))
#s(approx (* -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (*.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta))
#s(approx (* -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (fma.f32 #s(literal -281474976710656/89596277111961 binary32) (.f32 c cosTheta) (.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta)))
#s(approx (+ 16777216/9465531 (* -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c)))) (+.f32 #s(literal 16777216/9465531 binary32) (*.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta)))
#s(approx (+ 16777216/9465531 (* -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c)))) (+.f32 #s(literal 16777216/9465531 binary32) (fma.f32 #s(literal -281474976710656/89596277111961 binary32) (.f32 c cosTheta) (.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta))))
#s(approx (* cosTheta (+ 16777216/9465531 (* -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta))))
#s(approx (* cosTheta (+ 7311685/16777216 c)) (*.f32 c cosTheta))
#s(approx (* -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (.f32 #s(literal -281474976710656/89596277111961 binary32) (.f32 c cosTheta)))

Calls

6 calls:

Time	Variable	Point
3.0ms	cosTheta	0
2.0ms	cosTheta	inf
2.0ms	cosTheta	-inf
1.0ms	c	0
1.0ms	c	inf

rewrite923.0ms (5.3%)

Memory

17.6MiB live, 159.6MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	457
0	86	457
1	369	457
2	2507	446
3	21940	446
4	39998	446
0	50790	43

Stop Event

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

Counts

43 → 0

Calls

Call 1

Inputs
#s(literal 1 binary32)
c
(+.f32 #s(literal 1 binary32) c)
cosTheta
(neg.f32 cosTheta)
(*.f32 (neg.f32 cosTheta) cosTheta)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)
#s(approx (- 1 cosTheta) #s(literal 1 binary32))
#s(literal -2 binary32)
(*.f32 #s(literal -2 binary32) cosTheta)
(+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))
#s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32))
(-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)
(sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta))
(/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)
(sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))))
(/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)
#s(literal 16777216/9465531 binary32)
(*.f32 #s(literal 16777216/9465531 binary32) cosTheta)
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))
#s(literal -281474976710656/89596277111961 binary32)
#s(literal 7311685/16777216 binary32)
(+.f32 #s(literal 7311685/16777216 binary32) c)
(*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))
(.f32 #s(literal -281474976710656/89596277111961 binary32) (.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c)))
(+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))
(.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))))
(.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(*.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta))
(.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta))
(.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs

eval5.0ms (0.0%)

Memory: -1.5MiB live, 45.2MiB allocated; 1ms collecting garbage
Compiler: Compiled 866 to 156 computations (82.0% saved)

prune6.0ms (0.0%)

Memory

8.8MiB live, 56.5MiB allocated; 1ms collecting garbage

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	0	3	3
Picked	3	2	5
Done	0	1	1
Total	53	11	64

Accuracy

99.9%

Counts

64 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
✓	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	92.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
✓	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	93.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))
▶	96.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
	96.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) #s(approx ( -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (*.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta)))))
✓	92.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))

Compiler

Compiled 285 to 118 computations (58.6% saved)

sample1.0ms (0.0%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

Calls

Call 1

Inputs
1
14868421/8388608
9465531/16777216
-2
4732765/8388608
-221069943033241/70368744177664
6479813/14868421

Outputs
#s(literal 1 binary32)
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)
#s(literal -2 binary32)
#s(literal 4732765/8388608 binary32)
#s(literal -13176795/4194304 binary32)
#s(literal 3655843/8388608 binary32)

Samples

0.0ms

1×

valid

Compiler

Compiled 9 to 9 computations (0.0% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total, 0.0 MiB)

series946.0ms (5.5%)

Memory

-15.0MiB live, 711.8MiB allocated; 37ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1431	13887

Stop Event

1×	iter-limit

Counts

43 → 33

Calls

Call 1

Inputs
#s(literal 1 binary32)
c
(+.f32 #s(literal 1 binary32) c)
cosTheta
(-.f32 #s(literal 1 binary32) cosTheta)
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(neg.f32 cosTheta)
(*.f32 (neg.f32 cosTheta) cosTheta)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)
#s(literal -2 binary32)
(*.f32 #s(literal -2 binary32) cosTheta)
(+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))
#s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
(sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))))
(/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)
#s(literal 4732765/8388608 binary32)
#s(literal -221069943033241/70368744177664 binary32)
#s(literal 6479813/14868421 binary32)
(+.f32 #s(literal 6479813/14868421 binary32) c)
(*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))
(.f32 #s(literal -221069943033241/70368744177664 binary32) (.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c)))
(+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))
(.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
(*.f32 cosTheta #s(literal 14868421/8388608 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))
(.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta))
(*.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))
(.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta))
(.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))

Outputs
#s(approx 1 #s(literal 0 binary32))
#s(approx cosTheta cosTheta)
#s(approx (- 1 cosTheta) #s(literal 1 binary32))
#s(approx (- 1 cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -1 binary32) cosTheta)))
#s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (-.f32 (.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1 binary32)))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (-.f32 (.f32 cosTheta (-.f32 (*.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1/2 binary32))) #s(literal 1 binary32)))))
#s(approx (neg cosTheta) (*.f32 #s(literal -1 binary32) cosTheta))
#s(approx (* -2 cosTheta) (*.f32 #s(literal -2 binary32) cosTheta))
#s(approx (* cosTheta (+ 6479813/14868421 c)) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c)))
#s(approx (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))) (.f32 #s(literal -221069943033241/70368744177664 binary32) (.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))
#s(approx (+ 14868421/8388608 (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c)))) #s(literal 14868421/8388608 binary32))
#s(approx (+ 14868421/8388608 (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c)))) (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c)))))
#s(approx (* cosTheta (+ 14868421/8388608 (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))))) (*.f32 #s(literal 14868421/8388608 binary32) cosTheta))
#s(approx (* cosTheta (+ 14868421/8388608 (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 4732765/8388608 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 8388608/4732765 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* 4732765/8388608 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 8388608/4732765 binary32) (.f32 #s(literal -70368744177664/22399064545225 binary32) (*.f32 cosTheta (+.f32 #s(literal 3655843/8388608 binary32) c))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))))
#s(approx c c)
#s(approx (+ 1 c) (+.f32 #s(literal 1 binary32) c))
#s(approx (+ 6479813/14868421 c) #s(literal 6479813/14868421 binary32))
#s(approx (+ 6479813/14868421 c) (+.f32 #s(literal 6479813/14868421 binary32) c))
#s(approx (* cosTheta (+ 6479813/14868421 c)) (*.f32 #s(literal 6479813/14868421 binary32) cosTheta))
#s(approx (* cosTheta (+ 6479813/14868421 c)) (fma.f32 #s(literal 6479813/14868421 binary32) cosTheta (*.f32 c cosTheta)))
#s(approx (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))) (*.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta))
#s(approx (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))) (fma.f32 #s(literal -221069943033241/70368744177664 binary32) (.f32 c cosTheta) (.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta)))
#s(approx (+ 14868421/8388608 (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c)))) (+.f32 #s(literal 14868421/8388608 binary32) (*.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta)))
#s(approx (+ 14868421/8388608 (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c)))) (+.f32 #s(literal 14868421/8388608 binary32) (fma.f32 #s(literal -221069943033241/70368744177664 binary32) (.f32 c cosTheta) (.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta))))
#s(approx (* cosTheta (+ 14868421/8388608 (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta))))
#s(approx (* cosTheta (+ 6479813/14868421 c)) (*.f32 c cosTheta))
#s(approx (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))) (.f32 #s(literal -221069943033241/70368744177664 binary32) (.f32 c cosTheta)))

Calls

6 calls:

Time	Variable	Point
507.0ms	cosTheta	-inf
17.0ms	c	-inf
6.0ms	cosTheta	inf
4.0ms	cosTheta	0
2.0ms	c	0

rewrite1.0s (5.8%)

Memory

-1.7MiB live, 193.7MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	456
0	99	456
1	417	454
2	2854	445
3	23860	445
4	42900	445
0	50069	43

Stop Event

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

Counts

43 → 0

Calls

Call 1

Inputs
#s(literal 1 binary32)
c
(+.f32 #s(literal 1 binary32) c)
cosTheta
(-.f32 #s(literal 1 binary32) cosTheta)
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(neg.f32 cosTheta)
(*.f32 (neg.f32 cosTheta) cosTheta)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
#s(literal 14868421/8388608 binary32)
#s(literal 9465531/16777216 binary32)
#s(literal -2 binary32)
(*.f32 #s(literal -2 binary32) cosTheta)
(+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))
#s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
(sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta))))
(/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)
#s(literal 4732765/8388608 binary32)
#s(literal -221069943033241/70368744177664 binary32)
#s(literal 6479813/14868421 binary32)
(+.f32 #s(literal 6479813/14868421 binary32) c)
(*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))
(.f32 #s(literal -221069943033241/70368744177664 binary32) (.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c)))
(+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))
(.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
(*.f32 cosTheta #s(literal 14868421/8388608 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))
(.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta))
(*.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))
(.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta))
(.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))

Outputs

eval4.0ms (0.0%)

Memory: 4.8MiB live, 52.5MiB allocated; 1ms collecting garbage
Compiler: Compiled 741 to 157 computations (78.8% saved)

prune134.0ms (0.8%)

Memory

-24.2MiB live, 166.1MiB allocated; 7ms collecting garbage

Pruning

12 alts after pruning (4 fresh and 8 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	3	3
Picked	0	5	5
Done	0	3	3
Total	51	12	63

Accuracy

99.9%

Counts

63 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
✓	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	92.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
✓	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
✓	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	93.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))
✓	96.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
	96.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) #s(approx ( -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))) (*.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta)))))
	96.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) #s(approx ( -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (*.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta)))))
✓	92.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))

Compiler

Compiled 173 to 67 computations (61.3% saved)

regimes3.0s (17.3%)

Memory

62.1MiB live, 472.8MiB allocated; 109ms collecting garbage

Counts

1 → 1

3 → 1

4 → 1

6 → 1

11 → 1

14 → 1

20 → 1

Calls

Call 1

Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))

Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))

Call 2

Inputs

#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))

#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))

#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))

Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))

Call 3

Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) #s(approx ( -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (*.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta)))))

Outputs

#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) #s(approx (* -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (*.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta)))))

Call 4

Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) #s(approx ( -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (*.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) #s(approx ( -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))) (*.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))))

Outputs

#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) #s(approx (* -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))) (*.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta)))))

Call 5

Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) #s(approx ( -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (*.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) #s(approx ( -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))) (*.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs

#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (*.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))

Call 6

Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) #s(approx ( -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (*.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) #s(approx ( -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))) (*.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs

(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Call 7

Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(literal 16777216/9465531 binary32) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta #s(literal 14868421/8388608 binary32)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) #s(approx ( -281474976710656/89596277111961 (* cosTheta (+ 7311685/16777216 c))) (*.f32 #s(literal -122669718568960/89596277111961 binary32) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) #s(approx ( -221069943033241/70368744177664 (* cosTheta (+ 6479813/14868421 c))) (*.f32 #s(literal -96344587685273/70368744177664 binary32) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* 9465531/16777216 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 16777216/9465531 binary32) (.f32 #s(literal -281474976710656/89596277111961 binary32) (*.f32 cosTheta (+.f32 #s(literal 7311685/16777216 binary32) c))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 14868421/8388608) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (+.f32 #s(literal 14868421/8388608 binary32) (.f32 #s(literal -221069943033241/70368744177664 binary32) (*.f32 cosTheta (+.f32 #s(literal 6479813/14868421 binary32) c))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 4732765/8388608 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(approx (- 1 cosTheta) #s(literal 1 binary32)) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) #s(literal 14868421/8388608 binary32)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs

(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 #s(literal 9465531/16777216 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Calls

42 calls:

2.8s	cosTheta
22.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
16.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
10.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
9.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Results

Accuracy	Segments	Branch
92.9%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
92.9%	1	`cosTheta`
92.9%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
92.9%	1	`(+.f32 #s(literal 1 binary32) c)`
92.9%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
92.9%	1	`c`
93.1%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
93.1%	1	`(+.f32 #s(literal 1 binary32) c)`
93.1%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
93.1%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
93.1%	1	`cosTheta`
93.1%	1	`c`
96.2%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.2%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.2%	1	`(+.f32 #s(literal 1 binary32) c)`
96.2%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.2%	1	`cosTheta`
96.2%	1	`c`
96.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.6%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.6%	1	`c`
96.6%	1	`(+.f32 #s(literal 1 binary32) c)`
96.6%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.6%	1	`cosTheta`
96.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.7%	1	`(+.f32 #s(literal 1 binary32) c)`
96.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.7%	1	`cosTheta`
96.7%	1	`c`
98.1%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
98.1%	1	`(+.f32 #s(literal 1 binary32) c)`
98.1%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.1%	1	`c`
98.1%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.1%	1	`cosTheta`
98.1%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
98.1%	1	`(+.f32 #s(literal 1 binary32) c)`
98.1%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.1%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.1%	1	`cosTheta`
98.1%	1	`c`

Compiler

Compiled 833 to 478 computations (42.6% saved)

derivations21.0ms (0.1%)

Memory

-3.9MiB live, 43.6MiB allocated; 6ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 75 to 45 computations (40.0% saved)

preprocess1.7s (10.0%)

Memory: -13.6MiB live, 124.4MiB allocated; 24ms collecting garbage
Compiler: Compiled 100 to 63 computations (37.0% saved)

end0.0ms (0.0%)

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

start0.0ms (0.0%)

analyze33.0ms (0.2%)

sample4.3s (24.9%)

preprocess611.0ms (3.5%)

sample0.0ms (0.0%)

series32.0ms (0.2%)

rewrite1.4s (8.0%)

eval2.0ms (0.0%)

prune2.0ms (0.0%)

sample0.0ms (0.0%)

series1.2s (7.2%)

rewrite996.0ms (5.8%)

eval3.0ms (0.0%)

prune4.0ms (0.0%)

sample1.0ms (0.0%)

series895.0ms (5.2%)

rewrite923.0ms (5.3%)

eval5.0ms (0.0%)

prune6.0ms (0.0%)

sample1.0ms (0.0%)

series946.0ms (5.5%)

rewrite1.0s (5.8%)

eval4.0ms (0.0%)

prune134.0ms (0.8%)

regimes3.0s (17.3%)

derivations21.0ms (0.1%)

preprocess1.7s (10.0%)

end0.0ms (0.0%)

Profiling