Beckmann Sample, normalization factor

Time bar (total: 11.2s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze49.0ms (0.4%)

Memory
-13.9MiB live, 45.1MiB allocated; 37ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%12.3%87.7%0%0%0%0
0%0%12.3%87.7%0%0%0%1
50%6.2%6.2%87.7%0%0%0%2
50%6.2%6.2%87.7%0%0%0%3
75%9.2%3.1%87.7%0%0%0%4
75%9.2%3.1%87.7%0%0%0%5
87.5%10.8%1.5%87.7%0%0%0%6
87.5%10.8%1.5%87.7%0%0%0%7
93.8%11.5%0.8%87.7%0%0%0%8
93.8%11.5%0.8%87.7%0%0%0%9
96.9%11.9%0.4%87.7%0%0%0%10
96.9%11.9%0.4%87.7%0%0%0%11
98.4%12.1%0.2%87.7%0%0%0%12
Compiler

Compiled 41 to 29 computations (29.3% saved)

sample2.9s (25.8%)

Memory
61.4MiB live, 3 659.4MiB allocated; 812ms collecting garbage
Samples
2.0s8 256×0valid
32.0ms76×0invalid
Precisions
Click to see histograms. Total time spent on operations: 1.6s
ival-mult: 263.0ms (17% of total)
ival-div: 227.0ms (14.6% of total)
ival-<: 184.0ms (11.9% of total)
ival-sub: 167.0ms (10.8% of total)
ival-sqrt: 167.0ms (10.8% of total)
const: 160.0ms (10.3% of total)
ival-add: 137.0ms (8.8% of total)
ival-exp: 86.0ms (5.5% of total)
ival-neg: 58.0ms (3.7% of total)
ival-pi: 54.0ms (3.5% of total)
ival-and: 25.0ms (1.6% of total)
exact: 16.0ms (1% of total)
adjust: 3.0ms (0.2% of total)
ival-assert: 3.0ms (0.2% of total)
Bogosity

explain382.0ms (3.4%)

Memory
-26.6MiB live, 364.7MiB allocated; 125ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(sqrt.f32 (PI.f32))
00-0-(PI.f32)
00-0-(*.f32 (neg.f32 cosTheta) cosTheta)
00-0-(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
00-0-(*.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)))
00-0-(+.f32 #s(literal 1 binary32) c)
00-0-cosTheta
00-0-(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
00-0-(+.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))))
00-0-c
00-0-(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
00-0-(/.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)))))
00-0-(-.f32 #s(literal 1 binary32) cosTheta)
00-0-(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
00-0-#s(literal 1 binary32)
00-0-(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
00-0-(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
00-0-(neg.f32 cosTheta)
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-01255
Precision?
0.0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-010
Precision?
0.0
Recall?
0/0
Samples
75.0ms512×0valid
Compiler

Compiled 281 to 58 computations (79.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 56.0ms
ival-add: 15.0ms (26.7% of total)
ival-div: 10.0ms (17.8% of total)
ival-mult: 9.0ms (16% of total)
ival-sqrt: 7.0ms (12.5% of total)
ival-sub: 5.0ms (8.9% of total)
ival-exp: 4.0ms (7.1% of total)
ival-neg: 3.0ms (5.3% of total)
ival-pi: 2.0ms (3.6% of total)
ival-true: 1.0ms (1.8% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess231.0ms (2.1%)

Memory
21.6MiB live, 395.1MiB allocated; 67ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044133
1138119
2470112
32027111
46514111
01825
03325
16023
217022
370322
4274822
0822921
Stop Event
iter limit
node limit
iter limit
node limit
Calls
Call 1
Inputs
(/.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
(/.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) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
Compiler

Compiled 25 to 18 computations (28% saved)

eval0.0ms (0%)

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

Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory
2.1MiB live, 2.1MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.2%
(/.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 25 to 18 computations (28% saved)

simplify181.0ms (1.6%)

Memory
32.4MiB live, 364.4MiB allocated; 44ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.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)))))
cost-diff1
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
cost-diff1
(*.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)))
cost-diff2
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
018126
033126
160118
2170115
3703115
42748115
08229108
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.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)))))
#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) c)
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 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
Outputs
(/.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) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
#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))))
(fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32)))
(+.f32 #s(literal 1 binary32) c)
(+.f32 c #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 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)

localize51.0ms (0.5%)

Memory
-28.3MiB live, 116.5MiB allocated; 13ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.10546875
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy0.3203125
(/.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)))))
accuracy0.6198425781475362
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
accuracy1.0
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
Samples
35.0ms256×0valid
Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 26.0ms
ival-div: 8.0ms (30.8% of total)
ival-mult: 4.0ms (15.4% of total)
ival-add: 3.0ms (11.5% of total)
ival-sqrt: 3.0ms (11.5% of total)
ival-exp: 2.0ms (7.7% of total)
ival-sub: 2.0ms (7.7% of total)
ival-pi: 1.0ms (3.8% of total)
ival-neg: 1.0ms (3.8% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series24.0ms (0.2%)

Memory
5.6MiB live, 51.3MiB allocated; 6ms collecting garbage
Counts
5 → 50
Calls
Call 1
Inputs
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) 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) 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) (sqrt.f32 (PI.f32)))
Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
(- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
Calls

6 calls:

TimeVariablePointExpression
11.0ms
cosTheta
@-inf
((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
7.0ms
cosTheta
@inf
((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
2.0ms
cosTheta
@0
((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
1.0ms
c
@0
((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
1.0ms
c
@inf
((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))

simplify231.0ms (2.1%)

Memory
12.2MiB live, 246.2MiB allocated; 58ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03782856
112202772
256352702
085182591
Stop Event
iter limit
node limit
Counts
50 → 50
Calls
Call 1
Inputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
(- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1/2 binary32))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
1
#s(literal 1 binary32)
(+ 1 (* -2 cosTheta))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(* cosTheta (sqrt (PI)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (-.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (PI.f32))) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (-.f32 (*.f32 (-.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (PI.f32))) (-.f32 (*.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (*.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 (*.f32 (*.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3/2 binary32) (*.f32 (*.f32 (PI.f32) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (PI.f32)))) cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(fma.f32 (*.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(fma.f32 (*.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32)))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(*.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(fma.f32 (*.f32 #s(literal 1/2 binary32) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(literal -2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (*.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(fma.f32 (*.f32 #s(literal -1/8 binary32) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (fma.f32 (*.f32 #s(literal 1/2 binary32) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(literal -2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (*.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(fma.f32 (*.f32 #s(literal -1/8 binary32) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (fma.f32 (*.f32 #s(literal 1/16 binary32) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32)))) (fma.f32 (*.f32 #s(literal 1/2 binary32) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(literal -2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (*.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta))))))
(* -2 cosTheta)
(*.f32 #s(literal -2 binary32) cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta)
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
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(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
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(fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) #s(literal 1/2 binary32)) (/.f32 (*.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 #s(literal -1 binary32))) (pow.f32 (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32))) (fma.f32 (/.f32 (fma.f32 (*.f32 #s(literal 1/4 binary32) (/.f32 cosTheta (PI.f32))) (/.f32 (/.f32 (pow.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) #s(literal -2 binary32)) #s(literal 2 binary32)) (pow.f32 (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) #s(literal 3 binary32))) (/.f32 (*.f32 (*.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (*.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))) (pow.f32 (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32)))) (pow.f32 cosTheta #s(literal 4 binary32))) #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))
(-.f32 (fma.f32 (/.f32 (fma.f32 (*.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (/.f32 (*.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) (sqrt.f32 #s(literal -1 binary32))) (pow.f32 (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32))) (fma.f32 (*.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) #s(literal 1/2 binary32)) (/.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/4 binary32) (/.f32 cosTheta (PI.f32))) (/.f32 (/.f32 (pow.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) #s(literal -2 binary32)) #s(literal 2 binary32)) (pow.f32 (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) #s(literal 3 binary32))) (/.f32 (*.f32 (*.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (*.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))) (pow.f32 (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32)))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (*.f32 (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 #s(literal 2 binary32)))) (/.f32 (/.f32 (*.f32 (*.f32 #s(literal 1/16 binary32) (*.f32 cosTheta cosTheta)) (pow.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) #s(literal -2 binary32))) (*.f32 (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 4 binary32)) (PI.f32))) (pow.f32 (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) #s(literal 3 binary32))))) (pow.f32 cosTheta #s(literal 6 binary32))) #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))) (fma.f32 (/.f32 (pow.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) #s(literal -2 binary32)) (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (pow.f32 (*.f32 (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) cosTheta) #s(literal 3 binary32)))) #s(literal 1/4 binary32) (/.f32 (fma.f32 (*.f32 (*.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (/.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 2 binary32)) (sqrt.f32 #s(literal 2 binary32))) (*.f32 (*.f32 #s(literal -1/2 binary32) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (sqrt.f32 #s(literal 2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))))) (pow.f32 (fma.f32 (*.f32 (neg.f32 (sqrt.f32 #s(literal 2 binary32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32)))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(/.f32 (+.f32 (/.f32 (neg.f32 c) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))) #s(literal 1 binary32)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(fma.f32 (-.f32 (*.f32 (fma.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 4 binary32))) #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)))) c) (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))))
(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) c)) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) c) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/.f32 (-.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) c) #s(literal 3 binary32))) (/.f32 (+.f32 (/.f32 (neg.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32))) c) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))) c)) c)
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(/.f32 (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) c) #s(literal 1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) c) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal 1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32))) (neg.f32 c)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal 1 binary32)) (neg.f32 c))

rewrite257.0ms (2.3%)

Memory
6.5MiB live, 356.9MiB allocated; 102ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01866
03366
113359
297756
0836255
Stop Event
iter limit
node limit
iter limit
Counts
5 → 178
Calls
Call 1
Inputs
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) 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) 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) (sqrt.f32 (PI.f32)))
Outputs
(*.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)))
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(*.f32 (/.f32 (pow.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1/4 binary32)) (sqrt.f32 (PI.f32))) (/.f32 (pow.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1/4 binary32)) cosTheta))
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(+.f32 (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) c) (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) (-.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)))))
(+.f32 (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) (-.f32 c (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)))))
(+.f32 (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (*.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (-.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
(+.f32 (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (*.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (-.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))))))
(+.f32 (cosh.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32))) (sinh.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32))))
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
(neg.f32 (/.f32 #s(literal -1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(*.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32))) (neg.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32))))
(*.f32 (fabs.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32))) (fabs.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32))))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -1 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal -1 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal -1 binary32)))
(*.f32 (pow.f32 (neg.f32 (sqrt.f32 (PI.f32))) #s(literal -1/2 binary32)) (pow.f32 (neg.f32 (sqrt.f32 (PI.f32))) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal -1/2 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/4 binary32)))
(/.f32 #s(literal -1 binary32) (neg.f32 (neg.f32 (neg.f32 (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(pow.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) #s(literal 2 binary32))
(pow.f32 (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))) #s(literal -1 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)) #s(literal -1/6 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/4 binary32))
(pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))
(pow.f32 (PI.f32) #s(literal -1/2 binary32))
(+.f32 (cosh.f32 (*.f32 (log.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32))) (sinh.f32 (*.f32 (log.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32))))
(exp.f32 (neg.f32 (log.f32 (sqrt.f32 (PI.f32)))))
(exp.f32 (*.f32 (log.f32 (PI.f32)) #s(literal -1/2 binary32)))
(exp.f32 (*.f32 (log.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)))
(neg.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))

eval33.0ms (0.3%)

Memory
-31.0MiB live, 71.2MiB allocated; 11ms collecting garbage
Compiler

Compiled 11 168 to 1 378 computations (87.7% saved)

prune15.0ms (0.1%)

Memory
7.8MiB live, 54.5MiB allocated; 3ms collecting garbage
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New21216228
Fresh000
Picked101
Done000
Total21316229
Accuracy
99.9%
Counts
229 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.9%
(pow.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
98.5%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.2%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.7%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
97.9%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.4%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.2%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
92.2%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 #s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
97.4%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
96.9%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
34.0%
(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (fma.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (-.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
90.4%
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
5.1%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
97.4%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (-.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (PI.f32))) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
96.3%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
93.0%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
Compiler

Compiled 1 126 to 732 computations (35% saved)

simplify160.0ms (1.4%)

Memory
28.0MiB live, 253.0MiB allocated; 31ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c))
cost-diff0
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
cost-diff1
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
cost-diff1
(*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32))
cost-diff0
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff0
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff1
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
cost-diff1
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
cost-diff0
(+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
cost-diff0
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
cost-diff1
(/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
cost-diff5
(fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
cost-diff0
(/.f32 #s(literal 1 binary32) c)
cost-diff0
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
cost-diff0
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff0
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff1
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
cost-diff1
(*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
063670
0107638
1192628
2449618
31334614
44640614
08170581
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
c
(*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
(/.f32 #s(literal 1 binary32) c)
#s(literal 1 binary32)
c
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(+.f32 #s(literal 1 binary32) c)
c
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(*.f32 #s(literal 1/2 binary32) cosTheta)
#s(literal 1/2 binary32)
cosTheta
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
#s(literal -3/2 binary32)
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
c
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(sqrt.f32 (PI.f32))
(PI.f32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
(*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32))
(log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c))
(fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)
(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
(exp.f32 cosTheta)
cosTheta
(neg.f32 cosTheta)
(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)
(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
(/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) cosTheta)
#s(literal 1 binary32)
(PI.f32)
c
#s(literal -1 binary32)
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 c #s(literal 1 binary32))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(+.f32 #s(literal 1 binary32) c)
(+.f32 c #s(literal 1 binary32))
c
(*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(sqrt.f32 (PI.f32))
(PI.f32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
(/.f32 #s(literal 1 binary32) c)
#s(literal 1 binary32)
c
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 (*.f32 (*.f32 (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (+.f32 c #s(literal 1 binary32))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 (*.f32 (*.f32 (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (+.f32 c #s(literal 1 binary32)))
(+.f32 #s(literal 1 binary32) c)
(+.f32 c #s(literal 1 binary32))
c
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 (*.f32 (*.f32 (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 (*.f32 (*.f32 (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(-.f32 (*.f32 (*.f32 (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(*.f32 (*.f32 (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(*.f32 (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(*.f32 #s(literal 1/2 binary32) cosTheta)
#s(literal 1/2 binary32)
cosTheta
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
#s(literal -3/2 binary32)
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 c #s(literal 1 binary32))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(+.f32 #s(literal 1 binary32) c)
(+.f32 c #s(literal 1 binary32))
c
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(sqrt.f32 (PI.f32))
(PI.f32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
(exp.f32 (neg.f32 (log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) c))))
(*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32))
(neg.f32 (log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) c)))
(log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c))
(log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) c))
(fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)
(fma.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) c)
(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
(exp.f32 cosTheta)
cosTheta
(neg.f32 cosTheta)
(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)
(/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)
(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
(/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))
(/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) cosTheta)
#s(literal 1 binary32)
(PI.f32)
c
#s(literal -1 binary32)

localize232.0ms (2.1%)

Memory
-48.0MiB live, 395.6MiB allocated; 68ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.10546875
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy0.55078125
(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)
accuracy0.7890625
(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
accuracy3.069391840977482
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
accuracy0.04296875
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
accuracy0.10546875
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy0.3203125
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy0.38671875
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
accuracy0.2919558186542187
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
accuracy0.3203125
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
accuracy0.55859375
(/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy1.0
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy0.0
(/.f32 #s(literal 1 binary32) c)
accuracy30.35692129735482
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
accuracy0.10546875
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy0.3125
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy0.3203125
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy0.3359375
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
Samples
185.0ms256×0valid
Compiler

Compiled 595 to 54 computations (90.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 161.0ms
ival-mult: 47.0ms (29.2% of total)
ival-div: 28.0ms (17.4% of total)
ival-add: 28.0ms (17.4% of total)
ival-exp: 26.0ms (16.1% of total)
ival-pow: 16.0ms (9.9% of total)
ival-sqrt: 7.0ms (4.3% of total)
ival-sub: 4.0ms (2.5% of total)
ival-log1p: 3.0ms (1.9% of total)
ival-pi: 1.0ms (0.6% of total)
exact: 1.0ms (0.6% of total)
ival-neg: 1.0ms (0.6% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series50.0ms (0.4%)

Memory
31.4MiB live, 167.0MiB allocated; 9ms collecting garbage
Counts
24 → 150
Calls
Call 1
Inputs
(*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
(/.f32 #s(literal 1 binary32) c)
(fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32))
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
(log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)
Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(* -3/2 (sqrt (/ 1 (PI))))
(+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta))))
(+ (* -1 (* (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (sqrt (PI)))) (* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))))
(+ (* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))) (* cosTheta (+ (* -1 (* (sqrt (PI)) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* -1/2 (* cosTheta (+ (* -1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 2 (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))
(+ (* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))) (* cosTheta (+ (* -1 (* (sqrt (PI)) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* cosTheta (+ (* -1/2 (+ (* -1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 2 (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* -1/6 (* cosTheta (+ (* -6 (* (PI) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (+ (* 2 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3))) (* 6 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))))))
(+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))
(+ (log (sqrt (/ 1 (PI)))) (+ (* -1 (log cosTheta)) (* (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (sqrt (PI)))))
(+ (log (sqrt (/ 1 (PI)))) (+ (* -1 (log cosTheta)) (* cosTheta (+ (* 1/2 (* cosTheta (+ (* -1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 2 (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (* (sqrt (PI)) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(+ (log (sqrt (/ 1 (PI)))) (+ (* -1 (log cosTheta)) (* cosTheta (+ (* cosTheta (+ (* 1/6 (* cosTheta (+ (* -6 (* (PI) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (+ (* 2 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3))) (* 6 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))) (* 1/2 (+ (* -1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 2 (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) (* (sqrt (PI)) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(+ 1 (* -1 cosTheta))
(+ 1 (* cosTheta (- (* -1/2 cosTheta) 1)))
(+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1)))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
(* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI)))))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI))))))))
(* -1 (log (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
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c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(log (/ 1 c))
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Calls

6 calls:

TimeVariablePointExpression
14.0ms
cosTheta
@-inf
((* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (* (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) -1) (exp (* (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) -1)) (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sqrt (- (- 1 cosTheta) cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta))
14.0ms
cosTheta
@inf
((* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (* (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) -1) (exp (* (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) -1)) (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sqrt (- (- 1 cosTheta) cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta))
6.0ms
cosTheta
@0
((* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (* (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) -1) (exp (* (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) -1)) (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sqrt (- (- 1 cosTheta) cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta))
4.0ms
c
@-inf
((* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (* (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) -1) (exp (* (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) -1)) (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sqrt (- (- 1 cosTheta) cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta))
3.0ms
c
@0
((* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (* (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) -1) (exp (* (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) -1)) (log (+ 1 (+ (* (pow (exp cosTheta) (neg cosTheta)) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)) c))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sqrt (- (- 1 cosTheta) cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta))

simplify205.0ms (1.8%)

Memory
13.6MiB live, 378.9MiB allocated; 45ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07838097
127697792
090937369
Stop Event
iter limit
node limit
Counts
150 → 149
Calls
Call 1
Inputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(* -3/2 (sqrt (/ 1 (PI))))
(+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta))))
(+ (* -1 (* (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (sqrt (PI)))) (* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))))
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(+ 1 (* -1 cosTheta))
(+ 1 (* cosTheta (- (* -1/2 cosTheta) 1)))
(+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1)))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
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(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
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(* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI)))))))
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(* -1 (log (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
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(log (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
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(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
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(* (sqrt cosTheta) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))))
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
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(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
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(* -1 (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* 3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* 3/2 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(* -1 (log (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
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(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(* -1 (* (sqrt cosTheta) (* (sqrt -1) (sqrt 2))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
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(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(/ 1 c)
(* -1 (log (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* -1 (log (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))) (* -1 (/ c (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
(+ (* -1 (log (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))) (* c (- (* 1/2 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))))
(+ (* -1 (log (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))) (* c (- (* c (+ (* -1/3 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3))) (* 1/2 (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))))
(log (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
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(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(log (/ 1 c))
(+ (log (/ 1 c)) (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)))
(+ (log (/ 1 c)) (+ (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) (* 1/2 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2)))))
(+ (log (/ 1 c)) (+ (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) (+ (* -1/3 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3))) (* 1/2 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))))))
(* -1 (log (/ 1 c)))
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(+ (* -1 (log (/ 1 c))) (+ (* -1/2 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
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(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (+ (log -1) (* -1 (log (/ -1 c)))))
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(+ (* -1 (+ (log -1) (* -1 (log (/ -1 c))))) (* -1 (/ (+ 1 (+ (* -1/2 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c)) (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)))
(+ (* -1 (+ (log -1) (* -1 (log (/ -1 c))))) (* -1 (/ (+ 1 (+ (* -1 (/ (+ (* -1/3 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c)) (* 1/2 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) c)) (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)))
(+ (log -1) (* -1 (log (/ -1 c))))
(+ (log -1) (+ (* -1 (log (/ -1 c))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(+ (log -1) (+ (* -1 (log (/ -1 c))) (* -1 (/ (+ (* -1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) (* 1/2 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c))) c))))
(+ (log -1) (+ (* -1 (log (/ -1 c))) (* -1 (/ (+ (* -1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) (* -1 (/ (+ (* -1/2 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) (* 1/3 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c))) c))) c))))
Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta)
1
#s(literal 1 binary32)
(+ 1 (* -2 cosTheta))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(* cosTheta (sqrt (PI)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* -3/2 (sqrt (/ 1 (PI))))
(*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta)
(* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta))))
(fma.f32 (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32) (log.f32 cosTheta))
(+ (* -1 (* (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (sqrt (PI)))) (* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))))
(neg.f32 (fma.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta cosTheta) (sqrt.f32 (PI.f32)) (-.f32 (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (log.f32 cosTheta))))
(+ (* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))) (* cosTheta (+ (* -1 (* (sqrt (PI)) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* -1/2 (* cosTheta (+ (* -1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 2 (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))
(fma.f32 (fma.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (PI.f32)) (*.f32 #s(literal -1 binary32) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta (*.f32 (neg.f32 (sqrt.f32 (PI.f32))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta (fma.f32 (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32) (log.f32 cosTheta)))
(+ (* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))) (* cosTheta (+ (* -1 (* (sqrt (PI)) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* cosTheta (+ (* -1/2 (+ (* -1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 2 (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* -1/6 (* cosTheta (+ (* -6 (* (PI) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (+ (* 2 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3))) (* 6 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))))))
(fma.f32 (fma.f32 (neg.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (PI.f32)) (*.f32 (fma.f32 (*.f32 #s(literal -1/6 binary32) cosTheta) (fma.f32 (*.f32 #s(literal -6 binary32) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) #s(literal 2 binary32) (*.f32 (*.f32 (*.f32 #s(literal 6 binary32) (sqrt.f32 (PI.f32))) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 #s(literal 1/2 binary32) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (PI.f32)) (*.f32 #s(literal -1 binary32) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta)) cosTheta (fma.f32 (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32) (log.f32 cosTheta)))
(+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))
(-.f32 (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (log.f32 cosTheta))
(+ (log (sqrt (/ 1 (PI)))) (+ (* -1 (log cosTheta)) (* (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (sqrt (PI)))))
(fma.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta cosTheta) (sqrt.f32 (PI.f32)) (-.f32 (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (log.f32 cosTheta)))
(+ (log (sqrt (/ 1 (PI)))) (+ (* -1 (log cosTheta)) (* cosTheta (+ (* 1/2 (* cosTheta (+ (* -1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 2 (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (* (sqrt (PI)) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(fma.f32 (fma.f32 (fma.f32 #s(literal -1/2 binary32) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (PI.f32)) (*.f32 #s(literal 1 binary32) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta (*.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32)))) cosTheta (-.f32 (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (log.f32 cosTheta)))
(+ (log (sqrt (/ 1 (PI)))) (+ (* -1 (log cosTheta)) (* cosTheta (+ (* cosTheta (+ (* 1/6 (* cosTheta (+ (* -6 (* (PI) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (+ (* 2 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3))) (* 6 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))) (* 1/2 (+ (* -1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 2 (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) (* (sqrt (PI)) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(fma.f32 (fma.f32 (fma.f32 (*.f32 #s(literal 1/6 binary32) cosTheta) (fma.f32 (*.f32 #s(literal -6 binary32) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) #s(literal 2 binary32) (*.f32 (*.f32 (*.f32 #s(literal 6 binary32) (sqrt.f32 (PI.f32))) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 #s(literal -1/2 binary32) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (PI.f32)) (*.f32 #s(literal 1 binary32) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta (*.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32)))) cosTheta (-.f32 (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (log.f32 cosTheta)))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1/2 binary32))))) cosTheta)
(+ 1 (* -1 cosTheta))
(-.f32 #s(literal 1 binary32) cosTheta)
(+ 1 (* cosTheta (- (* -1/2 cosTheta) 1)))
(fma.f32 (-.f32 (*.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))
(+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1)))
(fma.f32 (-.f32 (*.f32 (-.f32 (*.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1/2 binary32)) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1/2 binary32)))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(*.f32 (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(fma.f32 (*.f32 #s(literal 1/2 binary32) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (*.f32 (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(fma.f32 (*.f32 #s(literal -1/8 binary32) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (fma.f32 (*.f32 #s(literal 1/2 binary32) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (*.f32 (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(fma.f32 (*.f32 #s(literal 1/16 binary32) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32)))) (fma.f32 (*.f32 #s(literal -1/8 binary32) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (fma.f32 (*.f32 #s(literal 1/2 binary32) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (*.f32 (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))))
(* -2 cosTheta)
(*.f32 #s(literal -2 binary32) cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta)
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (+.f32 c #s(literal 1 binary32))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
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(log (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(log1p.f32 (fma.f32 (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) c))
(+ (log (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))))
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(+ (log (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))) (+ (* 1/720 (/ (+ (* 30 (* (sqrt (/ (pow cosTheta 3) (pow (PI) 3))) (/ (pow (exp (* -1 (pow cosTheta 2))) 3) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (+ (* 45 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (* 45 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (pow cosTheta 6))) (+ (* 1/24 (/ (+ (* -3 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (* -3 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))))))
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(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) #s(literal -1/8 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32)))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) #s(literal -1/8 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))))
(* (sqrt cosTheta) (sqrt -2))
(*.f32 (sqrt.f32 cosTheta) (sqrt.f32 #s(literal -2 binary32)))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 #s(literal -2 binary32)) (*.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32))) cosTheta)
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))))
(*.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) #s(literal -1/8 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 #s(literal -2 binary32)) (*.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32)))) cosTheta)
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))))
(*.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32)))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) #s(literal -1/8 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 #s(literal -2 binary32)) (*.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32))))) cosTheta)
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(*.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -2 binary32)))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(*.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))) cosTheta)
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(*.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) #s(literal -1/8 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))) cosTheta)
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(*.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32)))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) #s(literal -1/8 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))))) cosTheta)
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(*.f32 (*.f32 (neg.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))) (sqrt.f32 #s(literal 2 binary32)))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(fma.f32 (*.f32 #s(literal -1/2 binary32) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (*.f32 (*.f32 (neg.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))) (sqrt.f32 #s(literal 2 binary32))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
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(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(fma.f32 (*.f32 (neg.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))) (sqrt.f32 #s(literal 2 binary32)) (fma.f32 (*.f32 #s(literal -1/2 binary32) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (fma.f32 (*.f32 #s(literal 1/8 binary32) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (*.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (*.f32 (*.f32 (*.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
(fma.f32 (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal 2 binary32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))))
(- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))))
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(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))
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(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
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(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) c)))
(+ (log -1) (+ (* -1 (log (/ -1 c))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(+.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) c))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)))
(+ (log -1) (+ (* -1 (log (/ -1 c))) (* -1 (/ (+ (* -1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) (* 1/2 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c))) c))))
(-.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) c))) (/.f32 (fma.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) c) #s(literal 1/2 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal -1 binary32))) c))
(+ (log -1) (+ (* -1 (log (/ -1 c))) (* -1 (/ (+ (* -1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) (* -1 (/ (+ (* -1/2 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) (* 1/3 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c))) c))) c))))
(-.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) c))) (/.f32 (-.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal -1 binary32)) (/.f32 (fma.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) c) #s(literal 1/3 binary32) (*.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) #s(literal -1/2 binary32))) c)) c))

rewrite402.0ms (3.6%)

Memory
11.9MiB live, 507.0MiB allocated; 116ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
063472
0107455
1395399
22926399
011368394
Stop Event
iter limit
node limit
iter limit
Counts
24 → 1 282
Calls
Call 1
Inputs
(*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
(/.f32 #s(literal 1 binary32) c)
(fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32))
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
(log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)
Outputs
(*.f32 (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (sqrt.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (sqrt.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))))
(*.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(*.f32 (sqrt.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (*.f32 (sqrt.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)))
(*.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta))
(*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))))
(*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (PI.f32))))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))
(*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))
(*.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (neg.f32 cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (neg.f32 cosTheta))
(/.f32 (*.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 #s(literal -1 binary32) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))
(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (neg.f32 cosTheta))) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))
(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))) (neg.f32 cosTheta))
(/.f32 (neg.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (*.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (neg.f32 cosTheta))
(/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (neg.f32 cosTheta))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (neg.f32 cosTheta)) #s(literal 1 binary32)) (*.f32 (neg.f32 (sqrt.f32 (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 (*.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) #s(literal 1 binary32)) (*.f32 (neg.f32 cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 (*.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1 binary32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 (*.f32 #s(literal 1 binary32) (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (neg.f32 cosTheta)))
(/.f32 (*.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))
(/.f32 (*.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal 1 binary32)) (*.f32 (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 (*.f32 #s(literal 1 binary32) (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 (*.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta)
(/.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (*.f32 (sqrt.f32 (PI.f32)) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(fma.f32 (cosh.f32 (*.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (*.f32 (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (cosh.f32 (*.f32 cosTheta cosTheta)) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 (*.f32 (cosh.f32 (*.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (*.f32 (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)))
(+.f32 (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (cosh.f32 (*.f32 cosTheta cosTheta))) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (*.f32 #s(literal 2 binary32) cosTheta) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 8 binary32) (pow.f32 cosTheta #s(literal 3 binary32)))) (+.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (*.f32 #s(literal 2 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)))))
(/.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta))) (neg.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(/.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))) (neg.f32 (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta)) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32))) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))))
(-.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (*.f32 cosTheta cosTheta) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(-.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))) (/.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta))
(*.f32 (neg.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32))) (neg.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32))))
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(/.f32 (sqrt.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta)))) (sqrt.f32 (neg.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(/.f32 (sqrt.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32))))) (sqrt.f32 (neg.f32 (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))))))
(/.f32 (sqrt.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta))) (sqrt.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(/.f32 (sqrt.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))) (sqrt.f32 (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(pow.f32 (exp.f32 (log.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal 1/2 binary32))
(pow.f32 (*.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1/4 binary32))
(pow.f32 (pow.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1/4 binary32)) #s(literal 2 binary32))
(pow.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1/2 binary32))
(+.f32 (cosh.f32 (*.f32 (log.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1/2 binary32))) (sinh.f32 (*.f32 (log.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1/2 binary32))))
(exp.f32 (*.f32 (log.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1/2 binary32)))
(*.f32 (neg.f32 (pow.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) #s(literal 1/4 binary32))) (neg.f32 (pow.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) #s(literal 1/4 binary32))))
(*.f32 (fabs.f32 (pow.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) #s(literal 1/4 binary32))) (fabs.f32 (pow.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) #s(literal 1/4 binary32))))
(*.f32 (pow.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) #s(literal 1/4 binary32)) (pow.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) #s(literal 1/4 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(*.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(sqrt.f32 (*.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (PI.f32))))
(sqrt.f32 (*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))) (pow.f32 (PI.f32) #s(literal 1/4 binary32)))
(/.f32 (sqrt.f32 (-.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) #s(literal 2 binary32)) (pow.f32 (/.f32 cosTheta (PI.f32)) #s(literal 2 binary32)))) (sqrt.f32 (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 cosTheta (PI.f32)))))
(/.f32 (sqrt.f32 (-.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (/.f32 cosTheta (PI.f32)) #s(literal 3 binary32)))) (sqrt.f32 (+.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) #s(literal 2 binary32)) (+.f32 (pow.f32 (/.f32 cosTheta (PI.f32)) #s(literal 2 binary32)) (*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 cosTheta (PI.f32)))))))
(/.f32 (sqrt.f32 (neg.f32 (neg.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (sqrt.f32 (neg.f32 (neg.f32 (PI.f32)))))
(/.f32 (sqrt.f32 (-.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (*.f32 (PI.f32) cosTheta))) (PI.f32))
(/.f32 (*.f32 #s(literal -1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (sqrt.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta))) (sqrt.f32 (*.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))
(/.f32 (sqrt.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))) (sqrt.f32 (*.f32 (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))) (PI.f32))))
(/.f32 (sqrt.f32 (neg.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (sqrt.f32 (neg.f32 (PI.f32))))
(/.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))
(pow.f32 (exp.f32 (log.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) #s(literal 1/2 binary32))
(pow.f32 (*.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1/4 binary32))
(pow.f32 (*.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32))
(pow.f32 (pow.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) #s(literal 1/4 binary32)) #s(literal 2 binary32))
(pow.f32 (*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1/2 binary32))
(pow.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) #s(literal 1/2 binary32))
(+.f32 (cosh.f32 (*.f32 (log.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1/2 binary32))) (sinh.f32 (*.f32 (log.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1/2 binary32))))
(exp.f32 (-.f32 (*.f32 (log.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1/2 binary32)) (log.f32 (sqrt.f32 (PI.f32)))))
(exp.f32 (fma.f32 #s(literal -1/2 binary32) (log.f32 (PI.f32)) (*.f32 (log.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1/2 binary32))))
(exp.f32 (fma.f32 (log.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1/2 binary32) (*.f32 #s(literal -1/2 binary32) (log.f32 (PI.f32)))))
(exp.f32 (*.f32 (log.f32 (*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal 1/2 binary32)))
(exp.f32 (*.f32 (log.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1/2 binary32)))
(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))
(*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))
(/.f32 (*.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (neg.f32 cosTheta))
(/.f32 (*.f32 #s(literal -1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) #s(literal -1 binary32)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (neg.f32 cosTheta))
(/.f32 (neg.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))) (neg.f32 (neg.f32 cosTheta)))
(/.f32 (neg.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (neg.f32 (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (*.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal -1 binary32)) (*.f32 (neg.f32 cosTheta) (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (*.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal 1 binary32)) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal -1 binary32)) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 #s(literal -1 binary32) (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (*.f32 (neg.f32 (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(/.f32 (*.f32 #s(literal -1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 #s(literal 1 binary32) (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (neg.f32 cosTheta))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(neg.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (neg.f32 cosTheta)))

eval255.0ms (2.3%)

Memory
4.2MiB live, 187.3MiB allocated; 24ms collecting garbage
Compiler

Compiled 55 490 to 6 204 computations (88.8% saved)

prune115.0ms (1%)

Memory
4.6MiB live, 96.1MiB allocated; 7ms collecting garbage
Pruning

26 alts after pruning (24 fresh and 2 done)

PrunedKeptTotal
New1 080191 099
Fresh6511
Picked325
Done000
Total1 089261 115
Accuracy
99.9%
Counts
1 115 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.9%
(pow.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
89.6%
(pow.f32 (exp.f32 #s(literal -1 binary32)) (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)))
96.3%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.2%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.7%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
96.5%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
97.9%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.4%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
97.4%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
96.9%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
95.7%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
92.1%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
97.2%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))) cosTheta))))
59.3%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (-.f32 (*.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta) cosTheta (/.f32 cosTheta (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta)))))
33.8%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))))))
10.8%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
98.2%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 c #s(literal 1 binary32)))))
97.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
96.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
95.7%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
97.3%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
34.0%
(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (fma.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (-.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
97.4%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
96.3%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
93.0%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
5.1%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
Compiler

Compiled 2 074 to 1 352 computations (34.8% saved)

simplify211.0ms (1.9%)

Memory
-4.6MiB live, 189.8MiB allocated; 35ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
cost-diff0
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
cost-diff2
(*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
cost-diff3
(-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))
cost-diff0
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
cost-diff0
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))
cost-diff0
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))
cost-diff0
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
cost-diff0
(fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
cost-diff0
(/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
cost-diff0
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
cost-diff0
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
cost-diff0
(PI.f32)
cost-diff0
(sqrt.f32 (PI.f32))
cost-diff0
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
cost-diff0
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
cost-diff0
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff1
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
cost-diff1
(*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
cost-diff2
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
074799
0129800
1230777
2656763
32685751
08982746
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
c
(*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(cbrt.f32 (PI.f32))
(PI.f32)
(/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(pow.f32 (PI.f32) #s(literal 1/6 binary32))
#s(literal 1/6 binary32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(sqrt.f32 (PI.f32))
(PI.f32)
cosTheta
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(literal 1 binary32)
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))
#s(literal -3/2 binary32)
cosTheta
#s(literal -1 binary32)
(+.f32 c #s(literal 1 binary32))
c
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
#s(literal 1 binary32)
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
(/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
#s(literal -2 binary32)
cosTheta
(PI.f32)
(/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
(*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32)))
(-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))
(*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(neg.f32 cosTheta)
cosTheta
(fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))
(sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))
(pow.f32 (PI.f32) #s(literal 3 binary32))
(PI.f32)
#s(literal 3 binary32)
(pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+.f32 #s(literal 1 binary32) c)
#s(literal 1 binary32)
c
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
#s(literal 2 binary32)
(*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(*.f32 (PI.f32) #s(literal -3/2 binary32))
#s(literal -3/2 binary32)
(fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(sqrt.f32 (PI.f32))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (+.f32 c #s(literal 1 binary32))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (+.f32 c #s(literal 1 binary32)))
(+.f32 #s(literal 1 binary32) c)
(+.f32 c #s(literal 1 binary32))
c
(*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (pow.f32 (exp.f32 cosTheta) cosTheta))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(cbrt.f32 (PI.f32))
(PI.f32)
(/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(pow.f32 (PI.f32) #s(literal 1/6 binary32))
#s(literal 1/6 binary32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(sqrt.f32 (PI.f32))
(PI.f32)
cosTheta
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(literal 1 binary32)
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/.f32 (fma.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(fma.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32)))
(fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal 1 binary32)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))
#s(literal -3/2 binary32)
cosTheta
#s(literal -1 binary32)
(+.f32 c #s(literal 1 binary32))
c
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))))
#s(literal 1 binary32)
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))
(fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
(/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
#s(literal -2 binary32)
cosTheta
(PI.f32)
(/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta)
(/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (fma.f32 (*.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) cosTheta) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (*.f32 (PI.f32) (fma.f32 (fma.f32 #s(literal 3/2 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (neg.f32 c) #s(literal -1 binary32))))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
(*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(*.f32 (fma.f32 (fma.f32 (*.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) cosTheta) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (*.f32 (PI.f32) (fma.f32 (fma.f32 #s(literal 3/2 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (neg.f32 c) #s(literal -1 binary32))))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32)))
(fma.f32 (fma.f32 (*.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) cosTheta) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (*.f32 (PI.f32) (fma.f32 (fma.f32 #s(literal 3/2 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (neg.f32 c) #s(literal -1 binary32))))) cosTheta (sqrt.f32 (PI.f32)))
(-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))
(fma.f32 (*.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) cosTheta) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (*.f32 (PI.f32) (fma.f32 (fma.f32 #s(literal 3/2 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (neg.f32 c) #s(literal -1 binary32)))))
(*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(*.f32 (fma.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (*.f32 (*.f32 #s(literal 3/2 binary32) (PI.f32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(neg.f32 cosTheta)
cosTheta
(fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(fma.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (*.f32 (*.f32 #s(literal -3/2 binary32) (PI.f32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))
(sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))
(pow.f32 (PI.f32) #s(literal 3 binary32))
(PI.f32)
#s(literal 3 binary32)
(pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))
(pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(-.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+.f32 #s(literal 1 binary32) c)
(+.f32 c #s(literal 1 binary32))
#s(literal 1 binary32)
c
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
#s(literal 2 binary32)
(*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(*.f32 (*.f32 #s(literal -3/2 binary32) (PI.f32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(*.f32 (PI.f32) #s(literal -3/2 binary32))
(*.f32 #s(literal -3/2 binary32) (PI.f32))
#s(literal -3/2 binary32)
(fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(sqrt.f32 (PI.f32))

localize330.0ms (3%)

Memory
-41.0MiB live, 212.6MiB allocated; 30ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy1.0
(pow.f32 (PI.f32) #s(literal 3 binary32))
accuracy1.0
(*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
accuracy1.0
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy1.018580139073516
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
accuracy0.10682560262737048
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))
accuracy0.3203125
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
accuracy0.5885925781475362
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))
accuracy0.7890625
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
accuracy0.4151686205919121
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
accuracy0.5390625
(/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy0.9804924656910952
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32)))
accuracy1.0
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy0.0
(sqrt.f32 (PI.f32))
accuracy0.0
(PI.f32)
accuracy0.3359375
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
accuracy1.9794897155262812
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
accuracy0.10546875
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy0.2890625
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
accuracy0.3203125
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy0.3828125
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32)))
Samples
278.0ms256×0valid
Compiler

Compiled 701 to 69 computations (90.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 187.0ms
ival-mult: 82.0ms (43.8% of total)
ival-exp: 26.0ms (13.9% of total)
ival-sqrt: 25.0ms (13.4% of total)
ival-div: 15.0ms (8% of total)
ival-add: 14.0ms (7.5% of total)
ival-pow: 7.0ms (3.7% of total)
ival-sub: 6.0ms (3.2% of total)
const: 4.0ms (2.1% of total)
ival-cbrt: 2.0ms (1.1% of total)
ival-pow2: 2.0ms (1.1% of total)
ival-neg: 2.0ms (1.1% of total)
ival-pi: 1.0ms (0.5% of total)
exact: 1.0ms (0.5% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series206.0ms (1.8%)

Memory
38.1MiB live, 171.6MiB allocated; 16ms collecting garbage
Counts
26 → 167
Calls
Call 1
Inputs
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
(-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))
(*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
(*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32)))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(pow.f32 (PI.f32) #s(literal 3 binary32))
Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(* -1 (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))))
(- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))))
(* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (* -1 (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))))))))
(* (/ 1 cosTheta) (cbrt (/ 1 (PI))))
(/ (+ (cbrt (/ 1 (PI))) (* -1 (* cosTheta (cbrt (/ 1 (PI)))))) cosTheta)
(/ (+ (cbrt (/ 1 (PI))) (* cosTheta (+ (* -1 (cbrt (/ 1 (PI)))) (* -1/2 (* cosTheta (cbrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (cbrt (/ 1 (PI))) (* cosTheta (+ (* -1 (cbrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (cbrt (/ 1 (PI)))) (* -1/2 (* cosTheta (cbrt (/ 1 (PI)))))))))) cosTheta)
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(* -3/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ 1 (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ 1 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ 1 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(* cosTheta (+ (* -1 (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))) (* -1 (/ (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))) cosTheta))))
(* -1 (* (pow cosTheta 3) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))))
(* (pow cosTheta 3) (+ (* -1 (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))) (* -1 (/ (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))) cosTheta))))
(* (pow cosTheta 3) (+ (* -1 (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))) (+ (* -1 (/ (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))) cosTheta)) (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))))
(* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (* (cbrt (/ 1 (PI))) (/ 1 (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (* (cbrt (/ 1 (PI))) (/ 1 (pow (sqrt -2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (* (cbrt (/ 1 (PI))) (/ 1 (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (sqrt -2)))))
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(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
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(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta))))
(+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))
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(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))) (+ (/ (PI) cosTheta) (/ (* (PI) (- c (sqrt (/ 1 (PI))))) cosTheta))))))
(* -1 (* (pow cosTheta 3) (+ (* -3/2 (sqrt (PI))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))) (+ (/ (PI) cosTheta) (/ (* (PI) (- c (sqrt (/ 1 (PI))))) cosTheta))))))
(* -1 (* (pow cosTheta 3) (+ (* -3/2 (sqrt (PI))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))) (* -1 (/ (+ (* -1 (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI))))))) (* (/ 1 cosTheta) (sqrt (PI)))) cosTheta))))))
(* -1 (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (* (cbrt (/ 1 (PI))) (/ (sqrt -1) (sqrt 2))))))
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(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) cosTheta)
(+ c (+ (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))) (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))))
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(- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))
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(* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))))
(+ (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (* (* c (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI))))))) (sqrt (pow (PI) 3))))
(+ (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (* c (+ (* (* c cosTheta) (sqrt (pow (PI) 3))) (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI))))))))
(+ (* c (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI)))) (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))))
(+ (* c (+ (* (* c (pow cosTheta 3)) (sqrt (pow (PI) 3))) (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI))))) (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))))
(+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))
(+ 1 (+ c (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))
(- 1 (sqrt (/ 1 (PI))))
(- (+ 1 c) (sqrt (/ 1 (PI))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c)))))
(* c cosTheta)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))) c))))
(* (* (pow c 2) cosTheta) (sqrt (pow (PI) 3)))
(* (pow c 2) (- (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3)))) (/ (PI) c)))
(* (pow c 2) (- (+ (* -1 (/ (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) (pow c 2))) (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3))))) (+ (* -1 (* (/ 1 (pow c 2)) (sqrt (PI)))) (+ (/ (PI) c) (/ (PI) (pow c 2))))))
(* (pow c 2) (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* -1 (/ (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) (pow c 2))) (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3))))))
(* (* (pow c 2) (pow cosTheta 3)) (sqrt (pow (PI) 3)))
(* (pow c 2) (+ (* (pow cosTheta 3) (sqrt (pow (PI) 3))) (/ (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI))) c)))
(* (pow c 2) (+ (* (pow cosTheta 3) (sqrt (pow (PI) 3))) (+ (/ (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))) (pow c 2)) (/ (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI))) c))))
(* c (+ 1 (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))))
(* c (- (+ 1 (/ 1 c)) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (+ (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) c)) 1)))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) c)))))
(* (pow c 2) (+ (* -1 (/ (- (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (PI))) c)) (* cosTheta (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* -1 (/ (- (+ (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (/ (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI))))) c))) (* -1 (PI))) c)) (* cosTheta (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* 2 (* (/ (* cosTheta (- 1 (sqrt (/ 1 (PI))))) c) (sqrt (pow (PI) 3)))) (* cosTheta (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* -1 (/ (+ (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (/ (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) c)) c)) (* cosTheta (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* -1 (/ (* (pow cosTheta 2) (- (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (PI)))) c)) (* (pow cosTheta 3) (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* -1 (/ (+ (* -1 (/ (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))) c)) (* (pow cosTheta 2) (- (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (PI))))) c)) (* (pow cosTheta 3) (sqrt (pow (PI) 3)))))
(* -1 (* c (- (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))) c)) 1)))
(* -1 (* c (- (* -1 (/ (- 1 (sqrt (/ 1 (PI)))) c)) 1)))
Calls

6 calls:

TimeVariablePointExpression
87.0ms
cosTheta
@0
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34.0ms
cosTheta
@-inf
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29.0ms
c
@inf
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19.0ms
cosTheta
@inf
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16.0ms
c
@0
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simplify215.0ms (1.9%)

Memory
-19.7MiB live, 163.2MiB allocated; 31ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07716809
127306520
084916245
Stop Event
iter limit
node limit
Counts
167 → 166
Calls
Call 1
Inputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)
(sqrt (/ 1 (PI)))
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)
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(/ (+ (cbrt (/ 1 (PI))) (* cosTheta (+ (* -1 (cbrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (cbrt (/ 1 (PI)))) (* -1/2 (* cosTheta (cbrt (/ 1 (PI)))))))))) cosTheta)
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(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(* -3/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
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(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(* cosTheta (+ (* -1 (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))) (* -1 (/ (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))) cosTheta))))
(* -1 (* (pow cosTheta 3) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))))
(* (pow cosTheta 3) (+ (* -1 (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))) (* -1 (/ (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))) cosTheta))))
(* (pow cosTheta 3) (+ (* -1 (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))) (+ (* -1 (/ (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))) cosTheta)) (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))))
(* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (* (cbrt (/ 1 (PI))) (/ 1 (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (sqrt -2))))
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(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
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(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
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(- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))
(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
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(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))
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(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta))))
(+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2))))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))) (+ (/ (PI) cosTheta) (/ (* (PI) (- c (sqrt (/ 1 (PI))))) cosTheta))))))
(* -1 (* (pow cosTheta 3) (+ (* -3/2 (sqrt (PI))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))) (+ (/ (PI) cosTheta) (/ (* (PI) (- c (sqrt (/ 1 (PI))))) cosTheta))))))
(* -1 (* (pow cosTheta 3) (+ (* -3/2 (sqrt (PI))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))) (* -1 (/ (+ (* -1 (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI))))))) (* (/ 1 cosTheta) (sqrt (PI)))) cosTheta))))))
(* -1 (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (* (cbrt (/ 1 (PI))) (/ (sqrt -1) (sqrt 2))))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (* (cbrt (/ 1 (PI))) (/ (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (* (cbrt (/ 1 (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (* (cbrt (/ 1 (PI))) (/ (sqrt -1) (sqrt 2))))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (* (cbrt (/ 1 (PI))) (/ (sqrt -1) (pow (sqrt 2) 5))))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (* (cbrt (/ 1 (PI))) (/ (sqrt -1) (pow (sqrt 2) 3))))))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) cosTheta)
(+ c (+ (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))) (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))))
(- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))
(- (+ (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (* c (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI)))) (+ (PI) (* -1 (sqrt (PI)))))
(- (+ (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (* c (- (+ (* (* c cosTheta) (sqrt (pow (PI) 3))) (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3)))) (PI)))) (+ (PI) (* -1 (sqrt (PI)))))
(* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))))
(+ (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (* (* c (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI))))))) (sqrt (pow (PI) 3))))
(+ (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (* c (+ (* (* c cosTheta) (sqrt (pow (PI) 3))) (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI))))))))
(+ (* c (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI)))) (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))))
(+ (* c (+ (* (* c (pow cosTheta 3)) (sqrt (pow (PI) 3))) (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI))))) (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))))
(+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))
(+ 1 (+ c (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))
(- 1 (sqrt (/ 1 (PI))))
(- (+ 1 c) (sqrt (/ 1 (PI))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c)))))
(* c cosTheta)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))) c))))
(* (* (pow c 2) cosTheta) (sqrt (pow (PI) 3)))
(* (pow c 2) (- (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3)))) (/ (PI) c)))
(* (pow c 2) (- (+ (* -1 (/ (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) (pow c 2))) (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3))))) (+ (* -1 (* (/ 1 (pow c 2)) (sqrt (PI)))) (+ (/ (PI) c) (/ (PI) (pow c 2))))))
(* (pow c 2) (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* -1 (/ (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) (pow c 2))) (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3))))))
(* (* (pow c 2) (pow cosTheta 3)) (sqrt (pow (PI) 3)))
(* (pow c 2) (+ (* (pow cosTheta 3) (sqrt (pow (PI) 3))) (/ (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI))) c)))
(* (pow c 2) (+ (* (pow cosTheta 3) (sqrt (pow (PI) 3))) (+ (/ (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))) (pow c 2)) (/ (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI))) c))))
(* c (+ 1 (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))))
(* c (- (+ 1 (/ 1 c)) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (+ (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) c)) 1)))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) c)))))
(* (pow c 2) (+ (* -1 (/ (- (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (PI))) c)) (* cosTheta (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* -1 (/ (- (+ (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (/ (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI))))) c))) (* -1 (PI))) c)) (* cosTheta (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* 2 (* (/ (* cosTheta (- 1 (sqrt (/ 1 (PI))))) c) (sqrt (pow (PI) 3)))) (* cosTheta (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* -1 (/ (+ (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (/ (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) c)) c)) (* cosTheta (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* -1 (/ (* (pow cosTheta 2) (- (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (PI)))) c)) (* (pow cosTheta 3) (sqrt (pow (PI) 3)))))
(* (pow c 2) (+ (* -1 (/ (+ (* -1 (/ (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))) c)) (* (pow cosTheta 2) (- (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (PI))))) c)) (* (pow cosTheta 3) (sqrt (pow (PI) 3)))))
(* -1 (* c (- (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))) c)) 1)))
(* -1 (* c (- (* -1 (/ (- 1 (sqrt (/ 1 (PI)))) c)) 1)))
Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1/2 binary32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(/.f32 (fma.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
1
#s(literal 1 binary32)
(+ 1 (* -2 cosTheta))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(* cosTheta (sqrt (PI)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (-.f32 (*.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (fma.f32 (-.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (*.f32 (sqrt.f32 (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (-.f32 (*.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (*.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)))) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) (*.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))) cosTheta (neg.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) c) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))))
(fma.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) c) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(fma.f32 (-.f32 (*.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1/2 binary32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* -1 (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))))
(neg.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))
(- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))))
(neg.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) cosTheta (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))))
(* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))))
(*.f32 (neg.f32 cosTheta) (-.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI))))))))))
(*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (* -1 (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (neg.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) cosTheta (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* (/ 1 cosTheta) (cbrt (/ 1 (PI))))
(/.f32 (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (cbrt (/ 1 (PI))) (* -1 (* cosTheta (cbrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (cbrt (/ 1 (PI))) (* cosTheta (+ (* -1 (cbrt (/ 1 (PI)))) (* -1/2 (* cosTheta (cbrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 (*.f32 (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (cbrt (/ 1 (PI))) (* cosTheta (+ (* -1 (cbrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (cbrt (/ 1 (PI)))) (* -1/2 (* cosTheta (cbrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1/2 binary32))) cosTheta) (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))
(+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) c)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) #s(literal -1/8 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) #s(literal -1/8 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32)))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(fma.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal -2 binary32)) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(fma.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal -2 binary32)) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(fma.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 (*.f32 #s(literal 1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (fma.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal -2 binary32)) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32)))))))
(* -2 cosTheta)
(*.f32 #s(literal -2 binary32) cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta)
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(fma.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c)))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(fma.f32 (/.f32 (fma.f32 (/.f32 #s(literal -1/4 binary32) (*.f32 (PI.f32) #s(literal -2 binary32))) (/.f32 (*.f32 (pow.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) cosTheta) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 3 binary32))) (*.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (/.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 2 binary32))))) (pow.f32 cosTheta #s(literal 4 binary32))) #s(literal -1 binary32) (fma.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(fma.f32 (/.f32 (fma.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (*.f32 (/.f32 (fma.f32 (/.f32 #s(literal -1/4 binary32) (*.f32 (PI.f32) #s(literal -2 binary32))) (/.f32 (*.f32 (pow.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) cosTheta) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 3 binary32))) (*.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (/.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 2 binary32))))) (sqrt.f32 #s(literal -2 binary32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c))) (*.f32 #s(literal 1/16 binary32) (fma.f32 (/.f32 (pow.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) (*.f32 (PI.f32) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 4 binary32)))) (/.f32 (*.f32 cosTheta cosTheta) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 3 binary32))) (*.f32 (/.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 2 binary32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))))))) (pow.f32 cosTheta #s(literal 6 binary32))) #s(literal -1 binary32) (-.f32 (/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c)) (fma.f32 (/.f32 #s(literal -1/4 binary32) (*.f32 (*.f32 (PI.f32) #s(literal -2 binary32)) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 3 binary32)))) (/.f32 (pow.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) (pow.f32 cosTheta #s(literal 3 binary32))) (fma.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 2 binary32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (pow.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c) #s(literal 2 binary32))))))))
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) c)
(+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+.f32 (+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))))) c)
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal -2 binary32)) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32)))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 (*.f32 #s(literal 1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (fma.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal -2 binary32)) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))))))))
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(*.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta)) cosTheta)
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))) cosTheta)
(* -3/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(*.f32 (*.f32 #s(literal -3/2 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta)) (*.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))) (*.f32 cosTheta cosTheta))
(+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32))
(+ 1 (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+.f32 (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32)) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32)))))
(+ 1 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+.f32 (fma.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal -2 binary32)) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32)))))) #s(literal 1 binary32))
(+ 1 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+.f32 (fma.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 (*.f32 #s(literal 1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (fma.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal -2 binary32)) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))))))) #s(literal 1 binary32))
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(*.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -2 binary32)))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(*.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))) cosTheta)
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(*.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) #s(literal -1/8 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))) cosTheta)
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(*.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) #s(literal -1/8 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32)))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))))) cosTheta)
(* cosTheta (+ (* -1 (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))) (* -1 (/ (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))) cosTheta))))
(*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)) (-.f32 (/.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) cosTheta) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))))))
(* -1 (* (pow cosTheta 3) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))))
(*.f32 (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32)) (-.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))))
(* (pow cosTheta 3) (+ (* -1 (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))) (* -1 (/ (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))) cosTheta))))
(*.f32 (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32)) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)) (-.f32 (/.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) cosTheta) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))))))
(* (pow cosTheta 3) (+ (* -1 (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))) (+ (* -1 (/ (+ (PI) (* (PI) (- c (sqrt (/ 1 (PI)))))) cosTheta)) (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))))
(*.f32 (fma.f32 #s(literal -1 binary32) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)) (-.f32 (/.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) cosTheta) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))))) (/.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta cosTheta))) (pow.f32 cosTheta #s(literal 3 binary32)))
(* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (sqrt -2)))
(*.f32 (*.f32 (sqrt.f32 #s(literal -2 binary32)) (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (* (cbrt (/ 1 (PI))) (/ 1 (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (sqrt -2))))
(fma.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (sqrt.f32 #s(literal -2 binary32))) (*.f32 (*.f32 (sqrt.f32 #s(literal -2 binary32)) (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (* (cbrt (/ 1 (PI))) (/ 1 (pow (sqrt -2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (* (cbrt (/ 1 (PI))) (/ 1 (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (sqrt -2)))))
(fma.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (sqrt.f32 #s(literal -2 binary32))) (*.f32 (*.f32 (sqrt.f32 #s(literal -2 binary32)) (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (* (cbrt (/ 1 (PI))) (/ 1 (pow (sqrt -2) 3))))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (* (cbrt (/ 1 (PI))) (/ 1 (pow (sqrt -2) 5))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (* (cbrt (/ 1 (PI))) (/ 1 (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (* (cbrt (/ 1 (PI))) (sqrt -2))))))
(fma.f32 (*.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 (*.f32 #s(literal 1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))))) (/.f32 (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (fma.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (sqrt.f32 #s(literal -2 binary32))) (*.f32 (*.f32 (sqrt.f32 #s(literal -2 binary32)) (cbrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(*.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 #s(literal 2 binary32))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(fma.f32 (neg.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -1 binary32)))) (sqrt.f32 #s(literal 2 binary32)) (*.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(fma.f32 (neg.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -1 binary32)))) (sqrt.f32 #s(literal 2 binary32)) (fma.f32 (*.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (*.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 2 binary32))) (*.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(fma.f32 (neg.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -1 binary32)))) (sqrt.f32 #s(literal 2 binary32)) (fma.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (*.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) (*.f32 (*.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (*.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(*.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (neg.f32 (*.f32 (sqrt.f32 #s(literal 2 binary32)) (sqrt.f32 #s(literal -1 binary32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(-.f32 (*.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32)))) (*.f32 (*.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(-.f32 (fma.f32 (*.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (*.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 2 binary32))) (*.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))))) (*.f32 (*.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(-.f32 (fma.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (*.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))))) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) (*.f32 (*.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (*.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))))) (*.f32 (*.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))))
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(+ (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (* (* c (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI))))))) (sqrt (pow (PI) 3))))
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(+ (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (* c (+ (* (* c cosTheta) (sqrt (pow (PI) 3))) (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))))))
(-.f32 (*.f32 (*.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (*.f32 cosTheta (+.f32 c (-.f32 #s(literal 2 binary32) (*.f32 #s(literal 2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) c) (*.f32 (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) cosTheta))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI))))))))
(*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(+ (* c (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI)))) (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))))
(fma.f32 (*.f32 c (*.f32 cosTheta cosTheta)) (-.f32 (*.f32 (*.f32 (-.f32 #s(literal 2 binary32) (*.f32 #s(literal 2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (PI.f32)) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
(+ (* c (+ (* (* c (pow cosTheta 3)) (sqrt (pow (PI) 3))) (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI))))) (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))))
(fma.f32 (fma.f32 (-.f32 (*.f32 (*.f32 (-.f32 #s(literal 2 binary32) (*.f32 #s(literal 2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (PI.f32)) (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) c) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) c (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
(+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))
(+ 1 (+ c (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))
(+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) c)
(- 1 (sqrt (/ 1 (PI))))
(-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(- (+ 1 c) (sqrt (/ 1 (PI))))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) c)) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/.f32 (-.f32 (+.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) (*.f32 c c)) #s(literal 1 binary32)) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/.f32 (-.f32 (-.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) c) #s(literal 3 binary32))) (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) (neg.f32 (*.f32 c c)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(fma.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) c c)
(* c (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c)))))
(fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c)) (/.f32 #s(literal 1 binary32) c)) c c)
(* c cosTheta)
(*.f32 c cosTheta)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))) c))))
(*.f32 (+.f32 (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) cosTheta) c)
(* (* (pow c 2) cosTheta) (sqrt (pow (PI) 3)))
(*.f32 (*.f32 (*.f32 c c) cosTheta) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))
(* (pow c 2) (- (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3)))) (/ (PI) c)))
(*.f32 (-.f32 (*.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 2 binary32) (*.f32 #s(literal 2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) cosTheta)) (/.f32 (PI.f32) c)) (*.f32 c c))
(* (pow c 2) (- (+ (* -1 (/ (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) (pow c 2))) (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3))))) (+ (* -1 (* (/ 1 (pow c 2)) (sqrt (PI)))) (+ (/ (PI) c) (/ (PI) (pow c 2))))))
(*.f32 (-.f32 (fma.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 2 binary32) (*.f32 #s(literal 2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) cosTheta) (*.f32 (/.f32 (neg.f32 cosTheta) c) (/.f32 (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) c))) (fma.f32 (/.f32 (sqrt.f32 (PI.f32)) (*.f32 c c)) #s(literal -1 binary32) (+.f32 (/.f32 (PI.f32) (*.f32 c c)) (/.f32 (PI.f32) c)))) (*.f32 c c))
(* (pow c 2) (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3)))))
(*.f32 (*.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 2 binary32) (*.f32 #s(literal 2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) cosTheta)) (*.f32 c c))
(* (pow c 2) (+ (* -1 (/ (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) (pow c 2))) (+ (* cosTheta (sqrt (pow (PI) 3))) (* (/ (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) c) (sqrt (pow (PI) 3))))))
(*.f32 (fma.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 2 binary32) (*.f32 #s(literal 2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) cosTheta) (*.f32 (/.f32 (neg.f32 cosTheta) c) (/.f32 (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) c))) (*.f32 c c))
(* (* (pow c 2) (pow cosTheta 3)) (sqrt (pow (PI) 3)))
(*.f32 (*.f32 c c) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))))
(* (pow c 2) (+ (* (pow cosTheta 3) (sqrt (pow (PI) 3))) (/ (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI))) c)))
(*.f32 (fma.f32 (*.f32 cosTheta cosTheta) (/.f32 (-.f32 (*.f32 (*.f32 (-.f32 #s(literal 2 binary32) (*.f32 #s(literal 2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (PI.f32)) c) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) (*.f32 c c))
(* (pow c 2) (+ (* (pow cosTheta 3) (sqrt (pow (PI) 3))) (+ (/ (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))) (pow c 2)) (/ (* (pow cosTheta 2) (- (* (* cosTheta (- 2 (* 2 (sqrt (/ 1 (PI)))))) (sqrt (pow (PI) 3))) (PI))) c))))
(*.f32 (fma.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (fma.f32 (/.f32 cosTheta c) (/.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) c) (*.f32 (*.f32 cosTheta cosTheta) (/.f32 (-.f32 (*.f32 (*.f32 (-.f32 #s(literal 2 binary32) (*.f32 #s(literal 2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (PI.f32)) c)))) (*.f32 c c))
(* c (+ 1 (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))))
(fma.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) c) c c)
(* c (- (+ 1 (/ 1 c)) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(*.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c)) c)
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (-.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) c) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal 1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32))) (neg.f32 c)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal 1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (* c (- (* -1 (/ (+ 1 (+ (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) c)) 1)))
(*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) c)))))
(*.f32 (neg.f32 c) (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c)))
(* (pow c 2) (+ (* -1 (/ (- (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (PI))) c)) (* cosTheta (sqrt (pow (PI) 3)))))
(*.f32 (fma.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) cosTheta (/.f32 (fma.f32 (*.f32 #s(literal -2 binary32) (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (PI.f32)) (neg.f32 c))) (*.f32 c c))
(* (pow c 2) (+ (* -1 (/ (- (+ (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (/ (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI))))) c))) (* -1 (PI))) c)) (* cosTheta (sqrt (pow (PI) 3)))))
(*.f32 (fma.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) cosTheta (/.f32 (fma.f32 (*.f32 #s(literal -2 binary32) (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (fma.f32 (/.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) c) #s(literal -1 binary32) (PI.f32))) (neg.f32 c))) (*.f32 c c))
(* (pow c 2) (+ (* 2 (* (/ (* cosTheta (- 1 (sqrt (/ 1 (PI))))) c) (sqrt (pow (PI) 3)))) (* cosTheta (sqrt (pow (PI) 3)))))
(*.f32 (*.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (fma.f32 #s(literal 2 binary32) (/.f32 (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) c) cosTheta)) (*.f32 c c))
(* (pow c 2) (+ (* -1 (/ (+ (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (/ (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) c)) c)) (* cosTheta (sqrt (pow (PI) 3)))))
(*.f32 (fma.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) cosTheta (/.f32 (fma.f32 cosTheta (/.f32 (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) c) (*.f32 (*.f32 #s(literal -2 binary32) (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) (neg.f32 c))) (*.f32 c c))
(* (pow c 2) (+ (* -1 (/ (* (pow cosTheta 2) (- (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (PI)))) c)) (* (pow cosTheta 3) (sqrt (pow (PI) 3)))))
(*.f32 (fma.f32 (*.f32 (neg.f32 cosTheta) cosTheta) (/.f32 (fma.f32 (*.f32 #s(literal -2 binary32) (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (PI.f32)) c) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) (*.f32 c c))
(* (pow c 2) (+ (* -1 (/ (+ (* -1 (/ (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2)))))) (+ (PI) (* -1 (sqrt (PI)))))))) c)) (* (pow cosTheta 2) (- (* -2 (* (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (pow (PI) 3)))) (* -1 (PI))))) c)) (* (pow cosTheta 3) (sqrt (pow (PI) 3)))))
(*.f32 (fma.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) c) (*.f32 (fma.f32 (*.f32 #s(literal -2 binary32) (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (PI.f32)) (*.f32 cosTheta cosTheta))) (neg.f32 c))) (*.f32 c c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))) c)) 1)))
(*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (* c (- (* -1 (/ (- 1 (sqrt (/ 1 (PI)))) c)) 1)))
(*.f32 (neg.f32 c) (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) #s(literal 1 binary32)))

rewrite251.0ms (2.2%)

Memory
6.7MiB live, 176.9MiB allocated; 41ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
074554
0129544
1491477
24158467
08161467
Stop Event
iter limit
node limit
iter limit
Counts
26 → 543
Calls
Call 1
Inputs
(*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
(-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))
(*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
(*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32)))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(pow.f32 (PI.f32) #s(literal 3 binary32))
Outputs
(*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) (pow.f32 (PI.f32) #s(literal 1/12 binary32))) (pow.f32 (PI.f32) #s(literal -1/12 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/6 binary32)))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(/.f32 (*.f32 #s(literal -1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta))) (neg.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta)) (pow.f32 (PI.f32) #s(literal -1/6 binary32))) (neg.f32 (cbrt.f32 (PI.f32))))
(/.f32 (*.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (pow.f32 (PI.f32) #s(literal -1/6 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta))
(/.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta))) (neg.f32 (cbrt.f32 (PI.f32))))
(/.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(/.f32 (neg.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta))) (neg.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(/.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) (pow.f32 (PI.f32) #s(literal 1/12 binary32))) (pow.f32 (PI.f32) #s(literal 1/12 binary32)))
(/.f32 (neg.f32 (/.f32 (*.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (pow.f32 (PI.f32) #s(literal -1/6 binary32))) cosTheta)) (neg.f32 (cbrt.f32 (PI.f32))))
(/.f32 (neg.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (neg.f32 (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta))))
(/.f32 (*.f32 #s(literal -1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta))) (*.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (neg.f32 (cbrt.f32 (PI.f32)))))
(/.f32 (*.f32 #s(literal -1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (*.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (cbrt.f32 (PI.f32))))
(/.f32 (*.f32 #s(literal -1 binary32) (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)))
(/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta))) (*.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (neg.f32 (cbrt.f32 (PI.f32)))))
(/.f32 (*.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta)) #s(literal -1 binary32)) (*.f32 (neg.f32 (cbrt.f32 (PI.f32))) (neg.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)))))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta)) #s(literal 1 binary32)) (*.f32 (neg.f32 (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) #s(literal -1 binary32)) (*.f32 (cbrt.f32 (PI.f32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)))))
(/.f32 (*.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) #s(literal -1 binary32)) (*.f32 (*.f32 (cbrt.f32 (PI.f32)) cosTheta) (neg.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)))))
(/.f32 (*.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) #s(literal 1 binary32)) (*.f32 (*.f32 (cbrt.f32 (PI.f32)) cosTheta) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(/.f32 (/.f32 (*.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (pow.f32 (PI.f32) #s(literal -1/6 binary32))) cosTheta) (cbrt.f32 (PI.f32)))
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(neg.f32 (neg.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)))
(*.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta))) (pow.f32 (PI.f32) #s(literal -1/6 binary32)))
(*.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (pow.f32 (PI.f32) #s(literal -1/6 binary32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)))
(*.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
(*.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))
(*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (*.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)))
(*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta))
(*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))
(*.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta) #s(literal 1 binary32))
(*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (cbrt.f32 (PI.f32)) cosTheta)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (pow.f32 (PI.f32) #s(literal -1/6 binary32))))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (PI.f32))))
(*.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(*.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta))
(/.f32 (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))
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(/.f32 (*.f32 (*.f32 #s(literal -3/2 binary32) (PI.f32)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(log.f32 (exp.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 5 binary32)) #s(literal 3/2 binary32)) (sqrt.f32 (PI.f32)))
(*.f32 (pow.f32 (*.f32 (cbrt.f32 (PI.f32)) (PI.f32)) #s(literal 3/2 binary32)) (PI.f32))
(*.f32 (pow.f32 (fabs.f32 (PI.f32)) #s(literal 3/2 binary32)) (pow.f32 (fabs.f32 (PI.f32)) #s(literal 3/2 binary32)))
(*.f32 (pow.f32 (neg.f32 (PI.f32)) #s(literal 3/2 binary32)) (pow.f32 (neg.f32 (PI.f32)) #s(literal 3/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (*.f32 (PI.f32) (cbrt.f32 (PI.f32))) #s(literal 2 binary32)) #s(literal 1 binary32)) (cbrt.f32 (PI.f32)))
(*.f32 (pow.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal 1 binary32)) (pow.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal 1 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 5/2 binary32)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(*.f32 (pow.f32 (neg.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32)) (pow.f32 (neg.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal 3 binary32)) (pow.f32 (cbrt.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal 3 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 3/2 binary32)) (pow.f32 (PI.f32) #s(literal 3/4 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 5/2 binary32)) (sqrt.f32 (PI.f32)))
(*.f32 (pow.f32 (*.f32 (PI.f32) (cbrt.f32 (PI.f32))) #s(literal 2 binary32)) (cbrt.f32 (PI.f32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 3/4 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 3/2 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (pow.f32 (*.f32 (cbrt.f32 (PI.f32)) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (*.f32 (cbrt.f32 (PI.f32)) (*.f32 (PI.f32) (PI.f32))))
(*.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))
(*.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))))
(*.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))
(*.f32 (sqrt.f32 (PI.f32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 5/2 binary32)) #s(literal 1 binary32)))
(*.f32 (sqrt.f32 (PI.f32)) (pow.f32 (PI.f32) #s(literal 5/2 binary32)))
(*.f32 (PI.f32) (pow.f32 (*.f32 (cbrt.f32 (PI.f32)) (PI.f32)) #s(literal 3/2 binary32)))
(*.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))
(sqrt.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)))
(pow.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal 1/2 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal 3/2 binary32))
(pow.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal 2 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 2 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)) #s(literal 1 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal 6 binary32))
(pow.f32 (cbrt.f32 (PI.f32)) #s(literal 9 binary32))
(pow.f32 (PI.f32) #s(literal 3 binary32))
(+.f32 (cosh.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 3 binary32))) (sinh.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 3 binary32))))
(exp.f32 (*.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal 3/2 binary32)))
(exp.f32 (*.f32 (/.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 3 binary32)) #s(literal 2 binary32)) #s(literal 2 binary32)))
(exp.f32 (*.f32 (*.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 3 binary32)) #s(literal 1/2 binary32)) #s(literal 2 binary32)))
(exp.f32 (*.f32 (*.f32 (log.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32)) #s(literal 2 binary32)))
(exp.f32 (*.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 3/2 binary32)) #s(literal 2 binary32)))
(exp.f32 (*.f32 (/.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 3 binary32)) #s(literal 3 binary32)) #s(literal 3 binary32)))
(exp.f32 (*.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 1 binary32)) #s(literal 3 binary32)))
(exp.f32 (*.f32 (log.f32 (pow.f32 (PI.f32) #s(literal 6 binary32))) #s(literal 1/2 binary32)))
(exp.f32 (*.f32 (log.f32 (*.f32 (PI.f32) (PI.f32))) #s(literal 3/2 binary32)))
(exp.f32 (*.f32 (log.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal 2 binary32)))
(exp.f32 (*.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 3 binary32)) #s(literal 1 binary32)))
(exp.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 3 binary32)))

eval296.0ms (2.7%)

Memory
-10.4MiB live, 553.7MiB allocated; 79ms collecting garbage
Compiler

Compiled 98 162 to 9 724 computations (90.1% saved)

prune66.0ms (0.6%)

Memory
0.2MiB live, 152.5MiB allocated; 23ms collecting garbage
Pruning

31 alts after pruning (26 fresh and 5 done)

PrunedKeptTotal
New1 612161 628
Fresh91019
Picked235
Done022
Total1 623311 654
Accuracy
100.0%
Counts
1 654 → 31
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.6%
(pow.f32 (pow.f32 #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
98.2%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.7%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
96.5%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
97.4%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
96.9%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
95.7%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
92.1%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
33.8%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))))))
10.8%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
98.2%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 c #s(literal 1 binary32)))))
97.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
96.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
96.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
97.3%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
96.7%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
92.3%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
53.0%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c)) (/.f32 #s(literal 1 binary32) c)) c c))))
96.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
54.1%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))) cosTheta))))
54.3%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
54.5%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
97.1%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
33.6%
(*.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)) #s(literal 3/2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (fma.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta) (-.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
97.4%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (/.f32 (*.f32 (-.f32 (pow.f32 (*.f32 (-.f32 (*.f32 (fma.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) #s(literal 2 binary32)) (PI.f32)) cosTheta) (-.f32 (*.f32 (-.f32 (*.f32 (fma.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) (sqrt.f32 (PI.f32)))))
96.8%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32))) cosTheta))
97.4%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (*.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
96.3%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
92.6%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)) cosTheta))
93.0%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
5.1%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
Compiler

Compiled 3 064 to 1 927 computations (37.1% saved)

simplify163.0ms (1.5%)

Memory
0.6MiB live, 234.3MiB allocated; 23ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f32 #s(literal 1 binary32) c)
cost-diff0
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff0
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff1
(*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
cost-diff0
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))))
cost-diff0
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
cost-diff1
(fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))
cost-diff2
(*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))
cost-diff0
(fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
cost-diff0
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
cost-diff0
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
cost-diff1
(/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
cost-diff0
#s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
cost-diff0
(/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
cost-diff0
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
cost-diff0
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
cost-diff0
(+.f32 #s(literal 1 binary32) c)
cost-diff0
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff0
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff1
(*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
073909
0116909
1208886
2592882
32164861
47852861
08890837
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
c
(*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
(/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
#s(literal -2 binary32)
cosTheta
(PI.f32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(literal 1 binary32)
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
#s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
cosTheta
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(literal 1 binary32)
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
#s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))
#s(literal -3/2 binary32)
cosTheta
#s(literal -1 binary32)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
#s(literal 1 binary32)
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))))
#s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))
(*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))
(neg.f32 cosTheta)
cosTheta
(fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))
#s(literal 3/2 binary32)
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))
(+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c)
(-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))
#s(literal -1 binary32)
(/.f32 #s(literal -1 binary32) cosTheta)
c
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
c
(*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta))
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(+.f32 #s(literal 1 binary32) c)
(+.f32 c #s(literal 1 binary32))
c
(*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))
(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
#s(literal -2 binary32)
cosTheta
(PI.f32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(literal 1 binary32)
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
#s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
cosTheta
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32))))))
#s(literal 1 binary32)
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)))))
(/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32))))
(fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
#s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
#s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))
(fma.f32 (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))
#s(literal -3/2 binary32)
cosTheta
#s(literal -1 binary32)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32))))))
#s(literal 1 binary32)
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)))))
#s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))
#s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32))))
(*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))
(fma.f32 (fma.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)))
(neg.f32 cosTheta)
cosTheta
(fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 3/2 binary32) (/.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (neg.f32 cosTheta))) (/.f32 (+.f32 c #s(literal 1 binary32)) (neg.f32 cosTheta)))
#s(literal 3/2 binary32)
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))
(/.f32 (fma.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal 1 binary32))) (neg.f32 cosTheta))
(+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32))
(fma.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c)
(fma.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)
(-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))
#s(literal -1 binary32)
(/.f32 #s(literal -1 binary32) cosTheta)
c
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (+.f32 c #s(literal 1 binary32))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (+.f32 c #s(literal 1 binary32)))
(+.f32 #s(literal 1 binary32) c)
(+.f32 c #s(literal 1 binary32))
c
(*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))
(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta))
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(sqrt.f32 (PI.f32))
(PI.f32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)

localize155.0ms (1.4%)

Memory
-3.6MiB live, 186.2MiB allocated; 17ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.3125
(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy0.3203125
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy0.3359375
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
accuracy0.8065082716096037
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta))
accuracy0.4151686205919121
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))))
accuracy0.6182213379159782
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c)
accuracy1.0
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy14.093483774793519
(*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))
accuracy0.5390625
(/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy0.958669846154463
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))
accuracy1.0
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy2.687466560202889
#s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
accuracy0.4151686205919121
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
accuracy0.5390625
(/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy1.0
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy1.8782175192203512
#s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
accuracy0.078125
(/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))
accuracy0.3203125
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy0.55078125
(/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)
accuracy0.7890625
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
Samples
98.0ms256×0valid
Compiler

Compiled 627 to 51 computations (91.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 74.0ms
ival-div: 29.0ms (39.3% of total)
ival-mult: 16.0ms (21.7% of total)
ival-add: 14.0ms (19% of total)
ival-sqrt: 6.0ms (8.1% of total)
ival-sub: 4.0ms (5.4% of total)
ival-exp: 2.0ms (2.7% of total)
ival-pi: 1.0ms (1.4% of total)
exact: 1.0ms (1.4% of total)
ival-neg: 1.0ms (1.4% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series55.0ms (0.5%)

Memory
23.9MiB live, 70.8MiB allocated; 3ms collecting garbage
Counts
29 → 160
Calls
Call 1
Inputs
(*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
#s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))
(fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))))
(*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)
(/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
#s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c)
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))))
(* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))
(/ (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (pow cosTheta 2))
(/ (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (* 3/2 (* cosTheta (sqrt (/ 1 (PI)))))))) (pow cosTheta 2))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ 1 (PI))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))
(+ 1 (* -1 (sqrt (/ 1 (PI)))))
(+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
1
(+ 1 (* -1 cosTheta))
(+ 1 (* cosTheta (- (* -1/2 cosTheta) 1)))
(+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1)))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(* -3/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(* 3/2 (sqrt (/ 1 (PI))))
(+ (* -1 (/ (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))
(+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))))
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* -2 (/ cosTheta (PI)))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (/ 1 cosTheta))))
(+ c (* -1 (sqrt (/ 1 (PI)))))
(+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* (sqrt cosTheta) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
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(+ 1 c)
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(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))) c)
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c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
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(* c cosTheta)
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Calls

6 calls:

TimeVariablePointExpression
29.0ms
c
@0
((* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (* (neg cosTheta) (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta)))) (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (/ (+ (* -2 cosTheta) 1) (PI)) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))
5.0ms
cosTheta
@inf
((* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (* (neg cosTheta) (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta)))) (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (/ (+ (* -2 cosTheta) 1) (PI)) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))
5.0ms
cosTheta
@-inf
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4.0ms
c
@inf
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4.0ms
c
@-inf
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simplify297.0ms (2.7%)

Memory
-10.3MiB live, 281.2MiB allocated; 34ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07145896
124825643
087015343
Stop Event
iter limit
node limit
Counts
160 → 159
Calls
Call 1
Inputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
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1
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(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
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(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta))))
(+ (* -1 (/ (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* -1 (* (sqrt cosTheta) (* (sqrt -1) (sqrt 2))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
(+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ 1 c)
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) cosTheta)
(+ c (+ (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))) (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(+ c (* -1 (* cosTheta (+ (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))))))
(+ (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))
(+ (* -1 (/ c cosTheta)) (+ (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))))
(+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))
(+ 1 (+ c (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))
(* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))
(+ c (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1)))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)))) c)
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (/ 1 c)))
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c)))))
(* c cosTheta)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))) c))))
(* c (+ 1 (* -1 (/ (* cosTheta (+ (* -1 (+ (* (/ (- (/ 1 cosTheta) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* 3/2 (sqrt (/ 1 (PI)))))) c))))
(* -1 (/ c cosTheta))
(* c (- (+ (* -1 (/ (+ (* (/ (- (/ 1 cosTheta) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 cosTheta)) c)) (* 3/2 (* (/ 1 c) (sqrt (/ 1 (PI)))))) (/ 1 cosTheta)))
(* c (+ 1 (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))))
(* c (+ 1 (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI))))))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (+ (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) c)) 1)))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) c)))))
(* -1 (* c (- (/ (* cosTheta (+ (* -1 (+ (* (/ (- (/ 1 cosTheta) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* 3/2 (sqrt (/ 1 (PI)))))) c) 1)))
(* -1 (* c (+ (* -1 (/ (+ (* -1 (+ (* (/ (- (/ 1 cosTheta) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* 3/2 (sqrt (/ 1 (PI))))) c)) (/ 1 cosTheta))))
(* -1 (* c (- (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))) c)) 1)))
(* -1 (* c (- (* -1 (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI))))) 1)))
Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta)
(* cosTheta (sqrt (PI)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (*.f32 (neg.f32 (sqrt.f32 (PI.f32))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 (*.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 (*.f32 (PI.f32) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta (neg.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
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(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
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(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
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(* -3/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
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(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
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(* 3/2 (sqrt (/ 1 (PI))))
(*.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (/ (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))
(fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 cosTheta)))
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(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(*.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -2 binary32)))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
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(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
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(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
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(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
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(* -2 (/ cosTheta (PI)))
(*.f32 (/.f32 cosTheta (PI.f32)) #s(literal -2 binary32))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta)
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (/ 1 cosTheta))))
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(+ c (* -1 (sqrt (/ 1 (PI)))))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c)
(* (sqrt cosTheta) (sqrt -2))
(*.f32 (sqrt.f32 cosTheta) (sqrt.f32 #s(literal -2 binary32)))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))))
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(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
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(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(-.f32 (*.f32 (*.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (*.f32 (*.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 #s(literal -1 binary32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
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(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(-.f32 (fma.f32 (*.f32 (*.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) (fma.f32 (*.f32 (*.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (*.f32 (*.f32 (*.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (*.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))))) (*.f32 (*.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 #s(literal -1 binary32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 #s(literal -1 binary32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
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(/.f32 (-.f32 (-.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) c) #s(literal 3 binary32))) (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) (neg.f32 (*.f32 c c)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(fma.f32 (+.f32 #s(literal 1 binary32) (*.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))) c #s(literal 1 binary32))
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) c)) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/.f32 (-.f32 (+.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) (*.f32 c c)) #s(literal 1 binary32)) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/.f32 (-.f32 (-.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) c) #s(literal 3 binary32))) (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) (neg.f32 (*.f32 c c)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(fma.f32 (+.f32 #s(literal 1 binary32) (*.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))) c #s(literal 1 binary32))
(* c (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c)))))
(+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c))) c #s(literal 1 binary32)) c)
(* c cosTheta)
(*.f32 c cosTheta)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))) c))))
(*.f32 (+.f32 (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) cosTheta) c)
(* c (+ 1 (* -1 (/ (* cosTheta (+ (* -1 (+ (* (/ (- (/ 1 cosTheta) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* 3/2 (sqrt (/ 1 (PI)))))) c))))
(fma.f32 (/.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta)))) c) c c)
(* -1 (/ c cosTheta))
(/.f32 (neg.f32 c) cosTheta)
(* c (- (+ (* -1 (/ (+ (* (/ (- (/ 1 cosTheta) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 cosTheta)) c)) (* 3/2 (* (/ 1 c) (sqrt (/ 1 (PI)))))) (/ 1 cosTheta)))
(*.f32 (-.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal 3/2 binary32) (/.f32 (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta)) c)) (/.f32 #s(literal 1 binary32) cosTheta)) c)
(* c (+ 1 (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))))
(fma.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) c) c c)
(* c (+ 1 (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI))))))
(fma.f32 (*.f32 c (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) c)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (-.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) c) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal 1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32))) (neg.f32 c)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal 1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (-.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) c) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal 1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32))) (neg.f32 c)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal 1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (* c (- (* -1 (/ (+ 1 (+ (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) c)) 1)))
(*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) c)))))
(*.f32 (neg.f32 c) (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c)))
(* -1 (* c (- (/ (* cosTheta (+ (* -1 (+ (* (/ (- (/ 1 cosTheta) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* 3/2 (sqrt (/ 1 (PI)))))) c) 1)))
(*.f32 (neg.f32 c) (-.f32 (/.f32 (*.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta))) cosTheta) c) #s(literal 1 binary32)))
(* -1 (* c (+ (* -1 (/ (+ (* -1 (+ (* (/ (- (/ 1 cosTheta) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* 3/2 (sqrt (/ 1 (PI))))) c)) (/ 1 cosTheta))))
(*.f32 (neg.f32 c) (fma.f32 (/.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta))) c) #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))) c)) 1)))
(*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (* c (- (* -1 (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI))))) 1)))
(*.f32 (neg.f32 c) (-.f32 (/.f32 (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) #s(literal 1 binary32)))

rewrite250.0ms (2.2%)

Memory
-1.2MiB live, 277.6MiB allocated; 26ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
073744
0116744
1451675
23841675
08237659
Stop Event
iter limit
node limit
iter limit
Counts
29 → 442
Calls
Call 1
Inputs
(*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
#s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))
(fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta))))))
(*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)
(/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
#s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c)
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
Outputs
(*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (PI.f32))))
(*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))
(*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))
(*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta))
(/.f32 (/.f32 (*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (*.f32 (neg.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (neg.f32 cosTheta))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (sqrt.f32 (PI.f32)))
(/.f32 (*.f32 (neg.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)))
(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))) (neg.f32 cosTheta))
(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32)))
(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))))) (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)))
(/.f32 (neg.f32 (*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))) (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)))
(/.f32 (neg.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))) (neg.f32 cosTheta))
(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) cosTheta)
(/.f32 (*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(fma.f32 (cosh.f32 (*.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (*.f32 (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (cosh.f32 (*.f32 cosTheta cosTheta)) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 (*.f32 (cosh.f32 (*.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) (*.f32 (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
(+.f32 (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (cosh.f32 (*.f32 cosTheta cosTheta))) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(*.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))))
(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (fma.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) (-.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
(*.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)))
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))))
(pow.f32 (exp.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) c))) #s(literal -1 binary32))
(pow.f32 (*.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))) #s(literal -1/2 binary32))
(pow.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (neg.f32 (neg.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))))) #s(literal -1 binary32))
(pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
(+.f32 (cosh.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) c)) #s(literal -1 binary32))) (sinh.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) c)) #s(literal -1 binary32))))
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
(neg.f32 (/.f32 #s(literal -1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 (-.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) #s(literal 2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))) (-.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) c) #s(literal 2 binary32))) (-.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) c)))
(/.f32 (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (neg.f32 cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) #s(literal 3 binary32))) (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (+.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) #s(literal 2 binary32)) (*.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (neg.f32 cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))))))
(/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) c) #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) c) #s(literal 2 binary32)) (*.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) c)))))
(/.f32 (neg.f32 (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) (neg.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))))
(/.f32 (neg.f32 (+.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (neg.f32 (fma.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) (-.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)))))
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (-.f32 c #s(literal 1 binary32)) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 (*.f32 c c) #s(literal 1 binary32)))) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 c #s(literal 1 binary32))))
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (-.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 c c)))) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c)))
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (-.f32 (fma.f32 c c #s(literal 1 binary32)) c) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)))) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 (fma.f32 c c #s(literal 1 binary32)) c)))
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)))) (*.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (fma.f32 (-.f32 (*.f32 c c) #s(literal 1 binary32)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (-.f32 c #s(literal 1 binary32)) (*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))))) (*.f32 (-.f32 c #s(literal 1 binary32)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
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(-.f32 c (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))))
(fma.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)) c)
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c)
(fma.f32 c #s(literal 1 binary32) (*.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
(fma.f32 #s(literal 1 binary32) c (*.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
(+.f32 (/.f32 (*.f32 (pow.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 3 binary32)) (pow.f32 (PI.f32) #s(literal -3/2 binary32))) (fma.f32 c (-.f32 c (*.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) (*.f32 (pow.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (pow.f32 c #s(literal 3 binary32)) (fma.f32 c (-.f32 c (*.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) (*.f32 (pow.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))
(+.f32 (*.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) c)
(+.f32 c (*.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 (neg.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (neg.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)))) (neg.f32 (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta))))
(/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (neg.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)))
(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(neg.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta))))

eval113.0ms (1%)

Memory
-7.7MiB live, 221.5MiB allocated; 36ms collecting garbage
Compiler

Compiled 45 162 to 4 093 computations (90.9% saved)

prune83.0ms (0.7%)

Memory
47.7MiB live, 171.6MiB allocated; 37ms collecting garbage
Pruning

34 alts after pruning (27 fresh and 7 done)

PrunedKeptTotal
New75515770
Fresh91221
Picked235
Done145
Total76734801
Accuracy
100.0%
Counts
801 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.6%
(pow.f32 (pow.f32 #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
98.2%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.7%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
96.9%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
95.7%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
92.1%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
97.4%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
33.8%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))))))
10.8%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
98.2%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 #s(literal 1 binary32) c))))
95.7%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
97.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
97.3%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
96.7%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
96.7%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
92.3%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
96.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
53.0%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c))) c #s(literal 1 binary32)) c))))
54.1%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))) cosTheta))))
54.3%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) (/.f32 (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
54.1%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 cosTheta)))))))))
54.0%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta))))))))
49.6%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
52.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (neg.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (*.f32 cosTheta cosTheta)))))))
54.5%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
97.1%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
33.6%
(*.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)) #s(literal 3/2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (fma.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta) (-.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
96.3%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
97.4%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (/.f32 (*.f32 (-.f32 (pow.f32 (*.f32 (-.f32 (*.f32 (fma.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) #s(literal 2 binary32)) (PI.f32)) cosTheta) (-.f32 (*.f32 (-.f32 (*.f32 (fma.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) (sqrt.f32 (PI.f32)))))
96.8%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32))) cosTheta))
97.4%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (*.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
92.6%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)) cosTheta))
93.0%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
5.1%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
Compiler

Compiled 5 346 to 1 719 computations (67.8% saved)

regimes188.0ms (1.7%)

Memory
2.9MiB live, 353.7MiB allocated; 88ms collecting garbage
Counts
67 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (neg.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (*.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c))) c #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c)) (/.f32 #s(literal 1 binary32) c)) c c))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) (/.f32 (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 cosTheta)))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 #s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 #s(literal 1 binary32) c))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (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) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (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) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (-.f32 (*.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta) cosTheta (/.f32 cosTheta (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (*.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (-.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (PI.f32))) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 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 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (*.f32 (*.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32))) cosTheta))
(pow.f32 (pow.f32 #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
(pow.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (exp.f32 #s(literal -1 binary32)) (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (/.f32 (*.f32 (-.f32 (pow.f32 (*.f32 (-.f32 (*.f32 (fma.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) #s(literal 2 binary32)) (PI.f32)) cosTheta) (-.f32 (*.f32 (-.f32 (*.f32 (fma.f32 (pow.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) (sqrt.f32 (PI.f32)))))
(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (fma.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (-.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
(*.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)) #s(literal 3/2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (fma.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta) (-.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
Calls

6 calls:

79.0ms
c
36.0ms
(+.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))))
22.0ms
cosTheta
17.0ms
(*.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)))
16.0ms
(/.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)))))
Results
AccuracySegmentsBranch
98.7%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)))
98.7%1(+.f32 #s(literal 1 binary32) c)
98.7%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))))
98.7%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)))))
98.7%1cosTheta
98.7%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes84.0ms (0.8%)

Memory
-18.8MiB live, 218.1MiB allocated; 20ms collecting garbage
Counts
48 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (neg.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (*.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c))) c #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c)) (/.f32 #s(literal 1 binary32) c)) c c))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) (/.f32 (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 cosTheta)))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 #s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 #s(literal 1 binary32) c))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
Calls

6 calls:

15.0ms
(/.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)))))
15.0ms
(*.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)))
13.0ms
cosTheta
13.0ms
(+.f32 #s(literal 1 binary32) c)
12.0ms
c
Results
AccuracySegmentsBranch
98.2%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)))
98.2%1(+.f32 #s(literal 1 binary32) c)
98.2%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))))
98.2%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)))))
98.2%1cosTheta
98.2%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes88.0ms (0.8%)

Memory
25.5MiB live, 202.4MiB allocated; 26ms collecting garbage
Counts
46 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (neg.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (*.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c))) c #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c)) (/.f32 #s(literal 1 binary32) c)) c c))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) (/.f32 (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 cosTheta)))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 #s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 #s(literal 1 binary32) c))))
Outputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 c #s(literal 1 binary32)))))
Calls

6 calls:

24.0ms
(*.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)))
15.0ms
(+.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))))
13.0ms
c
13.0ms
(/.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)))))
11.0ms
cosTheta
Results
AccuracySegmentsBranch
98.2%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)))
98.2%1(+.f32 #s(literal 1 binary32) c)
98.2%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))))
98.2%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)))))
98.2%1cosTheta
98.2%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes150.0ms (1.3%)

Memory
-4.0MiB live, 142.9MiB allocated; 125ms collecting garbage
Counts
44 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (neg.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (*.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c))) c #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c)) (/.f32 #s(literal 1 binary32) c)) c c))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) (/.f32 (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 cosTheta)))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 #s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
Outputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
Calls

6 calls:

78.0ms
c
26.0ms
cosTheta
11.0ms
(+.f32 #s(literal 1 binary32) c)
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)))
10.0ms
(/.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)))))
Results
AccuracySegmentsBranch
97.9%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)))
97.9%1(+.f32 #s(literal 1 binary32) c)
97.9%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))))
97.9%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)))))
97.9%1cosTheta
97.9%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes85.0ms (0.8%)

Memory
14.7MiB live, 110.5MiB allocated; 29ms collecting garbage
Counts
42 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (neg.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (*.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c))) c #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c)) (/.f32 #s(literal 1 binary32) c)) c c))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) (/.f32 (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)) #s(literal 1 binary32)) (neg.f32 cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 cosTheta)))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 #s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
Calls

6 calls:

30.0ms
(+.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))))
13.0ms
c
10.0ms
(/.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)))))
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)))
10.0ms
cosTheta
Results
AccuracySegmentsBranch
97.4%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)))
97.4%1(+.f32 #s(literal 1 binary32) c)
97.4%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))))
97.4%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)))))
97.4%1cosTheta
97.4%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes54.0ms (0.5%)

Memory
-12.5MiB live, 77.4MiB allocated; 17ms collecting garbage
Counts
28 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (neg.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (*.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c))) c #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1 binary32)) (neg.f32 cosTheta))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c)) (/.f32 #s(literal 1 binary32) c)) c c))))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
Calls

6 calls:

11.0ms
(+.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))))
8.0ms
c
7.0ms
(*.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)))
7.0ms
cosTheta
7.0ms
(/.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)))))
Results
AccuracySegmentsBranch
96.9%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)))
96.9%1(+.f32 #s(literal 1 binary32) c)
96.9%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))))
96.9%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)))))
96.9%1cosTheta
96.9%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes41.0ms (0.4%)

Memory
19.4MiB live, 63.2MiB allocated; 9ms collecting garbage
Counts
23 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (neg.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (*.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
Outputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
Calls

6 calls:

10.0ms
cosTheta
6.0ms
c
6.0ms
(/.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)))))
6.0ms
(+.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))))
6.0ms
(*.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)))
Results
AccuracySegmentsBranch
96.9%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)))
96.9%1(+.f32 #s(literal 1 binary32) c)
96.9%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))))
96.9%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)))))
96.9%1cosTheta
96.9%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes50.0ms (0.4%)

Memory
-29.9MiB live, 64.4MiB allocated; 26ms collecting garbage
Counts
22 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (neg.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (*.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
Outputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
Calls

6 calls:

15.0ms
c
11.0ms
(*.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)))
6.0ms
(+.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))))
6.0ms
(/.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)))))
6.0ms
cosTheta
Results
AccuracySegmentsBranch
96.9%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)))
96.9%1(+.f32 #s(literal 1 binary32) c)
96.9%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))))
96.9%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)))))
96.9%1cosTheta
96.9%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes710.0ms (6.4%)

Memory
-198.7MiB live, 91.8MiB allocated; 1.1s collecting garbage
Counts
21 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (neg.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (*.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
Outputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
Calls

6 calls:

673.0ms
(/.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)))))
14.0ms
(*.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)))
6.0ms
c
6.0ms
(+.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))))
5.0ms
cosTheta
Results
AccuracySegmentsBranch
96.9%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)))
96.9%1(+.f32 #s(literal 1 binary32) c)
96.9%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))))
96.9%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)))))
96.9%1cosTheta
96.9%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes31.0ms (0.3%)

Memory
35.5MiB live, 83.1MiB allocated; 6ms collecting garbage
Counts
15 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
Outputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
Calls

6 calls:

8.0ms
(+.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))))
4.0ms
c
4.0ms
(*.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)))
4.0ms
(/.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)))))
4.0ms
cosTheta
Results
AccuracySegmentsBranch
96.9%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)))
96.9%1(+.f32 #s(literal 1 binary32) c)
96.9%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))))
96.9%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)))))
96.9%1cosTheta
96.9%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes28.0ms (0.3%)

Memory
-3.5MiB live, 89.9MiB allocated; 6ms collecting garbage
Counts
14 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (+ (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* -3/2 (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) #s(approx (+ (* 3/2 (sqrt (/ 1 (PI)))) (/ (+ (+ (* (sqrt (/ 1 (PI))) (- -1 (/ -1 cosTheta))) c) 1) (neg cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (neg.f32 cosTheta) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 c cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)))
Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
Calls

6 calls:

6.0ms
c
5.0ms
(+.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))))
4.0ms
(*.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)))
4.0ms
(/.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)))))
4.0ms
cosTheta
Results
AccuracySegmentsBranch
96.3%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)))
96.3%1(+.f32 #s(literal 1 binary32) c)
96.3%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))))
96.3%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)))))
96.3%1cosTheta
96.3%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes16.0ms (0.1%)

Memory
8.5MiB live, 54.2MiB allocated; 3ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
Calls

6 calls:

4.0ms
cosTheta
2.0ms
c
2.0ms
(*.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)))
2.0ms
(+.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))))
2.0ms
(/.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)))))
Results
AccuracySegmentsBranch
93.0%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)))
93.0%1(+.f32 #s(literal 1 binary32) c)
93.0%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))))
93.0%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)))))
93.0%1cosTheta
93.0%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes15.0ms (0.1%)

Memory
-27.3MiB live, 22.2MiB allocated; 13ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
Calls

6 calls:

10.0ms
(+.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))))
1.0ms
(*.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)))
1.0ms
(/.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)))))
1.0ms
c
1.0ms
cosTheta
Results
AccuracySegmentsBranch
5.1%1(+.f32 #s(literal 1 binary32) c)
5.1%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)))))
5.1%1cosTheta
5.1%1c
5.1%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)))
5.1%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))))
Compiler

Compiled 72 to 58 computations (19.4% saved)

simplify56.0ms (0.5%)

Memory
12.2MiB live, 58.2MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0119535
1204529
2471518
31474514
45670514
Stop Event
node limit
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 c #s(literal 1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ c 1)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))

derivations1.1s (9.6%)

Memory
23.9MiB live, 987.2MiB allocated; 233ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07716809
127306520
084916245
074554
0129544
1491477
24158467
08161467
07145896
124825643
087015343
07838097
127697792
090937369
03782856
112202772
256352702
085182591
01866
03366
113359
297756
0836255
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 535 to 122 computations (77.2% saved)

preprocess48.0ms (0.4%)

Memory
32.8MiB live, 77.5MiB allocated; 6ms collecting garbage
Compiler

Compiled 1 120 to 280 computations (75% saved)

end0.0ms (0%)

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

Profiling

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