Beckmann Sample, normalization factor

Time bar (total: 4.8s)

start0.0ms (0%)

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

analyze17.0ms (0.4%)

Memory
30.1MiB live, 30.1MiB allocated; 0ms collecting garbage
Algorithm
1×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)

sample1.7s (34.4%)

Memory
-68.9MiB live, 2 151.8MiB allocated; 1.2s collecting garbage
Samples
775.0ms8 255×0valid
5.0ms61×0invalid
0.0ms1×1valid
Precisions
Click to see histograms. Total time spent on operations: 502.0ms
ival-mult!: 143.0ms (28.5% of total)
ival-div!: 82.0ms (16.4% of total)
ival-sqrt: 68.0ms (13.6% of total)
ival-exp: 66.0ms (13.2% of total)
ival-sub!: 54.0ms (10.8% of total)
ival-add!: 45.0ms (9% of total)
ival-neg: 41.0ms (8.2% of total)
adjust: 2.0ms (0.4% of total)
ival-pi: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-and: 0.0ms (0% of total)
ival-<: 0.0ms (0% of total)
Bogosity

explain218.0ms (4.5%)

Memory
-1.8MiB live, 376.2MiB allocated; 54ms 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
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
54.0ms512×0valid
Compiler

Compiled 281 to 58 computations (79.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 31.0ms
ival-mult!: 8.0ms (26.1% of total)
ival-neg: 5.0ms (16.3% of total)
ival-div!: 5.0ms (16.3% of total)
ival-exp: 4.0ms (13.1% of total)
ival-sqrt: 4.0ms (13.1% of total)
ival-add!: 3.0ms (9.8% of total)
ival-sub!: 2.0ms (6.5% of total)
adjust: 0.0ms (0% of total)

preprocess26.0ms (0.5%)

Memory
-22.9MiB live, 23.4MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
046158
1144142
2491134
32194132
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.1%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
Compiler

Compiled 50 to 36 computations (28% saved)

series34.0ms (0.7%)

Memory
14.2MiB live, 60.2MiB allocated; 2ms collecting garbage
Counts
18 → 111
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
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* -1 cosTheta)) cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 1))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* -1 cosTheta))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1)))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1)))))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 1))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (+ 1 (* -2 cosTheta))))
#s(approx (- 1 cosTheta) #s(hole binary32 1))
#s(approx (- 1 cosTheta) #s(hole binary32 (+ 1 (* -1 cosTheta))))
#s(approx cosTheta #s(hole binary32 cosTheta))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 1))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1)))))
#s(approx (* (neg cosTheta) cosTheta) #s(hole binary32 (* -1 (pow cosTheta 2))))
#s(approx (neg cosTheta) #s(hole binary32 (* -1 cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (- (+ (* -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))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (- (+ (* -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))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 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))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 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)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole 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))))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (+ (* 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))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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)))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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))))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (+ (* -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))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (+ (* -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)))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (* (sqrt (/ 1 cosTheta)) (sqrt -2))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -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))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -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)))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* (sqrt cosTheta) (sqrt -2))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* 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)))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* 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))))))))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (* -2 cosTheta)))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (* cosTheta (- (/ 1 cosTheta) 2))))
#s(approx (- 1 cosTheta) #s(hole binary32 (* -1 cosTheta)))
#s(approx (- 1 cosTheta) #s(hole binary32 (* cosTheta (- (/ 1 cosTheta) 1))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (exp (* -1 (pow cosTheta 2)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (+ (* 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)))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (- (+ (* -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))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (- (+ (* -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)))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 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)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 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))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 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)))) (+ (* -1/16 (* (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)))))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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)))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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)))) (+ (* -1/16 (* (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)))))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole 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))))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole 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)))))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3))))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -1 (* (sqrt cosTheta) (* (sqrt -1) (sqrt 2))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -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)))))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -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))))))))))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))))
#s(approx (- 1 cosTheta) #s(hole binary32 (* -1 (* cosTheta (- 1 (/ 1 cosTheta))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (+ 1 c) #s(hole binary32 1))
#s(approx (+ 1 c) #s(hole binary32 (+ 1 c)))
#s(approx c #s(hole binary32 c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 c))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ 1 c) #s(hole binary32 c))
#s(approx (+ 1 c) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
10.0ms
cosTheta
@-inf
((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))
9.0ms
cosTheta
@inf
((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))
5.0ms
c
@0
((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))
3.0ms
cosTheta
@0
((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))
2.0ms
c
@-inf
((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))

rewrite139.0ms (2.9%)

Memory
31.9MiB live, 218.5MiB allocated; 12ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06346295
06575601
037835289
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
129 → 177
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)
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#s(approx cosTheta #s(hole binary32 cosTheta))
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#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 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))))))))
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#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (+ (* -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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#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (* cosTheta (- (/ 1 cosTheta) 2))))
#s(approx (- 1 cosTheta) #s(hole binary32 (* -1 cosTheta)))
#s(approx (- 1 cosTheta) #s(hole binary32 (* cosTheta (- (/ 1 cosTheta) 1))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (exp (* -1 (pow cosTheta 2)))))
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#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (- (+ (* -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)))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 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)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 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))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 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)))) (+ (* -1/16 (* (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)))))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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)))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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)))) (+ (* -1/16 (* (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)))))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole 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))))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole 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)))))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3))))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -1 (* (sqrt cosTheta) (* (sqrt -1) (sqrt 2))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -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)))))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -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))))))))))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))))
#s(approx (- 1 cosTheta) #s(hole binary32 (* -1 (* cosTheta (- 1 (/ 1 cosTheta))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (+ 1 c) #s(hole binary32 1))
#s(approx (+ 1 c) #s(hole binary32 (+ 1 c)))
#s(approx c #s(hole binary32 c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 c))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ 1 c) #s(hole binary32 c))
#s(approx (+ 1 c) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))))
Outputs
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))))
(pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(literal 1 binary32)
(-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (neg.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))) (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))))) (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)))))
(/.f32 (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))) #s(literal 3 binary32))) (fma.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32)) (-.f32 (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)))) (*.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)))))))
(fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (+.f32 c #s(literal 1 binary32)))
(fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(+.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))) (+.f32 c #s(literal 1 binary32)))
(+.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))))
(+.f32 #s(literal 1 binary32) (+.f32 c (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)))))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 c c)) (-.f32 #s(literal 1 binary32) c))
(/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 c #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 c c) (*.f32 #s(literal 1 binary32) c))))
(+.f32 c #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) c)
c
(*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32)))
(/.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) cosTheta)
(/.f32 (*.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal -1 binary32) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(pow.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))
(sqrt.f32 (PI.f32))
(pow.f32 (PI.f32) #s(literal 1/2 binary32))
(PI.f32)
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(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)
(sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))
(pow.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) #s(literal 1/2 binary32))
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cosTheta
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(pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta)
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(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
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(neg.f32 cosTheta)
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#s(approx (- (- 1 cosTheta) cosTheta) #s(literal 1 binary32))
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#s(approx (- 1 cosTheta) #s(literal 1 binary32))
#s(approx (- 1 cosTheta) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)))
#s(approx cosTheta cosTheta)
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#s(approx (neg cosTheta) (neg.f32 cosTheta))
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#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.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))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (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 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32))) #s(literal -1 binary32) (/.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)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (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 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (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 (/.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)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (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 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 4 binary32))) #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 (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))) 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 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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) #s(literal 1 binary32)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.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) c) #s(literal 1 binary32)))
#s(approx (+ 1 c) #s(literal 1 binary32))
#s(approx (+ 1 c) (+.f32 c #s(literal 1 binary32)))
#s(approx c c)
#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 (fma.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 -1 binary32) #s(literal 1 binary32)) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.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 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 (-.f32 (fma.f32 (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)) #s(literal -1 binary32) #s(literal 1 binary32)) (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)) (*.f32 c c)) #s(literal -1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)))) c))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c)
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c))
#s(approx (+ 1 c) c)
#s(approx (+ 1 c) (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32)) c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (-.f32 (neg.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))) c)) #s(literal 1 binary32)) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (-.f32 (neg.f32 (/.f32 (-.f32 (neg.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))) 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))) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (neg.f32 (*.f32 (-.f32 (neg.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 1 binary32)) c)))

eval27.0ms (0.6%)

Memory
-2.7MiB live, 73.2MiB allocated; 9ms collecting garbage
Compiler

Compiled 8 043 to 1 125 computations (86% saved)

prune15.0ms (0.3%)

Memory
-10.3MiB live, 33.2MiB allocated; 4ms collecting garbage
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New15014164
Fresh000
Picked101
Done000
Total15114165
Accuracy
99.4%
Counts
165 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
30.1%
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))) #s(literal 3 binary32))) (fma.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32)) (-.f32 (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)))) (*.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))))))))
▶98.4%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶95.4%
(/.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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
▶92.2%
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
97.9%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (*.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%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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) #s(literal 1 binary32))))
98.2%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.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) c) #s(literal 1 binary32))))
92.4%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
▶55.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c)))
▶4.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
97.7%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (*.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32))))) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32))) (fma.f32 (*.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32) (neg.f32 (*.f32 (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32))) (pow.f32 (PI.f32) #s(literal 3/2 binary32))))))) (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) cosTheta (*.f32 (neg.f32 (PI.f32)) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
97.1%
#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) (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
96.0%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
93.2%
#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 1 408 to 800 computations (43.2% saved)

series175.0ms (3.6%)

Memory
71.9MiB live, 171.8MiB allocated; 81ms collecting garbage
Counts
41 → 253
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) 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 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
c
(*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32)))
(*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)
(sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
#s(literal -2 binary32)
cosTheta
(sqrt.f32 (PI.f32))
(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) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) cosTheta)
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(/.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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))
(/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)
(fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c))
(*.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c)
(+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32))
(fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c))
(/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c))
(*.f32 cosTheta c)
(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))
(/.f32 #s(literal 1 binary32) c)
Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)))
#s(approx (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (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)))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (/ (+ 1 (* -1 cosTheta)) cosTheta)))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (/ (+ 1 (* -1 cosTheta)) cosTheta)))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 1))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 (+ 1 (* -1 cosTheta))))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1)))))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1)))))
#s(approx (+ (* -2 cosTheta) 1) #s(hole binary32 1))
#s(approx (+ (* -2 cosTheta) 1) #s(hole binary32 (+ 1 (* -2 cosTheta))))
#s(approx cosTheta #s(hole binary32 cosTheta))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 1))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1)))))
#s(approx (* (neg cosTheta) cosTheta) #s(hole binary32 (* -1 (pow cosTheta 2))))
#s(approx (neg cosTheta) #s(hole binary32 (* -1 cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (/ 1 cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ 1 cosTheta) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) #s(hole binary32 (sqrt (/ 1 (PI)))))
#s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* c (* cosTheta (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c)))))) cosTheta)))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* c (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI)))))))) (* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))))) cosTheta)))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c)))) (* cosTheta (+ (* c (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))) (* c (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))))) cosTheta)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (/ (+ (* cosTheta (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c)))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (/ (+ (* cosTheta (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))))) (/ 1 c))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (/ (+ (* cosTheta (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))))) (/ 1 c))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)))
#s(approx (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) #s(hole binary32 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))))
#s(approx (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) #s(hole binary32 (/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)))
#s(approx (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) #s(hole binary32 (/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))))) (/ 1 c)))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)))
#s(approx (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) #s(hole binary32 (/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))))) (/ 1 c)))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) #s(hole binary32 (/ 1 (* c cosTheta))))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) #s(hole binary32 (/ (+ (* -1 (/ (pow cosTheta 2) c)) (/ 1 c)) cosTheta)))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) #s(hole binary32 (/ (+ (* (pow cosTheta 2) (- (* 1/2 (/ (pow cosTheta 2) c)) (/ 1 c))) (/ 1 c)) cosTheta)))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) #s(hole binary32 (/ (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ (* -1/6 (/ (pow cosTheta 2) c)) (* 1/2 (/ 1 c)))) (/ 1 c))) (/ 1 c)) cosTheta)))
#s(approx (* cosTheta c) #s(hole binary32 (* c cosTheta)))
#s(approx (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) #s(hole binary32 (sqrt (/ 1 (PI)))))
#s(approx (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))))
#s(approx (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
#s(approx (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))))
#s(approx (/ (+ (* -2 cosTheta) 1) (PI)) #s(hole binary32 (/ 1 (PI))))
#s(approx (/ (+ (* -2 cosTheta) 1) (PI)) #s(hole binary32 (+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
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Calls

6 calls:

TimeVariablePointExpression
127.0ms
cosTheta
@-inf
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13.0ms
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8.0ms
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7.0ms
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5.0ms
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rewrite260.0ms (5.4%)

Memory
22.3MiB live, 252.5MiB allocated; 84ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105715982
0112313802
1633613487
0842013069
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
294 → 456
Calls
Call 1
Inputs
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#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ 1 c) #s(hole binary32 1))
#s(approx (+ 1 c) #s(hole binary32 (+ 1 c)))
#s(approx c #s(hole binary32 c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (/ (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)))
#s(approx (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) #s(hole binary32 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)))
#s(approx (/ 1 c) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 c))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ 1 c) #s(hole binary32 c))
#s(approx (+ 1 c) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 c))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 c))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 1))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) (+ 1 (/ 1 c)))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (* -1 (/ (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1) c)))))
#s(approx (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) #s(hole binary32 (* -1 (/ (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1) c))))
Outputs
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))))
(pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
(exp.f32 (*.f32 (log1p.f32 (+.f32 c (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))) #s(literal -1 binary32)))
#s(literal 1 binary32)
(-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (neg.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))) (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))) (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))))))
(/.f32 (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))) (fma.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32)) (-.f32 (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))))) (*.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))))))))
(fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32)))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (+.f32 c #s(literal 1 binary32)))
(fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(+.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32)))
(+.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))
(+.f32 #s(literal 1 binary32) (+.f32 c (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))))))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 c c)) (-.f32 #s(literal 1 binary32) c))
(/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 c #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 c c) (*.f32 #s(literal 1 binary32) c))))
(+.f32 c #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) c)
c
(*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(*.f32 #s(literal 1 binary32) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) cosTheta)
(/.f32 (*.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 (neg.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(literal 1 binary32))
(*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta))
(/.f32 (*.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) cosTheta)
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (neg.f32 cosTheta))
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta)
(*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(literal 1 binary32))
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#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (neg.f32 (*.f32 (-.f32 (neg.f32 (/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) c)) #s(literal 1 binary32)) c)))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (neg.f32 (*.f32 (-.f32 (neg.f32 (*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)))) (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32))) c)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (fma.f32 (/.f32 (-.f32 (neg.f32 (*.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))) #s(literal 1 binary32)) c) #s(literal -1 binary32) #s(literal 1 binary32)))
#s(approx (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) (neg.f32 (/.f32 (-.f32 (neg.f32 (*.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))) #s(literal 1 binary32)) c)))

eval54.0ms (1.1%)

Memory
-5.2MiB live, 90.9MiB allocated; 13ms collecting garbage
Compiler

Compiled 24 463 to 2 832 computations (88.4% saved)

prune25.0ms (0.5%)

Memory
0.2MiB live, 46.2MiB allocated; 3ms collecting garbage
Pruning

26 alts after pruning (25 fresh and 1 done)

PrunedKeptTotal
New43424458
Fresh819
Picked415
Done000
Total44626472
Accuracy
99.8%
Counts
472 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.4%
(pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
95.4%
(pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
▶98.4%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
95.2%
(/.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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))) cosTheta))))
92.5%
(/.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 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
92.2%
(/.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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
92.0%
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))))))
84.8%
(/.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))) (*.f32 (exp.f32 (*.f32 (log.f32 cosTheta) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
95.4%
(/.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))) #s(approx (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
92.4%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
95.3%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
92.2%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
97.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))))
95.4%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
93.0%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
98.2%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) c) #s(literal 1 binary32))))
92.4%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
55.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (fma.f32 (pow.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) #s(literal -1 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1 binary32)) (*.f32 (/.f32 cosTheta (PI.f32)) #s(literal -2 binary32)))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c)))
55.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)))) #s(literal 1 binary32)) c)))
▶50.3%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
✓4.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
90.3%
(exp.f32 (*.f32 (log1p.f32 (+.f32 c (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))) #s(literal -1 binary32)))
87.6%
(exp.f32 (*.f32 (log1p.f32 (+.f32 c #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))) #s(literal -1 binary32)))
97.1%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
▶96.0%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
▶93.2%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
Compiler

Compiled 2 029 to 1 430 computations (29.5% saved)

series51.0ms (1.1%)

Memory
-17.9MiB live, 72.5MiB allocated; 7ms collecting garbage
Counts
39 → 297
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32))))
(+.f32 #s(literal 1 binary32) c)
c
(/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta)
(sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
cosTheta
#s(literal -2 binary32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
(sqrt.f32 (PI.f32))
(PI.f32)
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c))
(*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
(*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta)
(/.f32 #s(literal 1 binary32) c)
(pow.f32 (PI.f32) #s(literal -1/2 binary32))
#s(literal -1/2 binary32)
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta)
(fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32)))
(*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))
(+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c)
#s(literal -1 binary32)
(pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
(fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32)))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))
(+.f32 c #s(literal 1 binary32))
Outputs
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (/ (+ (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)))
#s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
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#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 c))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ 1 c) #s(hole binary32 c))
#s(approx (+ 1 c) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 c))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 c))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 1))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* -1 (* c (* (pow cosTheta 2) (PI))))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* c (+ (* -1 (* (pow cosTheta 2) (PI))) (/ (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))) c)))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* -1 (* c (* cosTheta (PI))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* c (+ (* -1 (* cosTheta (PI))) (+ (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)) (* (/ 1 c) (sqrt (PI))))))))
#s(approx (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI)) #s(hole binary32 (* c (PI))))
#s(approx (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI)) #s(hole binary32 (* c (+ (PI) (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))
#s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) #s(hole binary32 c))
#s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) #s(hole binary32 (* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))))
#s(approx (+ (* (pow (PI) -1/2) -1) c) #s(hole binary32 c))
#s(approx (+ (* (pow (PI) -1/2) -1) c) #s(hole binary32 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (/ 1 c)))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (/ (- (+ 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)))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) #s(hole binary32 c))
#s(approx (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ c 1) #s(hole binary32 c))
#s(approx (+ c 1) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) (+ 1 (/ 1 c)))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (* -1 (/ (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1) c)))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* -1 (* c (+ (* -1 (/ (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))) c)) (* (pow cosTheta 2) (PI)))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* -1 (* c (+ (* -1 (/ (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) c)) (* cosTheta (PI)))))))
#s(approx (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI)) #s(hole binary32 (* -1 (* c (+ (* -1 (PI)) (* -1 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))))
#s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))))
#s(approx (+ (* (pow (PI) -1/2) -1) c) #s(hole binary32 (* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (* -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))))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (* -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))))
#s(approx (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
12.0ms
cosTheta
@-inf
((/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+ 1 c) c (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (sqrt (PI)) (PI) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (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)))) (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (* (/ (/ 1 c) cosTheta) (pow (PI) -1/2)) (/ (/ 1 c) cosTheta) (/ 1 c) (pow (PI) -1/2) -1/2 (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI)) (+ (+ (* (pow (PI) -1/2) -1) c) 1) (+ (* (pow (PI) -1/2) -1) c) -1 (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (+ c 1))
7.0ms
cosTheta
@inf
((/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+ 1 c) c (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (sqrt (PI)) (PI) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (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)))) (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (* (/ (/ 1 c) cosTheta) (pow (PI) -1/2)) (/ (/ 1 c) cosTheta) (/ 1 c) (pow (PI) -1/2) -1/2 (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI)) (+ (+ (* (pow (PI) -1/2) -1) c) 1) (+ (* (pow (PI) -1/2) -1) c) -1 (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (+ c 1))
5.0ms
c
@-inf
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5.0ms
cosTheta
@0
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4.0ms
c
@0
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rewrite220.0ms (4.5%)

Memory
9.6MiB live, 242.2MiB allocated; 37ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0116320793
0122418228
1677318228
0803817738
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
336 → 465
Calls
Call 1
Inputs
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c
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cosTheta
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#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 c))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 c))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 1))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* -1 (* c (* (pow cosTheta 2) (PI))))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* c (+ (* -1 (* (pow cosTheta 2) (PI))) (/ (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))) c)))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* -1 (* c (* cosTheta (PI))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* c (+ (* -1 (* cosTheta (PI))) (+ (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)) (* (/ 1 c) (sqrt (PI))))))))
#s(approx (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI)) #s(hole binary32 (* c (PI))))
#s(approx (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI)) #s(hole binary32 (* c (+ (PI) (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))
#s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) #s(hole binary32 c))
#s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) #s(hole binary32 (* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))))
#s(approx (+ (* (pow (PI) -1/2) -1) c) #s(hole binary32 c))
#s(approx (+ (* (pow (PI) -1/2) -1) c) #s(hole binary32 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (/ 1 c)))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (/ (- (+ 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)))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) #s(hole binary32 c))
#s(approx (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ c 1) #s(hole binary32 c))
#s(approx (+ c 1) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) (+ 1 (/ 1 c)))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (* -1 (/ (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1) c)))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* -1 (* c (+ (* -1 (/ (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))) c)) (* (pow cosTheta 2) (PI)))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* -1 (* c (+ (* -1 (/ (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) c)) (* cosTheta (PI)))))))
#s(approx (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI)) #s(hole binary32 (* -1 (* c (+ (* -1 (PI)) (* -1 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))))
#s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))))
#s(approx (+ (* (pow (PI) -1/2) -1) c) #s(hole binary32 (* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (* -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))))
#s(approx (pow (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) -1) #s(hole binary32 (* -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))))
#s(approx (+ (* (exp (* (neg cosTheta) cosTheta)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI)))) (+ c 1)) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
Outputs
(*.f32 (pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 -1/2 binary32)) (pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 -1/2 binary32)))
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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) (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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))))
(pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 (cosh.f32 (*.f32 (log1p.f32 (+.f32 c (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))) #s(literal -1 binary32))) (sinh.f32 (*.f32 (log1p.f32 (+.f32 c (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))) #s(literal -1 binary32))))
(exp.f32 (*.f32 (log1p.f32 (+.f32 c (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))) #s(literal -1 binary32)))
#s(literal 1 binary32)
(-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (neg.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) (*.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32)))) (-.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 (-.f32 (*.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))) (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))) (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))))
(/.f32 (+.f32 (pow.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32))) (fma.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (-.f32 (*.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))) (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal 3 binary32))) (fma.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32)) (-.f32 (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) (*.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))))))
(fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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)))
(fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32)))
(+.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) c) #s(literal 1 binary32))
(+.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(+.f32 #s(literal 1 binary32) (+.f32 c (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 c c)) (-.f32 #s(literal 1 binary32) c))
(/.f32 (-.f32 (*.f32 c c) #s(literal 1 binary32)) (-.f32 c #s(literal 1 binary32)))
(/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 c #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 c c) (*.f32 #s(literal 1 binary32) c))))
(/.f32 (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 c c (-.f32 #s(literal 1 binary32) (*.f32 c #s(literal 1 binary32)))))
(+.f32 c #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) c)
c
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#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (-.f32 (neg.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))) c)) #s(literal 1 binary32)) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (-.f32 (neg.f32 (/.f32 (-.f32 (neg.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))) 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))) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (neg.f32 (*.f32 (-.f32 (neg.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 1 binary32)) c)))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (neg.f32 (*.f32 (-.f32 (neg.f32 (*.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))) c)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (fma.f32 (/.f32 (-.f32 (neg.f32 (*.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 -1 binary32) #s(literal 1 binary32)))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (neg.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) (PI.f32) (neg.f32 (/.f32 (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c))) c)))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (neg.f32 (*.f32 (fma.f32 (PI.f32) cosTheta (neg.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) c))) c)))
#s(approx (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI)) (neg.f32 (*.f32 (*.f32 #s(literal -1 binary32) (fma.f32 (PI.f32) (/.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) c) (PI.f32))) c)))
#s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) (neg.f32 (*.f32 (-.f32 (neg.f32 (/.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (*.f32 (-.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (-.f32 (neg.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))) c)) #s(literal 1 binary32)) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (-.f32 (neg.f32 (/.f32 (-.f32 (neg.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))) 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))) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (neg.f32 (*.f32 (-.f32 (neg.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 1 binary32)) c)))

eval44.0ms (0.9%)

Memory
-4.6MiB live, 86.7MiB allocated; 8ms collecting garbage
Compiler

Compiled 19 388 to 2 184 computations (88.7% saved)

prune28.0ms (0.6%)

Memory
16.6MiB live, 62.6MiB allocated; 3ms collecting garbage
Pruning

35 alts after pruning (32 fresh and 3 done)

PrunedKeptTotal
New37219391
Fresh71320
Picked325
Done011
Total38235417
Accuracy
99.9%
Counts
417 → 35
Alt Table
Click to see full alt table
StatusAccuracyProgram
95.8%
(pow.f32 (fma.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
95.4%
(pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
97.1%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
95.7%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
92.5%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
▶95.2%
(/.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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))) cosTheta))))
92.2%
(/.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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
▶92.0%
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))))))
95.4%
(/.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))) #s(approx (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
▶98.2%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
95.3%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
92.2%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
97.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (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))))
98.2%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+.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) c) #s(literal 1 binary32))))
92.4%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
95.4%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
▶93.0%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
55.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)))) #s(literal 1 binary32)) c)))
▶51.0%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
50.3%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
✓50.3%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
✓4.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
97.8%
(*.f32 (pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 -1/2 binary32)) (pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 -1/2 binary32)))
90.3%
(exp.f32 (*.f32 (log1p.f32 (+.f32 c (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))) #s(literal -1 binary32)))
87.6%
(exp.f32 (*.f32 (log1p.f32 (+.f32 c #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))) #s(literal -1 binary32)))
97.1%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
95.9%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
92.9%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
93.2%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
✓93.2%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
95.4%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (*.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) cosTheta)) cosTheta))
95.3%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (*.f32 (fma.f32 (neg.f32 cosTheta) (PI.f32) (fma.f32 (/.f32 #s(literal 1 binary32) c) (sqrt.f32 (PI.f32)) (/.f32 (*.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32))) c))) c)) cosTheta))
95.8%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (neg.f32 (*.f32 (fma.f32 (PI.f32) cosTheta (neg.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) c))) c))) cosTheta))
95.9%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (*.f32 (fma.f32 (*.f32 (neg.f32 cosTheta) cosTheta) (PI.f32) (/.f32 (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c)) c)))
54.5%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (*.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta))))
Compiler

Compiled 3 007 to 2 054 computations (31.7% saved)

series144.0ms (3%)

Memory
17.9MiB live, 76.2MiB allocated; 128ms collecting garbage
Counts
44 → 208
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
#s(literal 1 binary32)
(+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32))))
#s(approx (+ 1 c) #s(literal 1 binary32))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta)
(sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
cosTheta
#s(literal -2 binary32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c))
(*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))
(/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)
(*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(/.f32 #s(literal 1 binary32) c)
c
(pow.f32 (PI.f32) #s(literal -1/2 binary32))
#s(literal -1/2 binary32)
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32))))))
(+.f32 #s(literal 1 binary32) c)
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))))
(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32))))
(/.f32 #s(literal 1 binary32) cosTheta)
(/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32))
(/.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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))) cosTheta))
(/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))) cosTheta)
(fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
Outputs
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (/ (+ (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)))
#s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)))
#s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ 1 (* -1 cosTheta)) cosTheta)))
#s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta)))
#s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta)))
#s(approx (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) #s(hole binary32 (/ (+ 1 (* -1 cosTheta)) cosTheta)))
#s(approx (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)))
#s(approx (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)))
#s(approx (sqrt (+ (* cosTheta -2) 1)) #s(hole binary32 1))
#s(approx (sqrt (+ (* cosTheta -2) 1)) #s(hole binary32 (+ 1 (* -1 cosTheta))))
#s(approx (sqrt (+ (* cosTheta -2) 1)) #s(hole binary32 (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1)))))
#s(approx (sqrt (+ (* cosTheta -2) 1)) #s(hole binary32 (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1)))))
#s(approx (+ (* cosTheta -2) 1) #s(hole binary32 1))
#s(approx (+ (* cosTheta -2) 1) #s(hole binary32 (+ 1 (* -2 cosTheta))))
#s(approx cosTheta #s(hole binary32 cosTheta))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 1))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1)))))
#s(approx (* (neg cosTheta) cosTheta) #s(hole binary32 (* -1 (pow cosTheta 2))))
#s(approx (neg cosTheta) #s(hole binary32 (* -1 cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (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)))
#s(approx (/ 1 (* (sqrt (PI)) cosTheta)) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (sqrt (PI)) cosTheta) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* c (* cosTheta (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c)))))) cosTheta)))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* c (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI)))))))) (* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))))) cosTheta)))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c)))) (* cosTheta (+ (* c (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))) (* c (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))))) cosTheta)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (/ (+ (* cosTheta (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c)))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (/ (+ (* cosTheta (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))))) (/ 1 c))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (/ (+ (* cosTheta (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))))) (/ 1 c))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)))
#s(approx (/ (* (/ 1 c) (pow (PI) -1/2)) cosTheta) #s(hole binary32 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ 1 cosTheta) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
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#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole 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)))))))))
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#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ 1 c) #s(hole binary32 1))
#s(approx (+ 1 c) #s(hole binary32 (+ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
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#s(approx (* (/ 1 c) (pow (PI) -1/2)) #s(hole binary32 (* (/ 1 c) (sqrt (/ 1 (PI))))))
#s(approx (/ 1 c) #s(hole binary32 (/ 1 c)))
#s(approx c #s(hole binary32 c))
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#s(approx (+ 1 c) #s(hole binary32 c))
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#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 c)))
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Calls

6 calls:

TimeVariablePointExpression
101.0ms
cosTheta
@-inf
((/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (sqrt (PI)) (PI) (/ 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)))) (/ 1 (* (sqrt (PI)) cosTheta)) (* (sqrt (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)))) (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/ (* (/ 1 c) (pow (PI) -1/2)) cosTheta) (* (/ 1 c) (pow (PI) -1/2)) (/ 1 c) c (pow (PI) -1/2) -1/2 (/ 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)))) (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI)))) (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI))) (* (pow (PI) -1/2) (PI)) (/ 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)))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) (/ 1 (sqrt (PI))))
5.0ms
c
@inf
((/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (sqrt (PI)) (PI) (/ 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)))) (/ 1 (* (sqrt (PI)) cosTheta)) (* (sqrt (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)))) (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/ (* (/ 1 c) (pow (PI) -1/2)) cosTheta) (* (/ 1 c) (pow (PI) -1/2)) (/ 1 c) c (pow (PI) -1/2) -1/2 (/ 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)))) (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI)))) (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI))) (* (pow (PI) -1/2) (PI)) (/ 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)))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) (/ 1 (sqrt (PI))))
5.0ms
cosTheta
@inf
((/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (sqrt (PI)) (PI) (/ 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)))) (/ 1 (* (sqrt (PI)) cosTheta)) (* (sqrt (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)))) (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/ (* (/ 1 c) (pow (PI) -1/2)) cosTheta) (* (/ 1 c) (pow (PI) -1/2)) (/ 1 c) c (pow (PI) -1/2) -1/2 (/ 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)))) (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI)))) (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI))) (* (pow (PI) -1/2) (PI)) (/ 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)))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) (/ 1 (sqrt (PI))))
4.0ms
cosTheta
@0
((/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (sqrt (PI)) (PI) (/ 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)))) (/ 1 (* (sqrt (PI)) cosTheta)) (* (sqrt (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)))) (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/ (* (/ 1 c) (pow (PI) -1/2)) cosTheta) (* (/ 1 c) (pow (PI) -1/2)) (/ 1 c) c (pow (PI) -1/2) -1/2 (/ 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)))) (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI)))) (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI))) (* (pow (PI) -1/2) (PI)) (/ 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)))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) (/ 1 (sqrt (PI))))
3.0ms
c
@-inf
((/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (sqrt (PI)) (PI) (/ 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)))) (/ 1 (* (sqrt (PI)) cosTheta)) (* (sqrt (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)))) (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/ (* (/ 1 c) (pow (PI) -1/2)) cosTheta) (* (/ 1 c) (pow (PI) -1/2)) (/ 1 c) c (pow (PI) -1/2) -1/2 (/ 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)))) (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI)))) (/ 1 cosTheta) (/ 1 (* (pow (PI) -1/2) (PI))) (* (pow (PI) -1/2) (PI)) (/ 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)))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) (/ 1 (sqrt (PI))))

rewrite282.0ms (5.8%)

Memory
-8.0MiB live, 224.0MiB allocated; 34ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
097214055
0103212370
1593312001
0821811591
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
252 → 431
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
#s(literal 1 binary32)
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#s(approx (+ 1 c) #s(literal 1 binary32))
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(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
cosTheta
#s(literal -2 binary32)
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c
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#s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta)))
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#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (+ (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI)))))) (/ 1 c)))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (+ (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI)))))) (+ (* -1/2 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (/ 1 c))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (+ (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI)))))) (+ (* -1/2 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (+ (* 1/8 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (pow (sqrt 2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI)))))) (/ 1 c)))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (+ (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI)))))) (+ (* -1/2 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (+ (* -1/16 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (pow (sqrt 2) 5))) (sqrt (/ 1 (* (pow cosTheta 7) (PI)))))) (+ (* 1/8 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (pow (sqrt 2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI)))))) (/ 1 c))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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)))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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)))) (+ (* -1/16 (* (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)))))))))
#s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) #s(hole binary32 (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole 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)))))))))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ 1 c) #s(hole binary32 1))
#s(approx (+ 1 c) #s(hole binary32 (+ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole 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)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (/ (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)))
#s(approx (* (/ 1 c) (pow (PI) -1/2)) #s(hole binary32 (* (/ 1 c) (sqrt (/ 1 (PI))))))
#s(approx (/ 1 c) #s(hole binary32 (/ 1 c)))
#s(approx c #s(hole binary32 c))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 c))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ 1 c) #s(hole binary32 c))
#s(approx (+ 1 c) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 c))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 c))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 1))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) (+ 1 (/ 1 c)))))))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) #s(hole binary32 (+ 1 (* -1 (/ (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1) c)))))
Outputs
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32))))
(pow.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32))) #s(literal -1 binary32))
(exp.f32 (*.f32 (log.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32)))) #s(literal -1 binary32)))
#s(literal 1 binary32)
(/.f32 (-.f32 (pow.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32))) (-.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))))))
(/.f32 (+.f32 (pow.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))) (fma.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (+ 1 c) #s(literal 1 binary32)) (-.f32 (pow.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32)) (*.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))))))))
(fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32)))
(+.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))) #s(approx (+ 1 c) #s(literal 1 binary32)))
(+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))))
#s(approx (+ 1 c) #s(literal 1 binary32))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))))
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c
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#s(literal -1/2 binary32)
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#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) (neg.f32 (/.f32 (-.f32 (neg.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))) c)) #s(literal 1 binary32)) c)))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) (neg.f32 (/.f32 (-.f32 (neg.f32 (/.f32 (-.f32 (neg.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))) 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))) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (neg.f32 (*.f32 (-.f32 (neg.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 1 binary32)) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (-.f32 (neg.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))) c)) #s(literal 1 binary32)) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (neg.f32 (/.f32 (-.f32 (neg.f32 (/.f32 (-.f32 (neg.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))) 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))) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (neg.f32 (*.f32 (-.f32 (neg.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 1 binary32)) c)))
#s(approx (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (neg.f32 (*.f32 (-.f32 (neg.f32 (*.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))) c)))
#s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (fma.f32 (/.f32 (-.f32 (neg.f32 (*.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 -1 binary32) #s(literal 1 binary32)))

eval49.0ms (1%)

Memory
-0.6MiB live, 86.7MiB allocated; 11ms collecting garbage
Compiler

Compiled 22 102 to 2 275 computations (89.7% saved)

prune46.0ms (0.9%)

Memory
-4.4MiB live, 95.3MiB allocated; 16ms collecting garbage
Pruning

33 alts after pruning (29 fresh and 4 done)

PrunedKeptTotal
New38017397
Fresh151227
Picked325
Done123
Total39933432
Accuracy
99.9%
Counts
432 → 33
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.8%
(pow.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32))) #s(literal -1 binary32))
92.4%
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
95.4%
(/.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))) #s(approx (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
✓98.2%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
95.7%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
95.9%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 #s(approx (sqrt (+ (* cosTheta -2) 1)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
96.9%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
95.5%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
95.3%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
92.2%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
92.2%
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
97.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (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))))
95.4%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
98.2%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+.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) c) #s(literal 1 binary32))))
92.7%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
92.7%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)) cosTheta))))
✓93.0%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
92.4%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
55.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)))) #s(literal 1 binary32)) c)))
85.1%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
✓4.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
97.8%
(*.f32 (pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 -1/2 binary32)) (pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 -1/2 binary32)))
90.2%
(exp.f32 (*.f32 (log.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32)))) #s(literal -1 binary32)))
85.0%
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
97.1%
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
95.9%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
93.2%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
✓93.2%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
95.4%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (*.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) cosTheta)) cosTheta))
95.3%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (*.f32 (fma.f32 (neg.f32 cosTheta) (PI.f32) (fma.f32 (/.f32 #s(literal 1 binary32) c) (sqrt.f32 (PI.f32)) (/.f32 (*.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32))) c))) c)) cosTheta))
95.8%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (neg.f32 (*.f32 (fma.f32 (PI.f32) cosTheta (neg.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) c))) c))) cosTheta))
95.9%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (*.f32 (fma.f32 (*.f32 (neg.f32 cosTheta) cosTheta) (PI.f32) (/.f32 (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c)) c)))
54.5%
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (*.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta))))
Compiler

Compiled 4 568 to 1 412 computations (69.1% saved)

regimes197.0ms (4.1%)

Memory
1.8MiB live, 183.5MiB allocated; 37ms collecting garbage
Counts
75 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
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(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)))) #s(literal 1 binary32)) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (*.f32 (fma.f32 (neg.f32 cosTheta) (PI.f32) (fma.f32 (/.f32 #s(literal 1 binary32) c) (sqrt.f32 (PI.f32)) (/.f32 (*.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32))) c))) c)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (fma.f32 (pow.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) #s(literal -1 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1 binary32)) (*.f32 (/.f32 cosTheta (PI.f32)) #s(literal -2 binary32)))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))))) (*.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
(*.f32 (pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 -1/2 binary32)) (pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 -1/2 binary32)))
#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) (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))) #s(literal 3 binary32))) (fma.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32)) (-.f32 (*.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)))) (*.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (fma.f32 (-.f32 (*.f32 (neg.f32 cosTheta) (fma.f32 (*.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32))))) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32))) (fma.f32 (*.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32) (neg.f32 (*.f32 (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32))) (pow.f32 (PI.f32) #s(literal 3/2 binary32))))))) (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (*.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) cosTheta (*.f32 (neg.f32 (PI.f32)) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
Calls

6 calls:

71.0ms
(+.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))))
47.0ms
(*.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)))
23.0ms
cosTheta
20.0ms
c
17.0ms
(/.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
98.4%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)))
98.4%1(+.f32 #s(literal 1 binary32) c)
98.4%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))))
98.4%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)))))
98.4%1cosTheta
98.4%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes129.0ms (2.7%)

Memory
-10.6MiB live, 182.3MiB allocated; 58ms collecting garbage
Counts
59 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.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 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(exp.f32 (*.f32 (log1p.f32 (+.f32 c #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.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 (exp.f32 (*.f32 (log.f32 cosTheta) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))))))
(pow.f32 (fma.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (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 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 #s(approx (sqrt (+ (* cosTheta -2) 1)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
(/.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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(pow.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32))) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.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) c) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) c) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+.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) c) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
(exp.f32 (*.f32 (log.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32)))) #s(literal -1 binary32)))
(pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (*.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 #s(approx (+ (* (neg cosTheta) (* (+ (+ (* (pow (PI) -1/2) -1) c) 1) (PI))) (sqrt (PI))) (*.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) cosTheta)) cosTheta))
(exp.f32 (*.f32 (log1p.f32 (+.f32 c (*.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))) #s(literal -1 binary32)))
(/.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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))) cosTheta))))
Outputs
(pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
Calls

6 calls:

34.0ms
cosTheta
27.0ms
(+.f32 #s(literal 1 binary32) c)
18.0ms
(/.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
c
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)))
Results
AccuracySegmentsBranch
98.4%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)))
98.4%1(+.f32 #s(literal 1 binary32) c)
98.4%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))))
98.4%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)))))
98.4%1cosTheta
98.4%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes130.0ms (2.7%)

Memory
50.5MiB live, 140.8MiB allocated; 14ms collecting garbage
Counts
54 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.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 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(exp.f32 (*.f32 (log1p.f32 (+.f32 c #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.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 (exp.f32 (*.f32 (log.f32 cosTheta) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))))))
(pow.f32 (fma.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (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 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 #s(approx (sqrt (+ (* cosTheta -2) 1)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
(/.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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(pow.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32))) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.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) c) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) c) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+.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) c) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
(exp.f32 (*.f32 (log.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32)))) #s(literal -1 binary32)))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
Calls

6 calls:

63.0ms
(+.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))))
16.0ms
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)))))
13.0ms
(*.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
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)

regimes91.0ms (1.9%)

Memory
-20.5MiB live, 169.8MiB allocated; 27ms collecting garbage
Counts
52 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.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 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(exp.f32 (*.f32 (log1p.f32 (+.f32 c #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.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 (exp.f32 (*.f32 (log.f32 cosTheta) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))))))
(pow.f32 (fma.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (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 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 #s(approx (sqrt (+ (* cosTheta -2) 1)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
(/.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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(pow.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32))) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.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) c) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) c) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (+.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) c) #s(literal 1 binary32))))
Outputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.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) c) #s(literal 1 binary32))))
Calls

6 calls:

16.0ms
(+.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))))
16.0ms
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
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)))))
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)

regimes105.0ms (2.2%)

Memory
21.2MiB live, 119.9MiB allocated; 17ms collecting garbage
Counts
49 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.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 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(exp.f32 (*.f32 (log1p.f32 (+.f32 c #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.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 (exp.f32 (*.f32 (log.f32 cosTheta) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))))))
(pow.f32 (fma.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (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 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 #s(approx (sqrt (+ (* cosTheta -2) 1)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (PI.f32)))))
(/.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 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(pow.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32))) #s(literal -1 binary32))
Outputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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) #s(literal 1 binary32))))
Calls

6 calls:

37.0ms
(*.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)))
20.0ms
c
12.0ms
(/.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)))))
12.0ms
(+.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))))
12.0ms
cosTheta
Results
AccuracySegmentsBranch
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%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%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes76.0ms (1.6%)

Memory
-12.6MiB live, 131.7MiB allocated; 10ms collecting garbage
Counts
42 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.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 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(exp.f32 (*.f32 (log1p.f32 (+.f32 c #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.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 (exp.f32 (*.f32 (log.f32 cosTheta) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)))))))
(pow.f32 (fma.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
Calls

6 calls:

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)))))
12.0ms
(+.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
c
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))))
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)

regimes61.0ms (1.3%)

Memory
1.4MiB live, 141.7MiB allocated; 4ms collecting garbage
Counts
38 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.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 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(exp.f32 (*.f32 (log1p.f32 (+.f32 c #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.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 (exp.f32 (*.f32 (log.f32 cosTheta) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
Calls

6 calls:

12.0ms
(/.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
c
9.0ms
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
9.0ms
(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
9.0ms
cosTheta
Results
AccuracySegmentsBranch
96.0%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)))
96.0%1(+.f32 #s(literal 1 binary32) c)
96.0%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))))
96.0%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)))))
96.0%1cosTheta
96.0%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes67.0ms (1.4%)

Memory
-24.4MiB live, 127.3MiB allocated; 19ms collecting garbage
Counts
34 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.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 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(exp.f32 (*.f32 (log1p.f32 (+.f32 c #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.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 (exp.f32 (*.f32 (log.f32 cosTheta) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
Calls

6 calls:

21.0ms
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)))
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)))))
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))))
8.0ms
cosTheta
Results
AccuracySegmentsBranch
95.9%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)))
95.9%1(+.f32 #s(literal 1 binary32) c)
95.9%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))))
95.9%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)))))
95.9%1cosTheta
95.9%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes63.0ms (1.3%)

Memory
3.3MiB live, 50.6MiB allocated; 0ms collecting garbage
Counts
29 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.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 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
Calls

6 calls:

26.0ms
(/.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)))))
7.0ms
(+.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))))
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
c
7.0ms
cosTheta
Results
AccuracySegmentsBranch
95.7%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)))
95.7%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))))
95.7%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)))))
95.7%1cosTheta
95.7%1(+.f32 #s(literal 1 binary32) c)
95.7%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes53.0ms (1.1%)

Memory
14.5MiB live, 109.3MiB allocated; 9ms collecting garbage
Counts
28 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.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 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.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 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) 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 (/ (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (* (pow (PI) -1/2) (PI)))) cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))))
Calls

6 calls:

12.0ms
(+.f32 #s(literal 1 binary32) c)
11.0ms
(/.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)))))
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
(+.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))))
7.0ms
c
Results
AccuracySegmentsBranch
95.5%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)))))
95.5%1cosTheta
95.5%1c
95.5%1(+.f32 #s(literal 1 binary32) c)
95.5%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)))
95.5%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)

regimes39.0ms (0.8%)

Memory
2.1MiB live, 92.5MiB allocated; 6ms collecting garbage
Counts
22 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) 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) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (pow (PI) -1/2) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (sqrt (PI)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 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 #s(approx (+ (* (neg cosTheta) (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (pow (PI) -1/2) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (*.f32 (pow.f32 (*.f32 cosTheta c) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 #s(approx (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (/.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) c)))
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:

8.0ms
cosTheta
7.0ms
(+.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)))
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
c
Results
AccuracySegmentsBranch
93.2%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)))))
93.2%1cosTheta
93.2%1(+.f32 #s(literal 1 binary32) c)
93.2%1c
93.2%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)))
93.2%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))))
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes9.0ms (0.2%)

Memory
-32.9MiB live, 21.6MiB allocated; 3ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

6 calls:

3.0ms
(+.f32 #s(literal 1 binary32) c)
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
(+.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
Results
AccuracySegmentsBranch
4.8%1(+.f32 #s(literal 1 binary32) c)
4.8%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)))
4.8%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))))
4.8%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)))))
4.8%1cosTheta
4.8%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

derivations208.0ms (4.3%)

Memory
24.4MiB live, 263.6MiB allocated; 7ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 401 to 109 computations (72.8% saved)

preprocess95.0ms (2%)

Memory
-10.4MiB live, 224.1MiB allocated; 24ms collecting garbage
Compiler

Compiled 852 to 254 computations (70.2% saved)

end0.0ms (0%)

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

Profiling

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