Beckmann Sample, normalization factor

Time bar (total: 3.7s)

start0.0ms (0%)

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

analyze23.0ms (0.6%)

Memory
-8.5MiB live, 38.1MiB allocated; 7ms 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)

sample944.0ms (25.2%)

Memory
36.6MiB live, 2 028.8MiB allocated; 152ms collecting garbage
Samples
674.0ms8 255×0valid
8.0ms67×0invalid
0.0ms1×1valid
Precisions
Click to see histograms. Total time spent on operations: 477.0ms
ival-mult!: 122.0ms (25.6% of total)
ival-div!: 91.0ms (19.1% of total)
ival-exp: 72.0ms (15.1% of total)
ival-sqrt: 70.0ms (14.7% of total)
ival-add!: 44.0ms (9.2% of total)
ival-neg: 38.0ms (8% of total)
ival-sub!: 37.0ms (7.7% of total)
adjust: 2.0ms (0.4% of total)
ival-<: 1.0ms (0.2% of total)
ival-pi: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-and: 0.0ms (0% of total)
Bogosity

explain171.0ms (4.6%)

Memory
-15.1MiB live, 466.2MiB allocated; 20ms 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
45.0ms512×0valid
Compiler

Compiled 281 to 58 computations (79.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 28.0ms
ival-mult!: 8.0ms (28.6% of total)
ival-div!: 5.0ms (17.9% of total)
ival-exp: 4.0ms (14.3% of total)
ival-sqrt: 4.0ms (14.3% of total)
ival-add!: 3.0ms (10.7% of total)
ival-neg: 3.0ms (10.7% of total)
ival-sub!: 2.0ms (7.1% of total)
adjust: 0.0ms (0% of total)

preprocess26.0ms (0.7%)

Memory
-13.7MiB live, 33.0MiB 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
▶98.0%
(/.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)))))
Compiler

Compiled 50 to 36 computations (28% saved)

series34.0ms (0.9%)

Memory
41.4MiB live, 88.8MiB 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
11.0ms
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))
4.0ms
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))
3.0ms
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))
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))

rewrite199.0ms (5.3%)

Memory
13.9MiB live, 286.4MiB allocated; 87ms 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 (*.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)))))))
(-.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))))
(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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#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)))

eval35.0ms (0.9%)

Memory
-7.9MiB live, 80.6MiB allocated; 21ms collecting garbage
Compiler

Compiled 8 637 to 1 127 computations (87% saved)

prune43.0ms (1.2%)

Memory
-6.6MiB live, 57.4MiB allocated; 34ms collecting garbage
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New17018188
Fresh000
Picked101
Done000
Total17118189
Accuracy
99.5%
Counts
189 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
33.2%
(/.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))))))))
▶98.7%
(/.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)))))
98.6%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.0%
(/.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)) (+.f32 (cosh.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))))
97.8%
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
▶97.5%
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
96.7%
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
95.1%
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
96.2%
(/.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 (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
95.0%
(/.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 (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)))))))
97.8%
(/.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))))
▶98.0%
(/.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))))
92.5%
(/.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))))))
51.8%
(/.f32 #s(literal 1 binary32) #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))))
▶4.9%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
▶95.7%
#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 1 410 to 890 computations (36.9% saved)

series59.0ms (1.6%)

Memory
-28.7MiB live, 109.6MiB allocated; 22ms collecting garbage
Counts
49 → 318
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)
#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 (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)
(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)))
(*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))
(+.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 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c)
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
#s(literal -1 binary32)
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(/.f32 (sqrt.f32 (-.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)
#s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32))
(*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
(*.f32 cosTheta cosTheta)
#s(literal 1/2 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))))
#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 (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))
(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)
(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 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta)
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 (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (sqrt (PI))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (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 (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 cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 1))
#s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
#s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))))
#s(approx (- (* (* cosTheta cosTheta) 1/2) 1) #s(hole binary32 -1))
#s(approx (- (* (* cosTheta cosTheta) 1/2) 1) #s(hole binary32 (- (* 1/2 (pow cosTheta 2)) 1)))
#s(approx (* (* cosTheta cosTheta) 1/2) #s(hole binary32 (* 1/2 (pow cosTheta 2))))
#s(approx (* cosTheta cosTheta) #s(hole binary32 (pow cosTheta 2)))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #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 (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta)))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 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 (/ (+ (* -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 (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta)))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta)))
#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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#s(approx (+ 1 c) #s(hole binary32 1))
#s(approx (+ 1 c) #s(hole binary32 (+ 1 c)))
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#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) #s(hole binary32 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 c))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 c))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* c (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c 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 (* -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 (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -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) (* (+ (+ (* (/ 1 (sqrt (PI))) -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 (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) #s(hole binary32 (* -1 (* c (+ (* -1 (PI)) (* -1 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))))
#s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) #s(hole binary32 (* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1)))))
Calls

6 calls:

TimeVariablePointExpression
18.0ms
cosTheta
@0
((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg 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)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ 1 (sqrt (PI))) -1 (/ 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))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 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)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta))
11.0ms
cosTheta
@-inf
((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg 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)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ 1 (sqrt (PI))) -1 (/ 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))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 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)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta))
6.0ms
cosTheta
@inf
((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg 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)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ 1 (sqrt (PI))) -1 (/ 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))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 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)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta))
4.0ms
c
@0
((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg 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)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ 1 (sqrt (PI))) -1 (/ 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))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 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)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta))
4.0ms
c
@inf
((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg 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)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ 1 (sqrt (PI))) -1 (/ 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))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 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)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta))

rewrite260.0ms (7%)

Memory
5.7MiB live, 293.7MiB allocated; 88ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0108616918
0116814528
1595714226
0821713769
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
367 → 596
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)
#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 (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)
(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)))
(*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))
(+.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 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c)
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
#s(literal -1 binary32)
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(/.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)
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(fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32))
(*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
(*.f32 cosTheta cosTheta)
#s(literal 1/2 binary32)
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(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))
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#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
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#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (/ 1 cosTheta)))
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#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)))
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#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)))
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#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 1))
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#s(approx (+ (* -2 cosTheta) 1) #s(hole binary32 1))
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#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)))))
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#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)))))))))))))
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#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (sqrt (PI))))
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#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))))))
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#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)))
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#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))))
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#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 cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 1))
#s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
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#s(approx (- (* (* cosTheta cosTheta) 1/2) 1) #s(hole binary32 -1))
#s(approx (- (* (* cosTheta cosTheta) 1/2) 1) #s(hole binary32 (- (* 1/2 (pow cosTheta 2)) 1)))
#s(approx (* (* cosTheta cosTheta) 1/2) #s(hole binary32 (* 1/2 (pow cosTheta 2))))
#s(approx (* cosTheta cosTheta) #s(hole binary32 (pow cosTheta 2)))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
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#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
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#s(approx (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) #s(hole binary32 (sqrt (/ 1 (PI)))))
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#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))))
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#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta)))
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#s(approx (+ 1 c) #s(hole binary32 1))
#s(approx (+ 1 c) #s(hole binary32 (+ 1 c)))
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#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) #s(hole binary32 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 c))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 c))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* c (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c 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 (* -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 (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -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) (* (+ (+ (* (/ 1 (sqrt (PI))) -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 (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) #s(hole binary32 (* -1 (* c (+ (* -1 (PI)) (* -1 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))))
#s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) #s(hole binary32 (* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1)))))
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 (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(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 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 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 2 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 (+.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))) (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (-.f32 (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 2 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 (+.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))))
(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 (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 #s(literal 1 binary32) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.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 (neg.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (neg.f32 cosTheta))
(/.f32 (*.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) 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))
(*.f32 #s(literal 1 binary32) (/.f32 (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 (*.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) cosTheta)
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta)
(*.f32 (pow.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal -1/2 binary32)) (pow.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32)))
(sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))
(pow.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1/2 binary32))
(exp.f32 (*.f32 (log1p.f32 (*.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (*.f32 #s(literal 2 binary32) cosTheta) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta)) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 2 binary32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 2 binary32)) #s(literal 1 binary32)) (-.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 8 binary32) (pow.f32 cosTheta #s(literal 3 binary32)))) (+.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (*.f32 #s(literal 2 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)))))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32))) (+.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (fma.f32 cosTheta cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(/.f32 (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -8 binary32) (pow.f32 cosTheta #s(literal 3 binary32)))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 2 binary32)) (*.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))))))
(/.f32 (fma.f32 #s(literal -8 binary32) (pow.f32 cosTheta #s(literal 3 binary32)) #s(literal 1 binary32)) (+.f32 (pow.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (*.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32)))))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(+.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))
#s(literal -2 binary32)
cosTheta
(log.f32 (pow.f32 (exp.f32 (PI.f32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal 1/2 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32)) (pow.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32))
(sqrt.f32 (PI.f32))
(pow.f32 (PI.f32) #s(literal 1/2 binary32))
(exp.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 1/2 binary32)))
(PI.f32)
(-.f32 (cosh.f32 (*.f32 cosTheta cosTheta)) (sinh.f32 (*.f32 cosTheta cosTheta)))
(pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (pow.f32 cosTheta #s(literal 1 binary32))) (pow.f32 cosTheta #s(literal 1 binary32)))
(pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (fabs.f32 cosTheta)) (fabs.f32 cosTheta))
(pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (neg.f32 cosTheta)) (neg.f32 cosTheta))
(pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta)
(pow.f32 (exp.f32 #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta)
(+.f32 (cosh.f32 (*.f32 cosTheta cosTheta)) (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(exp.f32 (*.f32 (log.f32 (exp.f32 #s(literal -1 binary32))) (*.f32 cosTheta cosTheta)))
(exp.f32 (*.f32 (log.f32 (exp.f32 (neg.f32 cosTheta))) cosTheta))
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32))
(*.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(*.f32 cosTheta (neg.f32 cosTheta))
(neg.f32 (*.f32 cosTheta cosTheta))
(*.f32 #s(literal -1 binary32) cosTheta)
(*.f32 cosTheta #s(literal -1 binary32))
(neg.f32 cosTheta)
(/.f32 #s(literal -1 binary32) (neg.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
(pow.f32 (pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c) #s(literal -1 binary32))
(exp.f32 (*.f32 (log.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c)) #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 (fma.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
(*.f32 (fma.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta)
(*.f32 cosTheta (fma.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(fma.f32 (sqrt.f32 (PI.f32)) cosTheta (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta))
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#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) c)
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (*.f32 (fma.f32 (*.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) c)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1 binary32)) c))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) c)
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#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 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (-.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32))) c)))
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#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (neg.f32 (*.f32 (-.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 1 binary32)) c)))
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#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (neg.f32 (*.f32 (-.f32 (neg.f32 (*.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))) #s(literal 1 binary32)) c)))

eval56.0ms (1.5%)

Memory
43.6MiB live, 135.9MiB allocated; 6ms collecting garbage
Compiler

Compiled 29 421 to 3 089 computations (89.5% saved)

prune29.0ms (0.8%)

Memory
-31.7MiB live, 64.7MiB allocated; 7ms collecting garbage
Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New59419613
Fresh10313
Picked415
Done000
Total60823631
Accuracy
100.0%
Counts
631 → 23
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.2%
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
97.4%
(/.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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
95.8%
(/.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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
96.7%
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
97.8%
(/.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))))
98.0%
(/.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 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) c) #s(literal 1 binary32))))
97.8%
(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
96.7%
(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
95.1%
(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) c) #s(literal 1 binary32))))
▶97.5%
(/.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))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
51.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))))
▶10.6%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
92.5%
(/.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))))))
✓4.9%
(/.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)))
95.6%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
▶95.6%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
95.4%
#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)) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32))) cosTheta))
95.7%
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
▶95.6%
#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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.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 (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (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 1 929 to 1 292 computations (33% saved)

series38.0ms (1%)

Memory
-11.4MiB live, 81.7MiB allocated; 5ms collecting garbage
Counts
50 → 280
Calls
Call 1
Inputs
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
#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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.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 (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)
(sqrt.f32 (PI.f32))
(PI.f32)
#s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32))
(*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
(*.f32 cosTheta cosTheta)
#s(literal 1/2 binary32)
(+.f32 c #s(literal 1 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 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32)))
(+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c)
#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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta)
(fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32)))
(neg.f32 cosTheta)
(*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32))
(+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
#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))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #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))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32)))
(+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) 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))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta))
(/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
(+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)
(*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta))
(*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32)))
(pow.f32 (PI.f32) #s(literal -1/2 binary32))
#s(literal -1/2 binary32)
Outputs
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #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) (sqrt (PI))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (/ (/ (sqrt (+ (* cosTheta -2) 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 (/ (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 (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 1))
#s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
#s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))))
#s(approx (- (* (* cosTheta cosTheta) 1/2) 1) #s(hole binary32 -1))
#s(approx (- (* (* cosTheta cosTheta) 1/2) 1) #s(hole binary32 (- (* 1/2 (pow cosTheta 2)) 1)))
#s(approx (* (* cosTheta cosTheta) 1/2) #s(hole binary32 (* 1/2 (pow cosTheta 2))))
#s(approx (* cosTheta cosTheta) #s(hole binary32 (pow cosTheta 2)))
#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)))))))))))))
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#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) #s(hole binary32 (* -1 (* c (* cosTheta (PI))))))
#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) #s(hole binary32 (* c (+ (* -1 (* cosTheta (PI))) (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c))))))
#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 (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1)))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -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) (* (+ (+ (* (/ 1 (sqrt (PI))) -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 (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) #s(hole binary32 (* -1 (* c (+ (* -1 (PI)) (* -1 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))))
#s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) #s(hole binary32 (* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) #s(hole binary32 (* -1 (* c (+ (* -1 (/ (+ (* -1 (* (pow cosTheta 2) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (* cosTheta (sqrt (PI)))) c)) (* (pow cosTheta 2) (PI)))))))
#s(approx (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) #s(hole binary32 (* -1 (* c (+ (* (pow cosTheta 2) (PI)) (/ (* (pow cosTheta 2) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c))))))
#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) #s(hole binary32 (* -1 (* c (+ (* cosTheta (PI)) (/ (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c))))))
#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)))))
Calls

6 calls:

TimeVariablePointExpression
7.0ms
cosTheta
@-inf
((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ -1 (sqrt (PI))) -1 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (+ (* -2 cosTheta) 1) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (+ (* (pow (PI) -1/2) -1) (+ c 1)) (pow (PI) -1/2) -1/2)
5.0ms
cosTheta
@inf
((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ -1 (sqrt (PI))) -1 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (+ (* -2 cosTheta) 1) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (+ (* (pow (PI) -1/2) -1) (+ c 1)) (pow (PI) -1/2) -1/2)
4.0ms
cosTheta
@0
((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ -1 (sqrt (PI))) -1 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (+ (* -2 cosTheta) 1) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (+ (* (pow (PI) -1/2) -1) (+ c 1)) (pow (PI) -1/2) -1/2)
3.0ms
c
@-inf
((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ -1 (sqrt (PI))) -1 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (+ (* -2 cosTheta) 1) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (+ (* (pow (PI) -1/2) -1) (+ c 1)) (pow (PI) -1/2) -1/2)
3.0ms
c
@inf
((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ -1 (sqrt (PI))) -1 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (+ (* -2 cosTheta) 1) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (+ (* (pow (PI) -1/2) -1) (+ c 1)) (pow (PI) -1/2) -1/2)

rewrite210.0ms (5.6%)

Memory
24.0MiB live, 307.8MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0108414966
0115513265
1623813017
0836512553
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
330 → 517
Calls
Call 1
Inputs
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
#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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.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 (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)
(sqrt.f32 (PI.f32))
(PI.f32)
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#s(approx (+ c 1) #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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (+ (* -1 (* c (* (pow cosTheta 2) (PI)))) (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (+ (sqrt (PI)) (+ (* -1 (* c (* cosTheta (PI)))) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))))
#s(approx (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) #s(hole binary32 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))
#s(approx (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) #s(hole binary32 (+ (* c (PI)) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))
#s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) #s(hole binary32 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
#s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) #s(hole binary32 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) #s(hole binary32 (* -1 (sqrt (/ 1 (PI))))))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) #s(hole binary32 (+ c (* -1 (sqrt (/ 1 (PI)))))))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) #s(hole binary32 (+ (* -1 (* (pow cosTheta 2) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (* cosTheta (sqrt (PI))))))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) #s(hole binary32 (+ (* -1 (* c (* (pow cosTheta 2) (PI)))) (+ (* -1 (* (pow cosTheta 2) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (* cosTheta (sqrt (PI)))))))
#s(approx (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) #s(hole binary32 (* -1 (* (pow cosTheta 2) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
#s(approx (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) #s(hole binary32 (+ (* -1 (* c (* (pow cosTheta 2) (PI)))) (* -1 (* (pow cosTheta 2) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))))
#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) #s(hole binary32 (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) #s(hole binary32 (+ (* -1 (* c (* cosTheta (PI)))) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))))
#s(approx (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) #s(hole binary32 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))
#s(approx (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) #s(hole binary32 (+ (* c (PI)) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))
#s(approx (+ (* (pow (PI) -1/2) -1) (+ c 1)) #s(hole binary32 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
#s(approx (+ (* (pow (PI) -1/2) -1) (+ c 1)) #s(hole binary32 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 c))
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ 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) (* (* (/ 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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 c))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 c))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* c (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* -1 (* c (* (pow cosTheta 2) (PI))))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -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) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* -1 (* c (* cosTheta (PI))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -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 (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) #s(hole binary32 (* c (PI))))
#s(approx (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) #s(hole binary32 (* c (+ (PI) (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))
#s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) #s(hole binary32 c))
#s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) #s(hole binary32 (* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) #s(hole binary32 c))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) #s(hole binary32 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) #s(hole binary32 (* -1 (* c (* (pow cosTheta 2) (PI))))))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) #s(hole binary32 (* c (+ (* -1 (* (pow cosTheta 2) (PI))) (+ (* -1 (/ (* (pow cosTheta 2) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)) (* (/ cosTheta c) (sqrt (PI))))))))
#s(approx (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) #s(hole binary32 (* -1 (* c (* (pow cosTheta 2) (PI))))))
#s(approx (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) #s(hole binary32 (* c (+ (* -1 (* (pow cosTheta 2) (PI))) (* -1 (/ (* (pow cosTheta 2) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c))))))
#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) #s(hole binary32 (* -1 (* c (* cosTheta (PI))))))
#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) #s(hole binary32 (* c (+ (* -1 (* cosTheta (PI))) (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c))))))
#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 (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1)))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -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) (* (+ (+ (* (/ 1 (sqrt (PI))) -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 (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) #s(hole binary32 (* -1 (* c (+ (* -1 (PI)) (* -1 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))))
#s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) #s(hole binary32 (* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) #s(hole binary32 (* -1 (* c (+ (* -1 (/ (+ (* -1 (* (pow cosTheta 2) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (* cosTheta (sqrt (PI)))) c)) (* (pow cosTheta 2) (PI)))))))
#s(approx (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) #s(hole binary32 (* -1 (* c (+ (* (pow cosTheta 2) (PI)) (/ (* (pow cosTheta 2) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c))))))
#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) #s(hole binary32 (* -1 (* c (+ (* cosTheta (PI)) (/ (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c))))))
#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)))))
Outputs
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(pow.f32 (pow.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
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#s(literal 1 binary32)
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c
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#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (*.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) c)) c))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c)
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) c))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (neg.f32 (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) c)))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (*.f32 (fma.f32 (*.f32 (neg.f32 cosTheta) cosTheta) (PI.f32) (/.f32 (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c)) c))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (neg.f32 (*.f32 (*.f32 (PI.f32) cosTheta) c)))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (*.f32 (fma.f32 #s(literal -1 binary32) (fma.f32 (PI.f32) cosTheta (/.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) cosTheta) c)) (*.f32 (/.f32 #s(literal 1 binary32) c) (sqrt.f32 (PI.f32)))) c))
#s(approx (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (*.f32 (PI.f32) c))
#s(approx (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (*.f32 (fma.f32 (PI.f32) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) c) (PI.f32)) c))
#s(approx (+ (* (pow (PI) -1/2) -1) (+ c 1)) c)
#s(approx (+ (* (pow (PI) -1/2) -1) (+ c 1)) (*.f32 (+.f32 (fma.f32 (*.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) c)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) c)) c))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) c)
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (*.f32 (fma.f32 (*.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) c)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1 binary32)) c))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (neg.f32 (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) c)))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (*.f32 (fma.f32 (*.f32 (neg.f32 cosTheta) cosTheta) (PI.f32) (/.f32 (fma.f32 (*.f32 (neg.f32 cosTheta) cosTheta) (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) c)) c))
#s(approx (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) (neg.f32 (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) c)))
#s(approx (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) (*.f32 (*.f32 #s(literal -1 binary32) (fma.f32 (*.f32 cosTheta cosTheta) (/.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) c) (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)))) c))
#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) (neg.f32 (*.f32 (*.f32 (PI.f32) cosTheta) c)))
#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) (*.f32 (*.f32 #s(literal -1 binary32) (fma.f32 (PI.f32) cosTheta (/.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) cosTheta) c))) c))
#s(approx (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (*.f32 (PI.f32) c))
#s(approx (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (*.f32 (fma.f32 (PI.f32) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) c) (PI.f32)) c))
#s(approx (+ (* (pow (PI) -1/2) -1) (+ c 1)) c)
#s(approx (+ (* (pow (PI) -1/2) -1) (+ c 1)) (*.f32 (+.f32 (fma.f32 (*.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) c)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) c)) c))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (neg.f32 (/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (-.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32))) c)))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (neg.f32 (/.f32 (-.f32 (neg.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) #s(literal 2 binary32)) c) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))) c)) #s(literal 1 binary32)) c)))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (neg.f32 (/.f32 (-.f32 (neg.f32 (/.f32 (-.f32 (neg.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (pow.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) #s(literal 2 binary32))) c)) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32))) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (neg.f32 (*.f32 (-.f32 (neg.f32 (/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.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 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (-.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32))) 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 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) #s(literal 2 binary32)) c) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.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 (neg.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (pow.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) #s(literal 2 binary32))) c)) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.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)))) (neg.f32 (*.f32 (-.f32 (neg.f32 (/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (neg.f32 (*.f32 (-.f32 (neg.f32 (/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (neg.f32 (*.f32 (-.f32 (neg.f32 (*.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))) #s(literal 1 binary32)) c)))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (neg.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) (PI.f32) (neg.f32 (/.f32 (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c))) c)))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -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 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #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 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #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 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) c)) #s(literal 1 binary32)) c)))
#s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (neg.f32 (*.f32 (-.f32 (*.f32 (/.f32 #s(literal 1 binary32) c) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 1 binary32)) c)))
#s(approx (+ (* (sqrt (PI)) cosTheta) (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta)) (neg.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) (PI.f32) (neg.f32 (/.f32 (fma.f32 (*.f32 (neg.f32 cosTheta) cosTheta) (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) c))) c)))
#s(approx (* (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) cosTheta) (neg.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) (/.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) c) (*.f32 (*.f32 cosTheta cosTheta) (PI.f32))) c)))
#s(approx (* (* (+ (* (pow (PI) -1/2) -1) (+ c 1)) (PI)) (neg cosTheta)) (neg.f32 (*.f32 (fma.f32 (PI.f32) cosTheta (/.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) cosTheta) 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 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #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 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) c)) #s(literal 1 binary32)) c)))

eval64.0ms (1.7%)

Memory
-16.6MiB live, 130.6MiB allocated; 17ms collecting garbage
Compiler

Compiled 37 268 to 2 973 computations (92% saved)

prune40.0ms (1.1%)

Memory
-0.8MiB live, 93.3MiB allocated; 4ms collecting garbage
Pruning

26 alts after pruning (22 fresh and 4 done)

PrunedKeptTotal
New6229631
Fresh41317
Picked235
Done011
Total62826654
Accuracy
100.0%
Counts
654 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.5%
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
98.0%
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ c 1) #s(literal 1 binary32))))
97.4%
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
95.8%
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
98.1%
(/.f32 #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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
98.1%
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)))
▶96.7%
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
97.8%
(/.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))))
97.8%
(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
96.7%
(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
▶95.1%
(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) c) #s(literal 1 binary32))))
✓97.5%
(/.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))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
▶97.3%
(/.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 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
51.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))))
✓10.6%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
92.5%
(/.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))))))
✓4.9%
(/.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)))
95.6%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
95.6%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
95.5%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32) (*.f32 (*.f32 (neg.f32 cosTheta) (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32))) (PI.f32))) cosTheta))
95.7%
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
✓95.6%
#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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.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 (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (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 2 072 to 1 368 computations (34% saved)

series41.0ms (1.1%)

Memory
36.7MiB live, 83.2MiB allocated; 2ms collecting garbage
Counts
62 → 314
Calls
Call 1
Inputs
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
#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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.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 (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)
(sqrt.f32 (PI.f32))
(PI.f32)
#s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32))
(*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta))
(fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
#s(literal -1/6 binary32)
(*.f32 cosTheta cosTheta)
#s(literal 1/2 binary32)
(+.f32 c #s(literal 1 binary32))
c
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(*.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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) c) #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 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) c) #s(literal 1 binary32)))
(+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) c) #s(literal 1 binary32))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta)
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32)))))
(+.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))
(*.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)))
(/.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)
#s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32)))
(fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))
(neg.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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #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 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32)))
(+.f32 (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))
(fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c)
(sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta)))
#s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))
(*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta)
(-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32)))
(/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))
(/.f32 #s(literal 1 binary32) cosTheta)
(/.f32 #s(literal 2 binary32) (PI.f32))
#s(literal 2 binary32)
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta))
(/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)
(fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32))
(*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
Outputs
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #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) (sqrt (PI))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (/ (/ (sqrt (+ (* cosTheta -2) 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 (/ (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 (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 1))
#s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
#s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))))
#s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1)))))
#s(approx (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) #s(hole binary32 -1))
#s(approx (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) #s(hole binary32 (- (* 1/2 (pow cosTheta 2)) 1)))
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#s(approx (- 1 cosTheta) #s(hole binary32 1))
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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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
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#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #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)))))))))))
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#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (+ 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 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (+ 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 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (+ 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 (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) #s(hole binary32 (* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))))
#s(approx (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) #s(hole binary32 (* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
#s(approx (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) #s(hole binary32 (* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) #s(hole binary32 (* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))))
#s(approx (/ (+ (* -2 cosTheta) 1) (PI)) #s(hole binary32 (* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))))
#s(approx (+ (* -2 cosTheta) 1) #s(hole binary32 (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))))
#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 cosTheta) (PI)) (/ 2 (PI))) cosTheta) #s(hole binary32 (* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))))
#s(approx (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) #s(hole binary32 (* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) 1/2)))))
#s(approx (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) #s(hole binary32 (* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) (+ 1/2 (/ 1 (pow cosTheta 4))))))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
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#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ c 1) #s(hole binary32 1))
#s(approx (+ c 1) #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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (+ 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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 c))
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ 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) (* (* (/ 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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 c))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 c))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* c (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ 1 c) #s(hole binary32 c))
#s(approx (+ 1 c) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1)))))
Calls

6 calls:

TimeVariablePointExpression
13.0ms
cosTheta
@-inf
((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) (+ (* -1/6 (* cosTheta cosTheta)) 1/2) -1/6 (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (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)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (+ (* -2 cosTheta) 1) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) 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)))) (+ 1 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (* (- (/ (/ 1 cosTheta) (PI)) (/ 2 (PI))) cosTheta) (- (/ (/ 1 cosTheta) (PI)) (/ 2 (PI))) (/ (/ 1 cosTheta) (PI)) (/ 1 cosTheta) (/ 2 (PI)) 2 (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2))
6.0ms
cosTheta
@inf
((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) (+ (* -1/6 (* cosTheta cosTheta)) 1/2) -1/6 (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (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)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (+ (* -2 cosTheta) 1) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) 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)))) (+ 1 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (* (- (/ (/ 1 cosTheta) (PI)) (/ 2 (PI))) cosTheta) (- (/ (/ 1 cosTheta) (PI)) (/ 2 (PI))) (/ (/ 1 cosTheta) (PI)) (/ 1 cosTheta) (/ 2 (PI)) 2 (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2))
5.0ms
cosTheta
@0
((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) (+ (* -1/6 (* cosTheta cosTheta)) 1/2) -1/6 (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (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)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (+ (* -2 cosTheta) 1) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) 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)))) (+ 1 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (* (- (/ (/ 1 cosTheta) (PI)) (/ 2 (PI))) cosTheta) (- (/ (/ 1 cosTheta) (PI)) (/ 2 (PI))) (/ (/ 1 cosTheta) (PI)) (/ 1 cosTheta) (/ 2 (PI)) 2 (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2))
2.0ms
c
@0
((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) (+ (* -1/6 (* cosTheta cosTheta)) 1/2) -1/6 (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (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)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (+ (* -2 cosTheta) 1) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) 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)))) (+ 1 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (* (- (/ (/ 1 cosTheta) (PI)) (/ 2 (PI))) cosTheta) (- (/ (/ 1 cosTheta) (PI)) (/ 2 (PI))) (/ (/ 1 cosTheta) (PI)) (/ 1 cosTheta) (/ 2 (PI)) 2 (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) cosTheta) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2))
2.0ms
c
@-inf
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rewrite191.0ms (5.1%)

Memory
-20.5MiB live, 263.2MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0106115951
0114514088
0573813647
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
376 → 580
Calls
Call 1
Inputs
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
#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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.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)))
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(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
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(PI.f32)
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c
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#s(approx cosTheta #s(hole binary32 cosTheta))
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#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
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#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 1))
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#s(approx (- 1 cosTheta) #s(hole binary32 1))
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#s(approx (* (- (/ (/ 1 cosTheta) (PI)) (/ 2 (PI))) cosTheta) #s(hole binary32 (/ 1 (PI))))
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#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))))))))
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#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)))))))))
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#s(approx (- 1 cosTheta) #s(hole binary32 (* -1 (* cosTheta (- 1 (/ 1 cosTheta))))))
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#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ c 1) #s(hole binary32 1))
#s(approx (+ c 1) #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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (+ 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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 c))
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ 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) (* (* (/ 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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 c))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 c))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* c (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))))
#s(approx (+ 1 c) #s(hole binary32 c))
#s(approx (+ 1 c) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 1)))))
Outputs
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(pow.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(literal 1 binary32)
(/.f32 (-.f32 (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))) (*.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32)))) (-.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 (+.f32 (pow.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32))) (fma.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (-.f32 (*.f32 (+.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))) (*.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (+.f32 c #s(literal 1 binary32))))))
(fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32)))
(fma.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32)))
(+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32))
(+.f32 (*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (+.f32 c #s(literal 1 binary32)))
(+.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) cosTheta) cosTheta) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(/.f32 (neg.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (neg.f32 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)))
(pow.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) #s(literal 1/2 binary32))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal 2 binary32) cosTheta) (*.f32 #s(literal 2 binary32) cosTheta))) (+.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)))
(/.f32 (-.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta cosTheta)) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -2 binary32) cosTheta) (*.f32 #s(literal -2 binary32) cosTheta))) (-.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)))
(/.f32 (-.f32 (*.f32 (*.f32 #s(literal -2 binary32) cosTheta) (*.f32 #s(literal -2 binary32) cosTheta)) #s(literal 1 binary32)) (-.f32 (*.f32 #s(literal -2 binary32) cosTheta) #s(literal 1 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (*.f32 #s(literal 2 binary32) cosTheta) #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (fma.f32 (*.f32 #s(literal 2 binary32) cosTheta) (*.f32 #s(literal 2 binary32) cosTheta) (*.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)))))
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c
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#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) c)
#s(approx (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (*.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) c)) 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))))) (/.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 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c))
#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 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)))) c))
#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 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) c)) c))
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) c)
#s(approx (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (*.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) c)) c))
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c)
#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (neg.f32 (/.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (-.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32))) c)))
#s(approx (/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (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 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (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 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (-.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32))) 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 (+ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 1) (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 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (neg.f32 (*.f32 (-.f32 (neg.f32 (*.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))) #s(literal 1 binary32)) c)))

eval62.0ms (1.6%)

Memory
-9.1MiB live, 132.6MiB allocated; 12ms collecting garbage
Compiler

Compiled 36 881 to 3 027 computations (91.8% saved)

prune39.0ms (1%)

Memory
1.5MiB live, 95.6MiB allocated; 4ms collecting garbage
Pruning

31 alts after pruning (25 fresh and 6 done)

PrunedKeptTotal
New5969605
Fresh11617
Picked325
Done044
Total60031631
Accuracy
100.0%
Counts
631 → 31
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.0%
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ c 1) #s(literal 1 binary32))))
97.4%
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
95.8%
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
98.6%
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 #s(approx (+ (* -2 cosTheta) 1) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
98.5%
(/.f32 #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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
98.1%
(/.f32 #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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
98.1%
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)))
97.3%
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
97.8%
(/.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))))
95.1%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
97.8%
(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
96.7%
(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
✓95.1%
(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) c) #s(literal 1 binary32))))
✓97.5%
(/.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))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
96.8%
(/.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 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (/.f32 (-.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (*.f32 (PI.f32) #s(literal 2 binary32))) (*.f32 (PI.f32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
94.9%
(/.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 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
97.6%
(/.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 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) cosTheta)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
51.8%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))))
92.2%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32))))
✓10.6%
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
92.5%
(/.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))))))
✓4.9%
(/.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)))
95.6%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
95.6%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
95.5%
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32) (*.f32 (*.f32 (neg.f32 cosTheta) (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32))) (PI.f32))) cosTheta))
95.7%
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
✓95.6%
#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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.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 (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (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 3 881 to 1 287 computations (66.8% saved)

regimes91.0ms (2.4%)

Memory
27.0MiB live, 173.6MiB allocated; 18ms collecting garbage
Counts
56 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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) (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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) cosTheta) 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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 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)))) (+.f32 (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) cosTheta)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) 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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (/.f32 (-.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (*.f32 (PI.f32) #s(literal 2 binary32))) (*.f32 (PI.f32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #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 (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 #s(approx (+ (* -2 cosTheta) 1) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32) (*.f32 (*.f32 (neg.f32 cosTheta) (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32))) (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (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) (* (* (/ 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 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))))
(/.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 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.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) #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))))
(/.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)) (+.f32 (cosh.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sinh.f32 (*.f32 (neg.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 (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))))))))
Outputs
(/.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)))))
Calls

6 calls:

22.0ms
(+.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))))
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)))
14.0ms
cosTheta
14.0ms
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
98.7%1(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
98.7%1(+.f32 #s(literal 1 binary32) c)
98.7%1(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
98.7%1(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.7%1cosTheta
98.7%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes79.0ms (2.1%)

Memory
-24.1MiB live, 165.6MiB allocated; 9ms collecting garbage
Counts
51 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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) (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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) cosTheta) 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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 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)))) (+.f32 (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) cosTheta)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) 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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (/.f32 (-.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (*.f32 (PI.f32) #s(literal 2 binary32))) (*.f32 (PI.f32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #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 (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 #s(approx (+ (* -2 cosTheta) 1) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32) (*.f32 (*.f32 (neg.f32 cosTheta) (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32))) (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (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) (* (* (/ 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 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))))
(/.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 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
Calls

6 calls:

14.0ms
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)))
13.0ms
(+.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
98.6%1(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
98.6%1(+.f32 #s(literal 1 binary32) c)
98.6%1(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
98.6%1(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.6%1cosTheta
98.6%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes76.0ms (2%)

Memory
23.4MiB live, 166.6MiB allocated; 6ms 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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) (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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) cosTheta) 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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 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)))) (+.f32 (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) cosTheta)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) 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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (/.f32 (-.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (*.f32 (PI.f32) #s(literal 2 binary32))) (*.f32 (PI.f32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #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 (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 #s(approx (+ (* -2 cosTheta) 1) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32) (*.f32 (*.f32 (neg.f32 cosTheta) (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32))) (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (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) (* (* (/ 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 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (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))))
(/.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 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) c) #s(literal 1 binary32))))
Outputs
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 #s(approx (+ (* -2 cosTheta) 1) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
Calls

6 calls:

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)))
13.0ms
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
13.0ms
cosTheta
12.0ms
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)))))
Results
AccuracySegmentsBranch
98.6%1(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
98.6%1(+.f32 #s(literal 1 binary32) c)
98.6%1(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
98.6%1(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.6%1cosTheta
98.6%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes69.0ms (1.8%)

Memory
23.5MiB live, 150.3MiB allocated; 13ms collecting garbage
Counts
39 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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) (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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) cosTheta) 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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 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)))) (+.f32 (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) cosTheta)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) 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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (/.f32 (-.f32 (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (*.f32 (PI.f32) #s(literal 2 binary32))) (*.f32 (PI.f32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #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 (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
Outputs
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
Calls

6 calls:

14.0ms
(+.f32 #s(literal 1 binary32) 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)))))
11.0ms
c
10.0ms
(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
10.0ms
(+.f32 (+.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
98.5%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)))
98.5%1(+.f32 #s(literal 1 binary32) c)
98.5%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))))
98.5%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)))))
98.5%1cosTheta
98.5%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes91.0ms (2.4%)

Memory
-15.5MiB live, 166.0MiB allocated; 45ms 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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) (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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) cosTheta) 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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 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)))) (+.f32 (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) cosTheta)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
Outputs
(/.f32 #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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
Calls

6 calls:

20.0ms
(*.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)))
18.0ms
(+.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))))
18.0ms
cosTheta
17.0ms
c
9.0ms
(/.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
98.5%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)))
98.5%1(+.f32 #s(literal 1 binary32) c)
98.5%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))))
98.5%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)))))
98.5%1cosTheta
98.5%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes125.0ms (3.3%)

Memory
32.5MiB live, 83.8MiB allocated; 104ms collecting garbage
Counts
31 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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) (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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (fma.f32 #s(literal -1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
Outputs
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
Calls

6 calls:

85.0ms
(/.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
c
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
(*.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
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)

regimes51.0ms (1.4%)

Memory
-20.7MiB live, 78.6MiB allocated; 13ms 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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) (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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)))
Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) c) #s(literal 1 binary32)))
Calls

6 calls:

13.0ms
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))))
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 #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
cosTheta
Results
AccuracySegmentsBranch
98.1%1(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
98.1%1(+.f32 #s(literal 1 binary32) c)
98.1%1(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
98.1%1(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.1%1cosTheta
98.1%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes47.0ms (1.3%)

Memory
-18.2MiB live, 77.3MiB allocated; 7ms 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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) (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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ c 1) #s(literal 1 binary32))))
Outputs
(/.f32 #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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
Calls

6 calls:

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)))
8.0ms
cosTheta
8.0ms
c
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 #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
98.1%1(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
98.1%1(+.f32 #s(literal 1 binary32) c)
98.1%1(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
98.1%1(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
98.1%1cosTheta
98.1%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes42.0ms (1.1%)

Memory
26.5MiB live, 72.8MiB allocated; 2ms collecting garbage
Counts
26 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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) (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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
Calls

6 calls:

8.0ms
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
7.0ms
c
7.0ms
(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
7.0ms
(/.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
cosTheta
Results
AccuracySegmentsBranch
97.5%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)))
97.5%1(+.f32 #s(literal 1 binary32) c)
97.5%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))))
97.5%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)))))
97.5%1cosTheta
97.5%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes38.0ms (1%)

Memory
16.8MiB live, 63.0MiB allocated; 3ms collecting garbage
Counts
23 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #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) (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 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) cosTheta)) c) #s(literal 1 binary32))))
Outputs
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
Calls

6 calls:

7.0ms
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
c
6.0ms
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
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)))))
Results
AccuracySegmentsBranch
97.4%1(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
97.4%1(+.f32 #s(literal 1 binary32) c)
97.4%1(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
97.4%1(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
97.4%1cosTheta
97.4%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes34.0ms (0.9%)

Memory
-37.8MiB live, 57.5MiB allocated; 6ms collecting garbage
Counts
19 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) 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 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #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))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (- (* (+ (* -1/6 (* cosTheta cosTheta)) 1/2) (* cosTheta cosTheta)) 1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #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 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c) #s(literal 1 binary32))))
Calls

6 calls:

6.0ms
cosTheta
6.0ms
(+.f32 #s(literal 1 binary32) c)
5.0ms
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
5.0ms
(*.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)))
5.0ms
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
Results
AccuracySegmentsBranch
96.7%1(+.f32 #s(literal 1 binary32) c)
96.7%1c
96.7%1(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
96.7%1(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
96.7%1(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
96.7%1cosTheta
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes26.0ms (0.7%)

Memory
-2.7MiB live, 43.8MiB allocated; 2ms collecting garbage
Counts
14 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
#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 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (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)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) 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)))) (fma.f32 (/.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (+.f32 c #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (*.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
Calls

6 calls:

5.0ms
(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
4.0ms
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
4.0ms
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
4.0ms
c
4.0ms
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%1c
95.7%1(+.f32 #s(literal 1 binary32) c)
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes18.0ms (0.5%)

Memory
36.7MiB live, 36.7MiB allocated; 0ms collecting garbage
Counts
9 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
Outputs
#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 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
Calls

6 calls:

3.0ms
(+.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))))
3.0ms
(*.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)))
3.0ms
(/.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)))))
3.0ms
c
3.0ms
cosTheta
Results
AccuracySegmentsBranch
95.6%1(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
95.6%1(+.f32 #s(literal 1 binary32) c)
95.6%1(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
95.6%1(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
95.6%1cosTheta
95.6%1c
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes16.0ms (0.4%)

Memory
-16.6MiB live, 29.6MiB allocated; 2ms collecting garbage
Counts
7 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) 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 (/.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(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32))))
Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
Calls

6 calls:

4.0ms
(+.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))))
3.0ms
(/.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)))))
3.0ms
(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
2.0ms
c
2.0ms
cosTheta
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%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))))
93.2%1(+.f32 #s(literal 1 binary32) c)
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes8.0ms (0.2%)

Memory
18.7MiB live, 18.7MiB allocated; 0ms collecting garbage
Counts
2 → 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))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) 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 #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) c) #s(literal 1 binary32))))
Calls

6 calls:

2.0ms
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
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
(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
1.0ms
c
1.0ms
cosTheta
Results
AccuracySegmentsBranch
10.6%1(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
10.6%1cosTheta
10.6%1(+.f32 #s(literal 1 binary32) c)
10.6%1c
10.6%1(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
10.6%1(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes7.0ms (0.2%)

Memory
-30.8MiB live, 16.0MiB allocated; 2ms 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:

2.0ms
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
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
(*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
1.0ms
c
1.0ms
cosTheta
Results
AccuracySegmentsBranch
4.9%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)))
4.9%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))))
4.9%1c
4.9%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)))))
4.9%1cosTheta
4.9%1(+.f32 #s(literal 1 binary32) c)
Compiler

Compiled 72 to 58 computations (19.4% saved)

derivations304.0ms (8.1%)

Memory
15.1MiB live, 296.5MiB allocated; 70ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 610 to 128 computations (79% saved)

preprocess54.0ms (1.4%)

Memory
22.6MiB live, 113.6MiB allocated; 12ms collecting garbage
Compiler

Compiled 1 270 to 292 computations (77% saved)

end0.0ms (0%)

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

Profiling

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