GTR1 distribution

Time bar (total: 7.5s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze69.0ms (0.9%)

Memory
0.8MiB live, 146.5MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%0.6%99.4%0%0%0%0
0%0%0.6%99.4%0%0%0%1
0%0%0.6%99.4%0%0%0%2
0%0%0.6%99.4%0%0%0%3
0%0%0.6%99.4%0%0%0%4
50%0.3%0.3%99.4%0%0%0%5
50%0.3%0.3%99.4%0%0%0%6
75%0.5%0.2%99.4%0%0%0%7
75%0.5%0.2%99.4%0%0%0%8
87.5%0.6%0.1%99.4%0%0%0%9
87.5%0.6%0.1%99.4%0%0%0%10
93.7%0.6%0%99.4%0%0%0%11
93.7%0.6%0%99.4%0%0%0%12
Compiler

Compiled 40 to 23 computations (42.5% saved)

sample1.5s (20%)

Memory
37.8MiB live, 2 364.3MiB allocated
Samples
1.1s8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 885.0ms
ival-mult: 290.0ms (32.8% of total)
const: 140.0ms (15.8% of total)
ival-log: 99.0ms (11.2% of total)
ival-div: 95.0ms (10.7% of total)
ival-<=: 89.0ms (10.1% of total)
ival-add: 56.0ms (6.3% of total)
ival-sub: 42.0ms (4.7% of total)
ival-pi: 36.0ms (4.1% of total)
ival-and: 24.0ms (2.7% of total)
exact: 11.0ms (1.2% of total)
ival-assert: 3.0ms (0.3% of total)
Bogosity

explain179.0ms (2.4%)

Memory
9.2MiB live, 336.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
00-0-(PI.f32)
00-0-#s(literal 1 binary32)
00-0-cosTheta
00-0-alpha
00-0-(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
00-0-(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
00-0-(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
00-0-(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
00-0-(log.f32 (*.f32 alpha alpha))
00-0-(*.f32 alpha alpha)
00-0-(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
00-0-(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) 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
66.0ms512×0valid
Compiler

Compiled 212 to 43 computations (79.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 39.0ms
ival-mult: 19.0ms (48.8% of total)
ival-log: 6.0ms (15.4% of total)
ival-add: 5.0ms (12.8% of total)
ival-div: 4.0ms (10.3% of total)
ival-pi: 2.0ms (5.1% of total)
ival-sub: 2.0ms (5.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess243.0ms (3.3%)

Memory
26.0MiB live, 445.2MiB allocated
Algorithm
egg-herbie
Rules
5 554×lower-fma.f64
5 554×lower-fma.f32
3 140×lower-*.f64
3 130×lower-*.f32
2 428×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035130
1163122
2697120
34004120
01324
02324
15624
220524
398524
4439824
0861121
Stop Event
iter limit
node limit
iter limit
node limit
Calls
Call 1
Inputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (PI.f32))))
Symmetry

(abs alpha)

(abs cosTheta)

Compiler

Compiled 26 to 13 computations (50% saved)

eval0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
2.4MiB live, 2.4MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
Compiler

Compiled 26 to 13 computations (50% saved)

simplify205.0ms (2.7%)

Memory
-19.5MiB live, 392.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f32 alpha alpha)
cost-diff0
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff64
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
cost-diff64
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
Rules
5 554×lower-fma.f64
5 554×lower-fma.f32
3 140×lower-*.f64
3 130×lower-*.f32
2 428×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01391
02391
15691
220591
398591
4439891
0861181
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
cosTheta
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (PI.f32))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(*.f32 (log.f32 (*.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (PI.f32)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
cosTheta

localize66.0ms (0.9%)

Memory
-12.8MiB live, 65.2MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.13671875
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
accuracy0.203125
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
accuracy0.3046875
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
accuracy0.3662300293053261
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
Samples
24.0ms256×0valid
Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.0ms
ival-mult: 8.0ms (49.6% of total)
ival-log: 3.0ms (18.6% of total)
ival-div: 2.0ms (12.4% of total)
ival-pi: 1.0ms (6.2% of total)
ival-add: 1.0ms (6.2% of total)
ival-sub: 1.0ms (6.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series53.0ms (0.7%)

Memory
22.8MiB live, 103.7MiB allocated
Counts
7 → 132
Calls
Call 1
Inputs
#<alt (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))>
#<alt (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))>
#<alt (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))>
#<alt (*.f32 alpha alpha)>
#<alt (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))>
#<alt (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)>
#<alt (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)>
Outputs
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (+ 1 (* -1 (pow cosTheta 2)))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt 1>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))>
#<alt (- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))>
#<alt (/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))>
#<alt (- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -1 cosTheta)>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
Calls

33 calls:

TimeVariablePointExpression
33.0ms
alpha
@0
(* (PI) (log (* alpha alpha)))
6.0ms
alpha
@inf
(* (PI) (log (* alpha alpha)))
2.0ms
alpha
@0
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms
alpha
@inf
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms
alpha
@-inf
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

simplify301.0ms (4%)

Memory
-71.5MiB live, 453.7MiB allocated
Algorithm
egg-herbie
Rules
4 812×lower-fma.f64
4 812×lower-fma.f32
4 528×lower-*.f64
4 528×lower-*.f32
2 768×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01972350
16582266
230532248
084832101
Stop Event
iter limit
node limit
Counts
132 → 132
Calls
Call 1
Inputs
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* -1 (pow cosTheta 2))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
Outputs
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(+ 1 (* -1 (pow cosTheta 2)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow alpha 2) (pow cosTheta 2))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(* (pow alpha 2) (pow cosTheta 2))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
1
#s(literal 1 binary32)
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
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(/.f32 #s(literal 1 binary32) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 #s(literal -1 binary32) (*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (*.f32 alpha alpha))) (*.f32 (*.f32 cosTheta cosTheta) (PI.f32))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (*.f32 alpha alpha)))) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (*.f32 alpha alpha))) (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/.f32 (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (*.f32 alpha alpha)))) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (*.f32 alpha alpha))) (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))) (/.f32 #s(literal -1 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (pow.f32 cosTheta #s(literal 6 binary32)))))) (*.f32 cosTheta cosTheta))
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(* 2 (* (PI) (log alpha)))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* 2 (* (PI) (log alpha)))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* 2 (* (PI) (log alpha)))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* 2 (* (PI) (log alpha)))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (neg.f32 (log.f32 alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (neg.f32 (log.f32 alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (neg.f32 (log.f32 alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (neg.f32 (log.f32 alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -1 cosTheta)
(neg.f32 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* (pow alpha 2) cosTheta)
(*.f32 alpha (*.f32 alpha cosTheta))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 (*.f32 alpha alpha) (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 (*.f32 alpha alpha) (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 (*.f32 alpha alpha) (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))
(* (pow alpha 2) cosTheta)
(*.f32 alpha (*.f32 alpha cosTheta))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 (*.f32 alpha alpha) (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 (*.f32 alpha alpha) (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 (*.f32 alpha alpha) (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow alpha 2) (pow cosTheta 2))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta (neg.f32 (/.f32 cosTheta (*.f32 alpha alpha))) (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta (neg.f32 (/.f32 cosTheta (*.f32 alpha alpha))) (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta (neg.f32 (/.f32 cosTheta (*.f32 alpha alpha))) (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (pow cosTheta 2))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta (neg.f32 (/.f32 cosTheta (*.f32 alpha alpha))) (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta (neg.f32 (/.f32 cosTheta (*.f32 alpha alpha))) (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta (neg.f32 (/.f32 cosTheta (*.f32 alpha alpha))) (*.f32 cosTheta cosTheta)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))

rewrite403.0ms (5.4%)

Memory
23.9MiB live, 502.1MiB allocated
Rules
5 214×lower-*.f64
5 204×lower-*.f32
4 464×lower-fma.f64
4 464×lower-fma.f32
4 218×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01365
02365
110365
284263
0849355
Stop Event
iter limit
node limit
iter limit
Counts
7 → 631
Calls
Call 1
Inputs
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(*.f32 alpha alpha)
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
Outputs
(neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(+.f32 (/.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(+.f32 (/.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(+.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal -1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(+.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(+.f32 (neg.f32 (neg.f32 (*.f32 alpha alpha))) #s(literal -1 binary32))
(+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32)))
(+.f32 (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)))
(+.f32 (*.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(+.f32 (*.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (+.f32 #s(literal -1 binary32) (neg.f32 alpha)))
(+.f32 (*.f32 alpha (+.f32 alpha #s(literal -1 binary32))) (*.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32))))
(+.f32 (*.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32))) (*.f32 alpha (+.f32 alpha #s(literal -1 binary32))))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal -1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) (neg.f32 alpha)))
(fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) (*.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32))))
(fma.f32 (*.f32 alpha alpha) #s(literal 1 binary32) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32)) (*.f32 alpha (+.f32 alpha #s(literal -1 binary32))))
(fma.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(fma.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal -1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(fma.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (+.f32 alpha #s(literal 1 binary32)) alpha (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32)))
(fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (*.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(fma.f32 (exp.f32 (log.f32 alpha)) (exp.f32 (log.f32 alpha)) #s(literal -1 binary32))
(fma.f32 (/.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(fma.f32 (/.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (/.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(fma.f32 (/.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (/.f32 (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 alpha #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(fma.f32 (/.f32 (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 alpha #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(-.f32 #s(literal 0 binary32) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(-.f32 #s(literal -1 binary32) (neg.f32 (*.f32 alpha alpha)))
(-.f32 (/.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(-.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))
(/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32)))))
(/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (neg.f32 (neg.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (neg.f32 (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))) (neg.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32)))
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(/.f32 (*.f32 cosTheta (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (*.f32 cosTheta (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (*.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) cosTheta) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (neg.f32 (*.f32 cosTheta (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)))) (neg.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (*.f32 cosTheta (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)))) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (neg.f32 (*.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) cosTheta)) (neg.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (+.f32 (pow.f32 (*.f32 cosTheta (*.f32 alpha alpha)) #s(literal 3 binary32)) (pow.f32 (*.f32 cosTheta #s(literal -1 binary32)) #s(literal 3 binary32))) (fma.f32 (*.f32 cosTheta (*.f32 alpha alpha)) (*.f32 cosTheta (*.f32 alpha alpha)) (-.f32 (*.f32 (*.f32 cosTheta #s(literal -1 binary32)) (*.f32 cosTheta #s(literal -1 binary32))) (*.f32 (*.f32 cosTheta (*.f32 alpha alpha)) (*.f32 cosTheta #s(literal -1 binary32))))))
(/.f32 (+.f32 (pow.f32 (*.f32 (*.f32 alpha alpha) cosTheta) #s(literal 3 binary32)) (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32))) (fma.f32 (*.f32 (*.f32 alpha alpha) cosTheta) (*.f32 (*.f32 alpha alpha) cosTheta) (-.f32 (*.f32 (neg.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (*.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)))))
(/.f32 (-.f32 (*.f32 (*.f32 cosTheta (*.f32 alpha alpha)) (*.f32 cosTheta (*.f32 alpha alpha))) (*.f32 (*.f32 cosTheta #s(literal -1 binary32)) (*.f32 cosTheta #s(literal -1 binary32)))) (-.f32 (*.f32 cosTheta (*.f32 alpha alpha)) (*.f32 cosTheta #s(literal -1 binary32))))
(/.f32 (-.f32 (*.f32 (*.f32 (*.f32 alpha alpha) cosTheta) (*.f32 (*.f32 alpha alpha) cosTheta)) (*.f32 (neg.f32 cosTheta) (neg.f32 cosTheta))) (-.f32 (*.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)))
(*.f32 #s(literal 1 binary32) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 cosTheta #s(literal 1 binary32)))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (neg.f32 (neg.f32 cosTheta)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (neg.f32 cosTheta))
(*.f32 #s(literal -1 binary32) (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(*.f32 (+.f32 alpha #s(literal 1 binary32)) (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta))
(*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(*.f32 (fma.f32 alpha cosTheta cosTheta) (+.f32 alpha #s(literal -1 binary32)))
(*.f32 (*.f32 cosTheta (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(*.f32 (*.f32 cosTheta (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(*.f32 (*.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(*.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(*.f32 (/.f32 cosTheta (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) #s(literal 1 binary32)))
(*.f32 (neg.f32 (neg.f32 cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(neg.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta (neg.f32 cosTheta))))
(+.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 cosTheta cosTheta)))
(+.f32 (*.f32 cosTheta (*.f32 cosTheta (*.f32 alpha alpha))) (*.f32 cosTheta (*.f32 cosTheta #s(literal -1 binary32))))
(+.f32 (*.f32 cosTheta (*.f32 (*.f32 alpha alpha) cosTheta)) (*.f32 cosTheta (neg.f32 cosTheta)))
(+.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha alpha)) (*.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(+.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha alpha)))
(+.f32 (*.f32 (*.f32 cosTheta (*.f32 alpha alpha)) cosTheta) (*.f32 (*.f32 cosTheta #s(literal -1 binary32)) cosTheta))
(+.f32 (*.f32 (*.f32 (*.f32 alpha alpha) cosTheta) cosTheta) (*.f32 cosTheta (neg.f32 cosTheta)))
(+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 cosTheta cosTheta)) (*.f32 cosTheta (neg.f32 cosTheta)))
(fma.f32 (*.f32 alpha alpha) (*.f32 cosTheta cosTheta) (*.f32 cosTheta (neg.f32 cosTheta)))
(fma.f32 cosTheta (neg.f32 cosTheta) (*.f32 (*.f32 alpha alpha) (*.f32 cosTheta cosTheta)))
(fma.f32 cosTheta (*.f32 cosTheta (*.f32 alpha alpha)) (*.f32 cosTheta (*.f32 cosTheta #s(literal -1 binary32))))
(fma.f32 cosTheta (*.f32 (*.f32 alpha alpha) cosTheta) (*.f32 cosTheta (neg.f32 cosTheta)))
(fma.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta) (*.f32 (*.f32 alpha alpha) (*.f32 cosTheta cosTheta)))
(fma.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha alpha) (*.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha alpha)))
(fma.f32 (neg.f32 cosTheta) cosTheta (*.f32 (*.f32 alpha alpha) (*.f32 cosTheta cosTheta)))
(fma.f32 (*.f32 cosTheta (*.f32 alpha alpha)) cosTheta (*.f32 (*.f32 cosTheta #s(literal -1 binary32)) cosTheta))
(fma.f32 (*.f32 (*.f32 alpha alpha) cosTheta) cosTheta (*.f32 cosTheta (neg.f32 cosTheta)))
(-.f32 #s(literal 0 binary32) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta (neg.f32 cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
(/.f32 (*.f32 cosTheta cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 (*.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (neg.f32 (*.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) (neg.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))
(*.f32 #s(literal 1 binary32) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (neg.f32 (*.f32 cosTheta (neg.f32 cosTheta))))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) (neg.f32 (neg.f32 cosTheta)))
(*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32))
(*.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 cosTheta (neg.f32 cosTheta)))
(*.f32 #s(literal -1 binary32) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta (neg.f32 cosTheta))))
(*.f32 (+.f32 alpha #s(literal 1 binary32)) (*.f32 (+.f32 alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))
(*.f32 (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) (neg.f32 cosTheta))
(*.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (neg.f32 cosTheta) (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(*.f32 (*.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(*.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(*.f32 (neg.f32 (neg.f32 cosTheta)) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))

eval184.0ms (2.5%)

Memory
-2.7MiB live, 144.0MiB allocated
Compiler

Compiled 35 719 to 2 786 computations (92.2% saved)

prune269.0ms (3.6%)

Memory
0.6MiB live, 280.7MiB allocated
Pruning

30 alts after pruning (30 fresh and 0 done)

PrunedKeptTotal
New87130901
Fresh000
Picked101
Done000
Total87230902
Accuracy
99.8%
Counts
902 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.5%
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
-0.0%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
98.2%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
97.8%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.3%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
97.9%
(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.0%
(/.f32 (/.f32 (-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.1%
(/.f32 (/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
97.8%
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
97.6%
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
97.9%
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.0%
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (/.f32 (+.f32 (pow.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32)) (-.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32))) (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32))))))
96.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
98.5%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
93.1%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.1%
(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.1%
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
65.3%
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
95.7%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
97.1%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))))
93.0%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
1.9%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
65.3%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
Compiler

Compiled 2 180 to 1 024 computations (53% saved)

simplify11.0ms (0.1%)

Memory
14.7MiB live, 14.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
cost-diff0
(*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
cost-diff0
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
cost-diff0
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff0
(*.f32 alpha alpha)
cost-diff0
(fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))
cost-diff0
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
cost-diff0
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff0
(*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
cost-diff0
(*.f32 alpha alpha)
cost-diff0
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff0
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff0
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
cost-diff0
(*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff0
(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff0
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
cost-diff0
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
cost-diff0
(*.f32 alpha alpha)
cost-diff0
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff0
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
Rules
38×lower-*.f64
30×lift-*.f32
22×lower-+.f64
18×lift-fma.f32
18×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050588
092588
Stop Event
iter limit
iter limit
unsound
iter limit
Calls
Call 1
Inputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
cosTheta
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(*.f32 cosTheta cosTheta)
cosTheta
#s(literal 1 binary32)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
#s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(PI.f32)
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(log.f32 alpha)
#s(literal 2 binary32)
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
cosTheta
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal -1 binary32)
(fma.f32 alpha alpha #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
alpha
(*.f32 alpha alpha)
#s(literal -1 binary32)
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))
(fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32)))
(+.f32 alpha #s(literal 1 binary32))
(fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))
(-.f32 #s(literal 1 binary32) alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
cosTheta
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(*.f32 cosTheta cosTheta)
cosTheta
#s(literal 1 binary32)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
#s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(PI.f32)
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(log.f32 alpha)
#s(literal 2 binary32)
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
cosTheta
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal -1 binary32)
(fma.f32 alpha alpha #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
alpha
(*.f32 alpha alpha)
#s(literal -1 binary32)
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))
(fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32)))
(+.f32 alpha #s(literal 1 binary32))
(fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))
(-.f32 #s(literal 1 binary32) alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta

localize270.0ms (3.6%)

Memory
-1.8MiB live, 234.9MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
accuracy0
(*.f32 alpha alpha)
accuracy0
(log.f32 (*.f32 alpha alpha))
accuracy29.987880231027383
(PI.f32)
accuracy0
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
accuracy0
(*.f32 alpha alpha)
accuracy0
(log.f32 (*.f32 alpha alpha))
accuracy29.987880231027383
(PI.f32)
accuracy0
(*.f32 alpha alpha)
accuracy0
(log.f32 alpha)
accuracy0
#s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
accuracy29.987880231027383
(PI.f32)
accuracy0
(*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
accuracy0
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
accuracy0
(*.f32 cosTheta cosTheta)
accuracy29.987880231027383
(PI.f32)
accuracy0
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
accuracy0
(*.f32 alpha alpha)
accuracy0
(log.f32 (*.f32 alpha alpha))
accuracy29.987880231027383
(PI.f32)
Samples
145.0ms256×0invalid
Compiler

Compiled 607 to 50 computations (91.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 85.0ms
ival-mult: 29.0ms (34.2% of total)
ival-div: 22.0ms (25.9% of total)
ival-log: 17.0ms (20% of total)
ival-add: 12.0ms (14.2% of total)
ival-sub: 2.0ms (2.4% of total)
ival-pi: 1.0ms (1.2% of total)
exact: 1.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series148.0ms (2%)

Memory
-4.6MiB live, 112.9MiB allocated
Counts
24 → 324
Calls
Call 1
Inputs
#<alt (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))>
#<alt (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))>
#<alt (*.f32 alpha alpha)>
#<alt (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))>
#<alt (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))>
#<alt (fma.f32 alpha alpha #s(literal -1 binary32))>
#<alt (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))>
#<alt (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))>
#<alt (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))>
#<alt (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))>
#<alt (/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))>
#<alt (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))>
#<alt (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))>
#<alt (/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))>
#<alt (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))>
#<alt (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))>
#<alt (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))>
#<alt (PI.f32)>
#<alt (log.f32 (*.f32 alpha alpha))>
#<alt (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))>
#<alt (*.f32 cosTheta cosTheta)>
#<alt (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))>
#<alt #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))>
#<alt (log.f32 alpha)>
Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))>
#<alt (- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))>
#<alt (/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))>
#<alt (- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (PI) (log (pow alpha 2)))>
#<alt (+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (+ 1 (* -1 (pow cosTheta 2)))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt 1>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
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#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (* -1 (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (pow alpha 4))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
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#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
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#<alt (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))>
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#<alt (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))>
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#<alt (/ (- (+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 4)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 4)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt -1>
#<alt (- (pow alpha 6) 1)>
#<alt (- (pow alpha 6) 1)>
#<alt (- (pow alpha 6) 1)>
#<alt (pow alpha 6)>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (pow alpha 6)>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt -1>
#<alt (- (pow alpha 3) 1)>
#<alt (- (pow alpha 3) 1)>
#<alt (- (pow alpha 3) 1)>
#<alt (pow alpha 3)>
#<alt (* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))>
#<alt (* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))>
#<alt (* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))>
#<alt (pow alpha 3)>
#<alt (* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))>
#<alt (* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))>
#<alt (* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
Calls

93 calls:

TimeVariablePointExpression
48.0ms
cosTheta
@0
(* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))
33.0ms
cosTheta
@0
(/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ (* alpha alpha) (- 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
24.0ms
alpha
@-inf
(log alpha)
6.0ms
alpha
@inf
(log alpha)
6.0ms
alpha
@0
(log alpha)

simplify763.0ms (10.2%)

Memory
1.7MiB live, 520.6MiB allocated
Algorithm
egg-herbie
Rules
7 332×lower-fma.f64
7 332×lower-fma.f32
6 190×lower-*.f64
6 190×lower-*.f32
3 708×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055110087
120789355
093008962
Stop Event
iter limit
node limit
Counts
324 → 324
Calls
Call 1
Inputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
-1
(- (pow alpha 6) 1)
(- (pow alpha 6) 1)
(- (pow alpha 6) 1)
(pow alpha 6)
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(pow alpha 6)
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
-1
(- (pow alpha 3) 1)
(- (pow alpha 3) 1)
(- (pow alpha 3) 1)
(pow alpha 3)
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(pow alpha 3)
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(log alpha)
(log alpha)
(log alpha)
(log alpha)
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (*.f32 alpha alpha) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (*.f32 alpha alpha) (+.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha alpha)) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (*.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (fma.f32 (*.f32 alpha alpha) (-.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (pow.f32 cosTheta #s(literal 4 binary32))) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (*.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 #s(literal -1/2 binary32) (neg.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (log.f32 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha)))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (neg.f32 (log.f32 alpha))))) (/.f32 #s(literal 1/2 binary32) (neg.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (log.f32 alpha)))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(fma.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (neg.f32 (/.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (neg.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (*.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (neg.f32 (log.f32 alpha))))) (*.f32 (*.f32 cosTheta cosTheta) (pow.f32 alpha #s(literal 4 binary32))))) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha)))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (neg.f32 (log.f32 alpha))))) (/.f32 #s(literal 1/2 binary32) (neg.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (log.f32 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(-.f32 (fma.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (/.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (neg.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (*.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (neg.f32 (log.f32 alpha))))) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha))))) (fma.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (neg.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (*.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (neg.f32 (log.f32 alpha))))) (*.f32 (*.f32 cosTheta cosTheta) (pow.f32 alpha #s(literal 4 binary32)))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (neg.f32 (log.f32 alpha))))) (/.f32 #s(literal 1/2 binary32) (neg.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (log.f32 alpha))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(fma.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (*.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))) (*.f32 (*.f32 cosTheta cosTheta) (pow.f32 alpha #s(literal 4 binary32)))) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(-.f32 (fma.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (*.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))) (fma.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (*.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))) (*.f32 (*.f32 cosTheta cosTheta) (pow.f32 alpha #s(literal 4 binary32)))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 (*.f32 cosTheta cosTheta) (/.f32 (neg.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) (/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (neg.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 (neg.f32 (*.f32 cosTheta cosTheta)) (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))) (/.f32 (neg.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/.f32 #s(literal 1 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
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-1
#s(literal -1 binary32)
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#s(literal 1 binary32)
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(/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (*.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))))
(/ (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))
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(/ (- (+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))
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(/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 4)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))
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-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
-1
#s(literal -1 binary32)
(- (pow alpha 6) 1)
(+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal -1 binary32))
(- (pow alpha 6) 1)
(+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal -1 binary32))
(- (pow alpha 6) 1)
(+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal -1 binary32))
(pow alpha 6)
(pow.f32 alpha #s(literal 6 binary32))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(pow alpha 6)
(pow.f32 alpha #s(literal 6 binary32))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
-1
#s(literal -1 binary32)
(- (pow alpha 3) 1)
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
(- (pow alpha 3) 1)
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
(- (pow alpha 3) 1)
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(*.f32 (*.f32 alpha (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha (*.f32 alpha alpha)))))
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(*.f32 (*.f32 alpha (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha (*.f32 alpha alpha)))))
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(*.f32 (*.f32 alpha (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha (*.f32 alpha alpha)))))
(pow alpha 3)
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(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(*.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) (neg.f32 (*.f32 alpha (*.f32 alpha alpha))))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
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(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(*.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) (neg.f32 (*.f32 alpha (*.f32 alpha alpha))))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))

rewrite60.0ms (0.8%)

Memory
13.0MiB live, 49.5MiB allocated
Rules
38×lower-*.f64
30×lift-*.f32
22×lower-+.f64
18×lift-fma.f32
18×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050329
092329
Stop Event
iter limit
iter limit
unsound
iter limit
Counts
24 → 28
Calls
Call 1
Inputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(*.f32 cosTheta cosTheta)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(log.f32 alpha)
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(+.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32))
(fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(*.f32 cosTheta cosTheta)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(log.f32 alpha)

eval125.0ms (1.7%)

Memory
2.7MiB live, 115.5MiB allocated
Compiler

Compiled 24 410 to 637 computations (97.4% saved)

prune134.0ms (1.8%)

Memory
-3.3MiB live, 188.8MiB allocated
Pruning

34 alts after pruning (34 fresh and 0 done)

PrunedKeptTotal
New61120631
Fresh111425
Picked505
Done000
Total62734661
Accuracy
99.9%
Counts
661 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.5%
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
-0.0%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
98.2%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.3%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
96.2%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
97.9%
(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
97.8%
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
97.6%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
80.6%
(/.f32 (/.f32 #s(approx (+ (* (* alpha alpha) (* alpha alpha)) -1) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
85.6%
(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.0%
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (/.f32 (+.f32 (pow.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32)) (-.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32))) (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
98.5%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
98.4%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (*.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))) (/.f32 (*.f32 (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha))) (*.f32 alpha alpha))))))
54.1%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (*.f32 alpha alpha)) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))))
93.1%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
96.5%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 #s(literal 2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
98.1%
(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.1%
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.5%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
98.6%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 #s(approx (- (* alpha alpha) 1) (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
65.3%
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
97.0%
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
92.5%
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))))
65.3%
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
92.2%
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ (* alpha alpha) (- 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (PI.f32) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
95.7%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (fma.f32 (*.f32 cosTheta cosTheta) (/.f32 (neg.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
93.0%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
1.9%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
65.3%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
Compiler

Compiled 2 200 to 1 096 computations (50.2% saved)

simplify18.0ms (0.2%)

Memory
-10.0MiB live, 32.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
cost-diff0
(/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
cost-diff0
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff64
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
cost-diff0
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
cost-diff0
(*.f32 alpha alpha)
cost-diff0
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff0
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
cost-diff0
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
cost-diff0
(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff0
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
cost-diff0
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
cost-diff0
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
cost-diff0
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff0
(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff0
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
cost-diff0
(*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
cost-diff0
(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff0
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
cost-diff0
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
Rules
40×lower-*.f64
36×lift-*.f32
20×lower-+.f64
16×lift-/.f32
16×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
063678
0106671
Stop Event
iter limit
iter limit
unsound
iter limit
Calls
Call 1
Inputs
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
#s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(PI.f32)
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(log.f32 alpha)
#s(literal 2 binary32)
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
#s(literal 1 binary32)
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
cosTheta
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
(fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
cosTheta
#s(literal 1 binary32)
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))
cosTheta
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(*.f32 cosTheta cosTheta)
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
(*.f32 alpha (*.f32 alpha alpha))
alpha
(*.f32 alpha alpha)
#s(literal -1 binary32)
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))
(fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32)))
(+.f32 alpha #s(literal 1 binary32))
(fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))
(-.f32 #s(literal 1 binary32) alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
Outputs
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
#s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(PI.f32)
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(log.f32 alpha)
#s(literal 2 binary32)
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
#s(literal 1 binary32)
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
cosTheta
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
(fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
cosTheta
#s(literal 1 binary32)
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))
cosTheta
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(*.f32 cosTheta cosTheta)
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
(*.f32 alpha (*.f32 alpha alpha))
alpha
(*.f32 alpha alpha)
#s(literal -1 binary32)
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))
(fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32)))
(+.f32 alpha #s(literal 1 binary32))
(fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))
(-.f32 #s(literal 1 binary32) alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta

localize175.0ms (2.4%)

Memory
3.1MiB live, 338.6MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f32 alpha (*.f32 alpha alpha))
accuracy0
(*.f32 alpha alpha)
accuracy0
(log.f32 (*.f32 alpha alpha))
accuracy29.987880231027383
(PI.f32)
accuracy0
(*.f32 alpha alpha)
accuracy0
(log.f32 (*.f32 alpha alpha))
accuracy0
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))
accuracy29.987880231027383
(PI.f32)
accuracy0
(*.f32 alpha alpha)
accuracy0
(log.f32 (*.f32 alpha alpha))
accuracy0
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy29.987880231027383
(PI.f32)
accuracy0
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
accuracy0
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
accuracy0
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
accuracy29.987880231027383
(PI.f32)
accuracy0
(log.f32 alpha)
accuracy0
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy0
#s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
accuracy29.987880231027383
(PI.f32)
Samples
81.0ms256×0invalid
Compiler

Compiled 610 to 49 computations (92% saved)

Precisions
Click to see histograms. Total time spent on operations: 60.0ms
ival-mult: 29.0ms (48.7% of total)
ival-add: 11.0ms (18.5% of total)
ival-div: 9.0ms (15.1% of total)
ival-log: 5.0ms (8.4% of total)
ival-sub: 3.0ms (5% of total)
ival-pi: 1.0ms (1.7% of total)
exact: 1.0ms (1.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series16.0ms (0.2%)

Memory
-5.2MiB live, 32.2MiB allocated
Counts
24 → 348
Calls
Call 1
Inputs
#<alt (/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))>
#<alt #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))>
#<alt (fma.f32 alpha alpha #s(literal -1 binary32))>
#<alt (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))>
#<alt (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))>
#<alt (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))>
#<alt #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))>
#<alt (/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))>
#<alt (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))>
#<alt (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))>
#<alt (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))>
#<alt (*.f32 alpha alpha)>
#<alt (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))>
#<alt (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))>
#<alt (/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))>
#<alt (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))>
#<alt (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))>
#<alt (PI.f32)>
#<alt #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))>
#<alt (log.f32 alpha)>
#<alt (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))>
#<alt (log.f32 (*.f32 alpha alpha))>
#<alt #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))>
#<alt (*.f32 alpha (*.f32 alpha alpha))>
Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))>
#<alt (- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))>
#<alt (/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))>
#<alt (- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
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#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
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#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))>
#<alt (* (PI) (log (pow alpha 2)))>
#<alt (+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
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#<alt (+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (+ 1 (* -1 (pow cosTheta 2)))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
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#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt 1>
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#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
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#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
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#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
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#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
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#<alt (- (* -1 (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (pow alpha 4))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 6) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
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#<alt (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))>
#<alt (+ (* -1 (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1)))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))) (/ (* (+ 1 (pow alpha 3)) (* (- (pow alpha 2) 1) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 3) 1)))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))))) (/ (* (+ 1 (pow alpha 3)) (* (- (pow alpha 2) 1) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 4)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 4)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt -1>
#<alt (- (pow alpha 6) 1)>
#<alt (- (pow alpha 6) 1)>
#<alt (- (pow alpha 6) 1)>
#<alt (pow alpha 6)>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (pow alpha 6)>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (+ 1 (* -1 (pow cosTheta 2)))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt 1>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
Calls

99 calls:

TimeVariablePointExpression
0.0ms
alpha
@-inf
(* alpha (* alpha alpha))
0.0ms
alpha
@0
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
0.0ms
alpha
@0
(/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ (* alpha alpha) (- 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
0.0ms
alpha
@-inf
(/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ (* alpha alpha) (- 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
0.0ms
alpha
@inf
(/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ (* alpha alpha) (- 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

simplify364.0ms (4.9%)

Memory
1.5MiB live, 592.6MiB allocated
Algorithm
egg-herbie
Rules
6 338×lower-fma.f64
6 338×lower-fma.f32
6 236×lower-*.f64
6 236×lower-*.f32
3 392×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04119928
115399332
087568957
Stop Event
iter limit
node limit
Counts
348 → 348
Calls
Call 1
Inputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
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(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (*.f32 alpha alpha) (fma.f32 (*.f32 alpha alpha) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (*.f32 alpha alpha) (fma.f32 (*.f32 alpha alpha) (fma.f32 (*.f32 alpha alpha) (/.f32 (*.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (pow.f32 cosTheta #s(literal 4 binary32))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 alpha alpha) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(fma.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (*.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (*.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 alpha alpha) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(fma.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (*.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32))))) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 alpha alpha) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (fma.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (*.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (*.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (fma.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (*.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(fma.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32))))) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (fma.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (*.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 (neg.f32 (*.f32 cosTheta cosTheta)) (/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 cosTheta (*.f32 cosTheta (-.f32 (/.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(fma.f32 cosTheta (*.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))) (/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))) (neg.f32 (/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/.f32 #s(literal 1 binary32) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 #s(literal -1 binary32) (*.f32 (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))) (fma.f32 alpha alpha #s(literal -1 binary32))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (*.f32 (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (fma.f32 alpha alpha #s(literal -1 binary32))))) (/.f32 #s(literal -1 binary32) (*.f32 (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))) (fma.f32 alpha alpha #s(literal -1 binary32)))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
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#s(literal -1 binary32)
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-1
#s(literal -1 binary32)
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(- (pow alpha 2) 1)
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(* (PI) (log (pow alpha 2)))
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(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
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(+ 1 (* -1 (pow cosTheta 2)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
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(* (pow alpha 2) (pow cosTheta 2))
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1
#s(literal 1 binary32)
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(* (pow cosTheta 2) (- (pow alpha 2) 1))
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(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
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(/.f32 (fma.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))) (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (-.f32 (/.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))) (/.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))) (*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 4)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))
(/.f32 (fma.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (/.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (*.f32 (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))))) (fma.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))) (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (-.f32 (/.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))) (/.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))) (*.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))))) (*.f32 cosTheta cosTheta))
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
-1
#s(literal -1 binary32)
(- (pow alpha 6) 1)
(+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal -1 binary32))
(- (pow alpha 6) 1)
(+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal -1 binary32))
(- (pow alpha 6) 1)
(+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal -1 binary32))
(pow alpha 6)
(pow.f32 alpha #s(literal 6 binary32))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(pow alpha 6)
(pow.f32 alpha #s(literal 6 binary32))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32)))))
(* 2 (* (PI) (log alpha)))
(*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(* 2 (* (PI) (log alpha)))
(*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(* 2 (* (PI) (log alpha)))
(*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(* 2 (* (PI) (log alpha)))
(*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (neg.f32 (log.f32 alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (neg.f32 (log.f32 alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (neg.f32 (log.f32 alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (neg.f32 (log.f32 alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(+ 1 (* -1 (pow cosTheta 2)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32))
(* (pow alpha 2) (pow cosTheta 2))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(* (pow alpha 2) (pow cosTheta 2))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
1
#s(literal 1 binary32)
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))

rewrite27.0ms (0.4%)

Memory
22.5MiB live, 58.0MiB allocated
Rules
40×lower-*.f64
36×lift-*.f32
20×lower-+.f64
16×lift-/.f32
16×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
063409
0106402
Stop Event
iter limit
iter limit
unsound
iter limit
Counts
24 → 26
Calls
Call 1
Inputs
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(PI.f32)
#s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(log.f32 alpha)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(log.f32 (*.f32 alpha alpha))
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))
(*.f32 alpha (*.f32 alpha alpha))
Outputs
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(PI.f32)
#s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(log.f32 alpha)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(log.f32 (*.f32 alpha alpha))
#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))
(*.f32 alpha (*.f32 alpha alpha))

eval47.0ms (0.6%)

Memory
-4.0MiB live, 113.8MiB allocated
Compiler

Compiled 22 779 to 519 computations (97.7% saved)

prune57.0ms (0.8%)

Memory
18.5MiB live, 134.6MiB allocated
Pruning

34 alts after pruning (33 fresh and 1 done)

PrunedKeptTotal
New5939602
Fresh52429
Picked415
Done000
Total60234636
Accuracy
99.9%
Counts
636 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.5%
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.3%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
96.2%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
97.8%
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
95.6%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
97.4%
(/.f32 (/.f32 (*.f32 #s(approx (+ (* alpha (* alpha alpha)) -1) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha (*.f32 alpha alpha))))))) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
80.6%
(/.f32 (/.f32 #s(approx (+ (* (* alpha alpha) (* alpha alpha)) -1) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
85.6%
(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.0%
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (/.f32 (+.f32 (pow.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32)) (-.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32))) (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
57.9%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 cosTheta (*.f32 cosTheta (+.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))))))
93.1%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
96.5%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 #s(literal 2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
98.1%
(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.1%
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.5%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
98.3%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
96.6%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
54.1%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (*.f32 alpha alpha)) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))))
93.0%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
98.2%
(/.f32 #s(approx (- (* alpha alpha) 1) (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
65.3%
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
-0.0%
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
97.0%
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
92.5%
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))))
65.3%
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
92.2%
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ (* alpha alpha) (- 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (PI.f32) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
95.7%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (fma.f32 (*.f32 cosTheta cosTheta) (/.f32 (neg.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
1.9%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
65.3%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
Compiler

Compiled 2 052 to 1 067 computations (48% saved)

simplify13.0ms (0.2%)

Memory
-26.8MiB live, 19.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
cost-diff0
(/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
cost-diff0
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
cost-diff64
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
cost-diff0
(*.f32 alpha alpha)
cost-diff0
(fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))
cost-diff0
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
cost-diff0
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
cost-diff0
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
cost-diff0
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
cost-diff0
#s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)))
cost-diff0
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
cost-diff0
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
cost-diff0
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff0
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
cost-diff0
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
cost-diff0
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))))
cost-diff0
(*.f32 alpha alpha)
cost-diff0
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff0
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
Rules
38×lower-*.f64
32×lift-*.f32
26×lower-+.f64
22×lower-fma.f64
20×lift-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057743
0104736
Stop Event
iter limit
iter limit
unsound
iter limit
Calls
Call 1
Inputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))
(/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 cosTheta cosTheta)
cosTheta
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))
(*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
#s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)))
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
alpha
(fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(fma.f32 alpha alpha #s(literal -1 binary32))
cosTheta
#s(literal 1 binary32)
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal -1 binary32)
(fma.f32 alpha alpha #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta)
(*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta)
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
cosTheta
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
(*.f32 alpha (*.f32 alpha alpha))
alpha
(*.f32 alpha alpha)
#s(literal -1 binary32)
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))
(fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32)))
(+.f32 alpha #s(literal 1 binary32))
(fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))
(-.f32 #s(literal 1 binary32) alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta)
(*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta)
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
cosTheta
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))
(/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 cosTheta cosTheta)
cosTheta
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))
(*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
#s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)))
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
alpha
(fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(fma.f32 alpha alpha #s(literal -1 binary32))
cosTheta
#s(literal 1 binary32)
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal -1 binary32)
(fma.f32 alpha alpha #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta)
(*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta)
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
cosTheta
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
(*.f32 alpha (*.f32 alpha alpha))
alpha
(*.f32 alpha alpha)
#s(literal -1 binary32)
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))
(fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32)))
(+.f32 alpha #s(literal 1 binary32))
(fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))
(-.f32 #s(literal 1 binary32) alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta)
(*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta)
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
cosTheta

localize180.0ms (2.4%)

Memory
3.8MiB live, 281.1MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f32 alpha alpha)
accuracy0
(log.f32 (*.f32 alpha alpha))
accuracy0
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
accuracy29.987880231027383
(PI.f32)
accuracy0
(*.f32 alpha alpha)
accuracy0
(log.f32 (*.f32 alpha alpha))
accuracy0
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
accuracy29.987880231027383
(PI.f32)
accuracy0
(log.f32 (*.f32 alpha alpha))
accuracy0
#s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)))
accuracy0
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
accuracy29.987880231027383
(PI.f32)
accuracy0
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
accuracy0
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
accuracy0
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
accuracy29.987880231027383
(PI.f32)
accuracy0
(*.f32 cosTheta cosTheta)
accuracy0
(*.f32 alpha alpha)
accuracy0
(log.f32 (*.f32 alpha alpha))
accuracy29.987880231027383
(PI.f32)
Samples
103.0ms256×0invalid
Compiler

Compiled 755 to 53 computations (93% saved)

Precisions
Click to see histograms. Total time spent on operations: 73.0ms
ival-mult: 37.0ms (51% of total)
ival-div: 14.0ms (19.3% of total)
ival-add: 14.0ms (19.3% of total)
ival-log: 3.0ms (4.1% of total)
ival-sub: 2.0ms (2.8% of total)
ival-pi: 1.0ms (1.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series27.0ms (0.4%)

Memory
-8.9MiB live, 33.9MiB allocated
Counts
22 → 312
Calls
Call 1
Inputs
#<alt (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))>
#<alt (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))>
#<alt (*.f32 alpha alpha)>
#<alt (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))))>
#<alt (/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))>
#<alt #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))>
#<alt (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))>
#<alt #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))>
#<alt (/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))>
#<alt #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)))>
#<alt (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))>
#<alt (/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))>
#<alt (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))>
#<alt (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))>
#<alt (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))>
#<alt (/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))>
#<alt (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))>
#<alt (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))>
#<alt (PI.f32)>
#<alt (log.f32 (*.f32 alpha alpha))>
#<alt (*.f32 cosTheta cosTheta)>
#<alt #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))>
Outputs
#<alt (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1)))))>
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#<alt (- (+ (* -1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (+ (* -2 (/ (- (* -1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (pow alpha 4))) (+ (* -1/2 (/ (- (pow cosTheta 4) 1) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (/ 1 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))))>
#<alt (- (+ (* -1 (/ (+ (* -2 (- (* 1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (+ (* -2 (- (* -1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (* -1/2 (/ (- (pow cosTheta 4) 1) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))))) (/ (* (- (* -1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (- (pow cosTheta 4) 1)) (pow cosTheta 4))) (pow alpha 6))) (+ (* -1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))))) (+ (* -2 (/ (- (* -1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (pow alpha 4))) (+ (* -1/2 (/ (- (pow cosTheta 4) 1) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (/ 1 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
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#<alt (- (+ (* -1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (+ (* -2 (/ (- (* -1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (pow alpha 4))) (+ (* -1/2 (/ (- (pow cosTheta 4) 1) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (/ 1 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))))>
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#<alt (/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))>
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#<alt (- (+ (* (pow cosTheta 2) (+ (* -1 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2))))) (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
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#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))>
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#<alt (/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))>
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#<alt (+ (* 2 (/ (* (PI) (* (log alpha) (- (pow cosTheta 4) 1))) (- (* -1 (pow cosTheta 2)) 1))) (* (pow alpha 2) (- (* -4 (/ (* (pow cosTheta 4) (* (PI) (log alpha))) (- (* -1 (pow cosTheta 2)) 1))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1)))) (pow (- (* -1 (pow cosTheta 2)) 1) 2))))))>
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#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1))))) (/ (pow alpha 4) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 4) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (+ (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1))))) (/ (pow alpha 4) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (+ (/ (pow alpha 4) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ (pow alpha 4) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt -1>
#<alt (- (pow alpha 4) 1)>
#<alt (- (pow alpha 4) 1)>
#<alt (- (pow alpha 4) 1)>
#<alt (pow alpha 4)>
#<alt (* (pow alpha 4) (- 1 (/ 1 (pow alpha 4))))>
#<alt (* (pow alpha 4) (- 1 (/ 1 (pow alpha 4))))>
#<alt (* (pow alpha 4) (- 1 (/ 1 (pow alpha 4))))>
#<alt (pow alpha 4)>
#<alt (* (pow alpha 4) (- 1 (/ 1 (pow alpha 4))))>
#<alt (* (pow alpha 4) (- 1 (/ 1 (pow alpha 4))))>
#<alt (* (pow alpha 4) (- 1 (/ 1 (pow alpha 4))))>
#<alt -1>
#<alt (- (pow alpha 3) 1)>
#<alt (- (pow alpha 3) 1)>
#<alt (- (pow alpha 3) 1)>
#<alt (pow alpha 3)>
#<alt (* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))>
#<alt (* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))>
#<alt (* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))>
#<alt (pow alpha 3)>
#<alt (* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))>
#<alt (* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))>
#<alt (* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (* -1 (* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
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#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (* -1 (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (pow alpha 4))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 6) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
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#<alt (- (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 6) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
#<alt (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))>
#<alt (+ (* -1 (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1)))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))) (/ (* (+ 1 (pow alpha 3)) (* (- (pow alpha 2) 1) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 3) 1)))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))))) (/ (* (+ 1 (pow alpha 3)) (* (- (pow alpha 2) 1) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 4)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 4)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt -1>
#<alt (- (pow alpha 6) 1)>
#<alt (- (pow alpha 6) 1)>
#<alt (- (pow alpha 6) 1)>
#<alt (pow alpha 6)>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (pow alpha 6)>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
Calls

90 calls:

TimeVariablePointExpression
2.0ms
alpha
@0
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1)))))
2.0ms
alpha
@inf
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1)))))
1.0ms
alpha
@inf
(* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1))))
1.0ms
alpha
@0
(* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1))))
1.0ms
alpha
@-inf
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1)))))

simplify313.0ms (4.2%)

Memory
9.7MiB live, 596.3MiB allocated
Algorithm
egg-herbie
Rules
5 214×lower-fma.f64
5 214×lower-fma.f32
4 852×lower-*.f64
4 852×lower-*.f32
2 790×lower--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
076611530
1293010898
0854210382
Stop Event
iter limit
node limit
Counts
312 → 312
Calls
Call 1
Inputs
(* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1)))))
(+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1))))) (* (pow alpha 2) (- (* 1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1))))) (/ (* (pow cosTheta 4) (- (* -1 (pow cosTheta 2)) 1)) (* (PI) (* (log alpha) (pow (- (pow cosTheta 4) 1) 2)))))))
(+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1))))) (* (pow alpha 2) (- (+ (* 1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1))))) (* (pow alpha 2) (- (* 1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1))))) (+ (* -2 (/ (* (pow cosTheta 4) (- (* 1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1))))) (/ (* (pow cosTheta 4) (- (* -1 (pow cosTheta 2)) 1)) (* (PI) (* (log alpha) (pow (- (pow cosTheta 4) 1) 2)))))) (- (pow cosTheta 4) 1))) (* -1/2 (/ (* (pow cosTheta 4) (- (* -1 (pow cosTheta 2)) 1)) (* (PI) (* (log alpha) (pow (- (pow cosTheta 4) 1) 2))))))))) (/ (* (pow cosTheta 4) (- (* -1 (pow cosTheta 2)) 1)) (* (PI) (* (log alpha) (pow (- (pow cosTheta 4) 1) 2)))))))
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(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(- (* -1 (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (pow alpha 4))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
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(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
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(- (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 6) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))
(+ (* -1 (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- (+ 1 (pow alpha 2)) alpha))))))
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(/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))
(/ (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))
(/ (- (+ (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 4)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))
(/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))
(/ (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))
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(/ (- (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 4)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (+ (* -1 (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 3) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
-1
(- (pow alpha 6) 1)
(- (pow alpha 6) 1)
(- (pow alpha 6) 1)
(pow alpha 6)
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(pow alpha 6)
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(* (pow alpha 6) (- 1 (/ 1 (pow alpha 6))))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
Outputs
(* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1)))))
(/.f32 (*.f32 #s(literal -1/2 binary32) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal -1 binary32))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (+.f32 (pow.f32 cosTheta #s(literal 4 binary32)) #s(literal -1 binary32)))))
(+ (* -1/2 (/ (- (* -1 (pow cosTheta 2)) 1) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1))))) (* (pow alpha 2) (- (* 1/2 (/ (- (* -2 (pow cosTheta 2)) 1) (* (PI) (* (log alpha) (- (pow cosTheta 4) 1))))) (/ (* (pow cosTheta 4) (- (* -1 (pow cosTheta 2)) 1)) (* (PI) (* (log alpha) (pow (- (pow cosTheta 4) 1) 2)))))))
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(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(*.f32 #s(literal -2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha alpha)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))
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(* (pow alpha 2) (- (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (+ (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- (pow cosTheta 4) 1))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* -1 (/ (* (- (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- (pow cosTheta 4) 1))) (pow cosTheta 2))) (/ (* (- (* -1 (pow cosTheta 2)) 1) (- (* 4 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (* (PI) (* (log (/ 1 alpha)) (- (* -1 (pow cosTheta 2)) 1)))))) (pow cosTheta 2))) (- (* -1 (pow cosTheta 2)) 1)) (* (pow alpha 6) (pow cosTheta 2)))) (* 4 (/ (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))) (pow alpha 2)))))) (+ (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- (* -1 (pow cosTheta 2)) 1))) (pow alpha 2))) (/ (* (- (* -1 (pow cosTheta 2)) 1) (- (* 4 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (* (PI) (* (log (/ 1 alpha)) (- (* -1 (pow cosTheta 2)) 1)))))) (* (pow alpha 4) (pow cosTheta 2))))))
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(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(*.f32 #s(literal -2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))
(* (pow alpha 2) (- (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* 4 (/ (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))) (pow alpha 2)))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (- (* -1 (pow cosTheta 2)) 1))) (pow alpha 2)))))
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(* (pow alpha 2) (- (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (+ (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (- (pow cosTheta 4) 1))) (* (pow alpha 4) (pow cosTheta 2)))) (* 4 (/ (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))) (pow alpha 2))))) (+ (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (- (* -1 (pow cosTheta 2)) 1))) (pow alpha 2))) (/ (* (- (* -1 (pow cosTheta 2)) 1) (- (* 4 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (* (PI) (* (log (/ -1 alpha)) (- (* -1 (pow cosTheta 2)) 1)))))) (* (pow alpha 4) (pow cosTheta 2))))))
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(* (pow alpha 2) (- (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (+ (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (- (pow cosTheta 4) 1))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* -1 (/ (* (- (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (- (pow cosTheta 4) 1))) (pow cosTheta 2))) (/ (* (- (* -1 (pow cosTheta 2)) 1) (- (* 4 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (* (PI) (* (log (/ -1 alpha)) (- (* -1 (pow cosTheta 2)) 1)))))) (pow cosTheta 2))) (- (* -1 (pow cosTheta 2)) 1)) (* (pow alpha 6) (pow cosTheta 2)))) (* 4 (/ (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))) (pow alpha 2)))))) (+ (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (- (* -1 (pow cosTheta 2)) 1))) (pow alpha 2))) (/ (* (- (* -1 (pow cosTheta 2)) 1) (- (* 4 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (* (PI) (* (log (/ -1 alpha)) (- (* -1 (pow cosTheta 2)) 1)))))) (* (pow alpha 4) (pow cosTheta 2))))))
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(* (PI) (log (pow alpha 2)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
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(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
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-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
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(neg.f32 (*.f32 (log.f32 alpha) #s(literal -2 binary32)))
(* -2 (log (/ -1 alpha)))
(*.f32 #s(literal -2 binary32) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (log (/ -1 alpha)))
(*.f32 #s(literal -2 binary32) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (log (/ -1 alpha)))
(*.f32 #s(literal -2 binary32) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (log (/ -1 alpha)))
(*.f32 #s(literal -2 binary32) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))

rewrite30.0ms (0.4%)

Memory
26.1MiB live, 64.2MiB allocated
Rules
38×lower-*.f64
32×lift-*.f32
26×lower-+.f64
22×lower-fma.f64
20×lift-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057374
0104367
Stop Event
iter limit
iter limit
unsound
iter limit
Counts
22 → 24
Calls
Call 1
Inputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
#s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)))
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 cosTheta cosTheta)
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
(*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
#s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)))
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32))
(fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))
(+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 cosTheta cosTheta)
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))

eval46.0ms (0.6%)

Memory
8.3MiB live, 120.3MiB allocated
Compiler

Compiled 23 713 to 769 computations (96.8% saved)

prune65.0ms (0.9%)

Memory
-16.4MiB live, 147.1MiB allocated
Pruning

36 alts after pruning (31 fresh and 5 done)

PrunedKeptTotal
New52510535
Fresh72128
Picked145
Done011
Total53336569
Accuracy
99.9%
Counts
569 → 36
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.5%
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.3%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
96.2%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
97.8%
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
95.6%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
97.4%
(/.f32 (/.f32 (*.f32 #s(approx (+ (* alpha (* alpha alpha)) -1) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha (*.f32 alpha alpha))))))) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
80.1%
(/.f32 (/.f32 #s(approx (+ (* (* alpha alpha) (* alpha alpha)) -1) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
84.8%
(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
98.0%
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (/.f32 (+.f32 (pow.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32)) (-.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32))) (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
57.9%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 cosTheta (*.f32 cosTheta (+.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))))))
93.1%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
96.5%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 #s(literal 2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
98.1%
(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.1%
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
96.2%
(/.f32 #s(approx (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
98.5%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
98.5%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
98.3%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
96.6%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
54.1%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (*.f32 alpha alpha)) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))))
93.0%
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
98.2%
(/.f32 #s(approx (- (* alpha alpha) 1) (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
65.3%
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
65.3%
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
63.6%
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
-0.0%
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
97.0%
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 alpha alpha) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (*.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
65.3%
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
92.2%
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ (* alpha alpha) (- 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (PI.f32) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
92.4%
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ (* alpha alpha) (- 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (+.f32 #s(literal 1 binary32) (fma.f32 alpha alpha alpha)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))))
95.7%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1))))) (fma.f32 (neg.f32 (*.f32 cosTheta cosTheta)) (/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
65.3%
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
Compiler

Compiled 3 197 to 839 computations (73.8% saved)

regimes77.0ms (1%)

Memory
-1.7MiB live, 156.3MiB allocated
Counts
70 → 1
Calls
Call 1
Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 #s(literal 2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 #s(approx (* (PI) (log (* alpha alpha))) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(approx (+ (* (* alpha alpha) (* alpha alpha)) -1) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(approx (+ (* (* alpha alpha) (* alpha alpha)) -1) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 cosTheta (*.f32 cosTheta (+.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (*.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ (* alpha alpha) (- 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (+.f32 #s(literal 1 binary32) (fma.f32 alpha alpha alpha)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))))
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ (* alpha alpha) (- 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (PI.f32) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32))))))
(/.f32 (/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))))))
(/.f32 (/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (/.f32 (*.f32 #s(approx (+ (* alpha (* alpha alpha)) -1) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha (*.f32 alpha alpha))))))) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (*.f32 alpha alpha)) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (*.f32 alpha alpha)) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (fma.f32 (*.f32 cosTheta cosTheta) (/.f32 (neg.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1))))) (fma.f32 (neg.f32 (*.f32 cosTheta cosTheta)) (/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 alpha alpha) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (*.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (*.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))) (/.f32 (*.f32 (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha))) (*.f32 alpha alpha))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))))
(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (/.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (/.f32 (+.f32 (pow.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32)) (-.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32))) (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) (*.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
Calls

4 calls:

19.0ms
(*.f32 alpha alpha)
19.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
18.0ms
cosTheta
18.0ms
alpha
Results
AccuracySegmentsBranch
98.6%1cosTheta
98.6%1alpha
98.6%1(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.6%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes40.0ms (0.5%)

Memory
-9.9MiB live, 56.2MiB allocated
Counts
21 → 1
Calls
Call 1
Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 #s(literal 2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
Outputs
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
Calls

4 calls:

20.0ms
alpha
6.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
6.0ms
(*.f32 alpha alpha)
6.0ms
cosTheta
Results
AccuracySegmentsBranch
98.5%1cosTheta
98.5%1alpha
98.5%1(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.5%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes26.0ms (0.3%)

Memory
11.8MiB live, 50.5MiB allocated
Counts
20 → 1
Calls
Call 1
Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 #s(literal 2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
Calls

4 calls:

7.0ms
(*.f32 alpha alpha)
6.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
6.0ms
alpha
6.0ms
cosTheta
Results
AccuracySegmentsBranch
96.6%1cosTheta
96.6%1alpha
96.6%1(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
96.6%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes39.0ms (0.5%)

Memory
-2.1MiB live, 37.3MiB allocated
Counts
16 → 1
Calls
Call 1
Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 #s(literal 2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
Outputs
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
Calls

4 calls:

22.0ms
(*.f32 alpha alpha)
5.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
5.0ms
cosTheta
5.0ms
alpha
Results
AccuracySegmentsBranch
96.6%1cosTheta
96.6%1alpha
96.6%1(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
96.6%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes27.0ms (0.4%)

Memory
-11.5MiB live, 27.2MiB allocated
Counts
14 → 1
Calls
Call 1
Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) -1) (+ (* (+ (* alpha alpha) -1) (* (* cosTheta cosTheta) (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))) -1)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
Calls

4 calls:

13.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
5.0ms
cosTheta
4.0ms
(*.f32 alpha alpha)
4.0ms
alpha
Results
AccuracySegmentsBranch
93.1%1cosTheta
93.1%1alpha
93.1%1(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
93.1%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes16.0ms (0.2%)

Memory
-7.4MiB live, 33.8MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (/ (+ (* (* alpha alpha) (* alpha alpha)) -1) (+ (* alpha alpha) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
Outputs
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
Calls

4 calls:

5.0ms
alpha
4.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
3.0ms
cosTheta
3.0ms
(*.f32 alpha alpha)
Results
AccuracySegmentsBranch
93.0%1cosTheta
93.0%1alpha
93.0%1(*.f32 alpha alpha)
93.0%1(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes13.0ms (0.2%)

Memory
-0.5MiB live, 36.2MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
Outputs
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
Calls

4 calls:

5.0ms
alpha
3.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
2.0ms
(*.f32 alpha alpha)
2.0ms
cosTheta
Results
AccuracySegmentsBranch
65.3%1cosTheta
65.3%1alpha
65.3%1(*.f32 alpha alpha)
65.3%1(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes10.0ms (0.1%)

Memory
19.1MiB live, 19.1MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (log.f32 alpha))))
Outputs
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
Calls

4 calls:

2.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
2.0ms
(*.f32 alpha alpha)
2.0ms
cosTheta
2.0ms
alpha
Results
AccuracySegmentsBranch
63.6%1cosTheta
63.6%1alpha
63.6%1(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
63.6%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes9.0ms (0.1%)

Memory
-23.0MiB live, 15.9MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
3 → 1
Calls
Call 1
Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
Outputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
Calls

4 calls:

3.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
2.0ms
alpha
2.0ms
(*.f32 alpha alpha)
2.0ms
cosTheta
Results
AccuracySegmentsBranch
-0.0%1alpha
-0.0%1(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
-0.0%1(*.f32 alpha alpha)
-0.0%1cosTheta
Compiler

Compiled 37 to 20 computations (45.9% saved)

simplify58.0ms (0.8%)

Memory
16.2MiB live, 52.6MiB allocated
Algorithm
egg-herbie
Rules
402×distribute-lft-neg-in_binary32
192×neg-sub0_binary32
192×neg-mul-1_binary32
180×sub-neg_binary32
170×cancel-sub-sign_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
065290
185290
297290
3122290
4175290
5224290
6270290
7291290
8305290
9314290
10331290
11356290
12386290
13440290
14532290
15655290
16795290
17917290
181001290
191060290
201096290
211122290
221135290
231146290
241159290
251171290
261175290
Stop Event
saturated
Calls
Call 1
Inputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (log.f32 alpha)) (*.f32 (PI.f32) #s(literal 2 binary32)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 cosTheta cosTheta #s(literal -1 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))

soundness743.0ms (10%)

Memory
-9.3MiB live, 710.4MiB allocated
Rules
7 332×lower-fma.f64
7 332×lower-fma.f32
6 338×lower-fma.f64
6 338×lower-fma.f32
6 236×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01972350
16582266
230532248
084832101
04119928
115399332
087568957
01365
02365
110365
284263
0849355
076611530
1293010898
0854210382
055110087
120789355
093008962
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 799 to 305 computations (61.8% saved)

preprocess48.0ms (0.6%)

Memory
1.0MiB live, 119.6MiB allocated
Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 818 to 382 computations (53.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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