GTR1 distribution

Time bar (total: 8.1s)

analyze68.0ms (0.8%)

Memory
-20.7MiB live, 97.6MiB allocated
Algorithm
1×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)

sample1.6s (19.5%)

Memory
29.9MiB live, 2 430.1MiB allocated
Samples
1.2s8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 979.0ms
ival-mult: 354.0ms (36.2% of total)
ival-<=: 163.0ms (16.7% of total)
const: 130.0ms (13.3% of total)
ival-log: 97.0ms (9.9% of total)
ival-div: 81.0ms (8.3% of total)
ival-add: 52.0ms (5.3% of total)
ival-sub: 38.0ms (3.9% of total)
ival-pi: 29.0ms (3% of total)
ival-and: 23.0ms (2.4% of total)
exact: 10.0ms (1% of total)
ival-assert: 3.0ms (0.3% of total)
Bogosity

preprocess382.0ms (4.7%)

Memory
36.8MiB live, 669.2MiB allocated
Algorithm
1×egg-herbie
Rules
12 798×lower-fma.f64
12 798×lower-fma.f32
4 578×lower-*.f64
4 568×lower-*.f32
2 370×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035130
1148122
2629120
33565120
47829120
01324
02324
15124
215924
364324
4269324
5440324
6770424
0855221
Stop Event
1×iter limit
1×node limit
1×iter limit
1×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 (PI.f32) (*.f32 (log.f32 (*.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
Symmetry

(abs alpha)

(abs cosTheta)

explain253.0ms (3.1%)

Memory
-10.1MiB live, 283.6MiB 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)))
01(1.2002969309729802e-24 0.9959656596183777)0-(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
00-0-(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
01(1.2002969309729802e-24 0.9959656596183777)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))
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
log.f32(log.f32 (*.f32 alpha alpha))sensitivity10
Confusion
Predicted +Predicted -
+00
-1255
Precision
0.0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-10255
Precision?
0.0
Recall?
0/0
Freqs
test
numberfreq
0255
11
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-100
Precision?
0.0
Recall?
0/0
Samples
50.0ms512×0valid
Compiler

Compiled 238 to 56 computations (76.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 34.0ms
ival-mult: 16.0ms (46.6% of total)
ival-log: 7.0ms (20.4% of total)
ival-div: 4.0ms (11.6% of total)
ival-pi: 2.0ms (5.8% of total)
ival-add: 2.0ms (5.8% of total)
ival-sub: 2.0ms (5.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
2.1MiB live, 2.1MiB 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)

simplify392.0ms (4.8%)

Memory
14.6MiB live, 521.6MiB allocated
Algorithm
1×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
12 798×lower-fma.f64
12 798×lower-fma.f32
4 578×lower-*.f64
4 568×lower-*.f32
2 370×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01391
02391
15191
215991
364391
4269391
5440391
6770491
0855281
Stop Event
1×iter limit
1×node limit
1×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 (PI.f32) (*.f32 (log.f32 (*.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(-.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 (PI.f32) (*.f32 (log.f32 (*.f32 alpha alpha)) (fma.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 (*.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

localize44.0ms (0.5%)

Memory
-21.4MiB live, 67.6MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy99.6%
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
✓accuracy99.4%
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓accuracy99.2%
(/.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))))
✓accuracy98.8%
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
Samples
25.0ms256×0valid
Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-mult: 7.0ms (41.3% of total)
ival-log: 3.0ms (17.7% of total)
ival-div: 2.0ms (11.8% of total)
ival-sub: 2.0ms (11.8% of total)
ival-pi: 1.0ms (5.9% of total)
ival-add: 1.0ms (5.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series68.0ms (0.8%)

Memory
-0.6MiB live, 153.3MiB 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
31.0ms
alpha
@0
(* (PI) (log (* alpha alpha)))
7.0ms
alpha
@inf
(* (PI) (log (* alpha alpha)))
7.0ms
alpha
@-inf
(* (PI) (log (* alpha alpha)))
3.0ms
alpha
@-inf
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms
alpha
@0
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite432.0ms (5.3%)

Memory
-9.1MiB live, 751.9MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
6 278×lower-*.f64
6 268×lower-*.f32
5 746×lower-fma.f64
5 746×lower-fma.f32
3 952×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01365
02365
19865
276863
0844655
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
7 → 609
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 (*.f32 alpha 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 (*.f32 alpha 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))) (neg.f32 (+.f32 alpha #s(literal 1 binary32))))
(+.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)) (neg.f32 (+.f32 alpha #s(literal 1 binary32))))
(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 (*.f32 alpha 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 (*.f32 alpha 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)) (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)) (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)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (*.f32 #s(literal 1 binary32) 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 (/.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 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 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (-.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (-.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha)))))
(/.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 #s(literal 1 binary32) (/.f32 (-.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha))) (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32)) (-.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))
(/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 alpha) (*.f32 (*.f32 alpha 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 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32))) (neg.f32 (-.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha)))))
(/.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 (*.f32 alpha 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)))
(/.f32 (-.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.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 (*.f32 (*.f32 (*.f32 alpha 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 (fma.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)))) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 (fma.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal 1 binary32)) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)))) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (*.f32 (fma.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 (fma.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 (fma.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal 1 binary32)) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (*.f32 (fma.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (*.f32 (*.f32 alpha 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 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))
(/.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 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.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 alpha #s(literal -1 binary32))) (*.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 alpha #s(literal -1 binary32))))
(/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 (neg.f32 (neg.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 (neg.f32 (neg.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (neg.f32 (neg.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 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (neg.f32 (*.f32 alpha alpha)))))
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(*.f32 (*.f32 (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(*.f32 (*.f32 (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (sqrt.f32 (PI.f32))) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(*.f32 (*.f32 (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))
(+.f32 (*.f32 cosTheta (*.f32 alpha alpha)) (*.f32 cosTheta #s(literal -1 binary32)))
(+.f32 (*.f32 cosTheta (*.f32 alpha alpha)) (*.f32 (*.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(+.f32 (*.f32 cosTheta #s(literal -1 binary32)) (*.f32 cosTheta (*.f32 alpha alpha)))
(+.f32 (*.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta))
(+.f32 (neg.f32 cosTheta) (*.f32 (*.f32 alpha alpha) cosTheta))
(+.f32 (*.f32 (fma.f32 alpha cosTheta cosTheta) alpha) (*.f32 (fma.f32 alpha cosTheta cosTheta) #s(literal -1 binary32)))
(+.f32 (*.f32 #s(literal 1 binary32) (*.f32 cosTheta (*.f32 alpha alpha))) (*.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -1 binary32))))
(+.f32 (*.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) cosTheta)) (*.f32 #s(literal 1 binary32) (neg.f32 cosTheta)))
(+.f32 (*.f32 alpha (fma.f32 alpha cosTheta cosTheta)) (*.f32 #s(literal -1 binary32) (fma.f32 alpha cosTheta cosTheta)))
(+.f32 (*.f32 (*.f32 (*.f32 alpha alpha) cosTheta) #s(literal 1 binary32)) (*.f32 (neg.f32 cosTheta) #s(literal 1 binary32)))
(fma.f32 alpha (fma.f32 alpha cosTheta cosTheta) (*.f32 #s(literal -1 binary32) (fma.f32 alpha cosTheta cosTheta)))
(fma.f32 (*.f32 alpha alpha) cosTheta (neg.f32 cosTheta))
(fma.f32 #s(literal 1 binary32) (*.f32 cosTheta (*.f32 alpha alpha)) (*.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -1 binary32))))
(fma.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) cosTheta) (*.f32 #s(literal 1 binary32) (neg.f32 cosTheta)))
(fma.f32 cosTheta (*.f32 alpha alpha) (*.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 cosTheta (*.f32 alpha alpha) (*.f32 (*.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 cosTheta #s(literal -1 binary32) (*.f32 cosTheta (*.f32 alpha alpha)))
(fma.f32 #s(literal -1 binary32) cosTheta (*.f32 (*.f32 alpha alpha) cosTheta))
(fma.f32 (*.f32 cosTheta (*.f32 alpha alpha)) #s(literal 1 binary32) (*.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 (*.f32 cosTheta (*.f32 alpha alpha)) #s(literal 1 binary32) (*.f32 (*.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (*.f32 (*.f32 alpha alpha) cosTheta) #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) #s(literal 1 binary32)))
(fma.f32 (fma.f32 alpha cosTheta cosTheta) alpha (*.f32 (fma.f32 alpha cosTheta cosTheta) #s(literal -1 binary32)))
(fma.f32 (*.f32 cosTheta alpha) alpha (*.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 (*.f32 cosTheta alpha) alpha (*.f32 (*.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta #s(literal 1 binary32)) (*.f32 alpha alpha) (*.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 (*.f32 cosTheta #s(literal 1 binary32)) (*.f32 alpha alpha) (*.f32 (*.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 cosTheta (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (*.f32 cosTheta (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)))))
(/.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 alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32)) 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)) cosTheta)))
(/.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 (*.f32 cosTheta (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 alpha) (*.f32 (*.f32 alpha 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 alpha) (*.f32 (*.f32 alpha 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 alpha) (*.f32 (*.f32 alpha 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 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (+.f32 alpha #s(literal 1 binary32)) (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta))
(*.f32 (fma.f32 alpha cosTheta cosTheta) (+.f32 alpha #s(literal -1 binary32)))
(*.f32 (*.f32 cosTheta (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 alpha) (*.f32 (*.f32 alpha 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 (*.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal 1 binary32))) (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta))
(*.f32 (*.f32 cosTheta (+.f32 alpha #s(literal -1 binary32))) (+.f32 alpha #s(literal 1 binary32)))
(*.f32 (*.f32 #s(literal 1 binary32) (fma.f32 alpha cosTheta cosTheta)) (+.f32 alpha #s(literal -1 binary32)))
(+.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 (neg.f32 cosTheta) cosTheta))
(+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 cosTheta cosTheta)) (*.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(+.f32 (*.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 alpha alpha) (*.f32 cosTheta cosTheta)))
(fma.f32 (*.f32 alpha alpha) (*.f32 cosTheta cosTheta) (*.f32 #s(literal -1 binary32) (*.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 (*.f32 cosTheta (*.f32 alpha alpha)) cosTheta (*.f32 (*.f32 cosTheta #s(literal -1 binary32)) cosTheta))
(fma.f32 (*.f32 (*.f32 alpha alpha) cosTheta) cosTheta (*.f32 (neg.f32 cosTheta) 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 alpha) (*.f32 (*.f32 alpha 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 alpha) (*.f32 (*.f32 alpha 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 alpha) (*.f32 (*.f32 alpha 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 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) 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 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 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) #s(literal 1 binary32))
(*.f32 (+.f32 alpha #s(literal 1 binary32)) (*.f32 (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta))
(*.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 (*.f32 (*.f32 cosTheta cosTheta) (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))
(*.f32 (*.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal 1 binary32))) (*.f32 (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta) cosTheta))
(*.f32 (*.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (*.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (+.f32 alpha #s(literal -1 binary32)))
(*.f32 (*.f32 (*.f32 cosTheta cosTheta) (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 (*.f32 cosTheta 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 (*.f32 cosTheta cosTheta) (+.f32 alpha #s(literal -1 binary32))) (+.f32 alpha #s(literal 1 binary32)))

simplify384.0ms (4.7%)

Memory
-7.8MiB live, 679.0MiB allocated
Algorithm
1×egg-herbie
Rules
8 466×lower-fma.f64
8 466×lower-fma.f32
5 952×lower-*.f64
5 952×lower-*.f32
4 632×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01972350
15822290
222312197
087302075
Stop Event
1×iter limit
1×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))))
(fma.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))) #s(literal 1 binary32))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))) #s(literal 1 binary32))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))) #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))))
(fma.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))) #s(literal 1 binary32))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))) #s(literal 1 binary32))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))) #s(literal 1 binary32))
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))
(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))
(/ -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) (fma.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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))) (/.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 alpha (*.f32 alpha (fma.f32 (*.f32 alpha alpha) (*.f32 (fma.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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))) (neg.f32 (/.f32 (*.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (fma.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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))))) (/.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 alpha (*.f32 alpha (fma.f32 (*.f32 alpha alpha) (*.f32 (/.f32 (fma.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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (fma.f32 cosTheta (neg.f32 cosTheta) (/.f32 (*.f32 alpha (*.f32 alpha (pow.f32 cosTheta #s(literal 4 binary32)))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (fma.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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))))) (/.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) (*.f32 (log.f32 alpha) (neg.f32 (PI.f32)))))
(- (/ 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 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (neg.f32 (PI.f32)))))) (/.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1/2 binary32)) (*.f32 (*.f32 alpha alpha) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (*.f32 (log.f32 alpha) (neg.f32 (PI.f32))))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (neg.f32 (PI.f32))))))
(- (+ (* -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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(* 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 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 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))) (pow cosTheta 2)))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 alpha (*.f32 alpha (*.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))))
(* (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))

eval81.0ms (1%)

Memory
41.7MiB live, 193.1MiB allocated
Compiler

Compiled 33 380 to 2 790 computations (91.6% saved)

prune132.0ms (1.6%)

Memory
-9.6MiB live, 317.3MiB allocated
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New85825883
Fresh000
Picked101
Done000
Total85925884
Accuracy
99.8%
Counts
884 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.9%
(fma.f32 (*.f32 alpha alpha) (fma.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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))
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))))
98.4%
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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))))
▶-0.0%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
96.1%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
98.3%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32)) (-.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha 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 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 (fma.f32 alpha 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))))
98.3%
(/.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))))
98.2%
(/.f32 (/.f32 (-.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.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))))
▶98.2%
(/.f32 (/.f32 (-.f32 (*.f32 (*.f32 (*.f32 alpha 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))))
98.3%
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (neg.f32 (*.f32 alpha 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 (*.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))))
98.2%
(/.f32 (/.f32 (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (+.f32 (fma.f32 alpha alpha #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))))
▶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))))
98.3%
(/.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))))
98.5%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (+.f32 (PI.f32) (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 (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))) (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 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
97.7%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
96.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(literal 1 binary32)))
98.3%
(/.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))))
63.8%
(/.f32 #s(literal -1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
63.9%
(/.f32 #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 1 758 to 838 computations (52.3% saved)

simplify12.0ms (0.1%)

Memory
-20.7MiB live, 17.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))
✓cost-diff0
(-.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32)))
✓cost-diff0
(/.f32 (-.f32 (*.f32 (*.f32 (*.f32 alpha 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))))
✓cost-diff0
(/.f32 (/.f32 (-.f32 (*.f32 (*.f32 (*.f32 alpha 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))))
✓cost-diff0
(fma.f32 alpha alpha #s(literal -1 binary32))
✓cost-diff0
(/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))
✓cost-diff0
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
✓cost-diff0
(/.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))))
✓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))))
✓cost-diff0
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
✓cost-diff0
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))
✓cost-diff0
(fma.f32 alpha alpha #s(literal -1 binary32))
✓cost-diff0
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
✓cost-diff0
(*.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)))))
✓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 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
Rules
34×lower-*.f64
28×lift-*.f32
22×lift-/.f32
22×lower-/.f64
12×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040563
078563
Stop Event
1×iter limit
1×iter limit
1×unsound
1×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 #s(literal 1 binary32) (fma.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 #s(literal 1 binary32) (fma.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 #s(literal 1 binary32) (fma.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)))
(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
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
cosTheta
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(PI.f32)
(/.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 (/.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))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (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))) (+.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 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 (*.f32 (*.f32 (*.f32 alpha 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 (*.f32 (*.f32 alpha 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 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))
(*.f32 alpha alpha)
alpha
(fma.f32 alpha alpha #s(literal 1 binary32))
#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 (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))) (/.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 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 #s(literal 1 binary32) (fma.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 #s(literal 1 binary32) (fma.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)))
(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
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
cosTheta
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(PI.f32)
(/.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 (/.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))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (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))) (+.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 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 (*.f32 (*.f32 (*.f32 alpha 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 (*.f32 (*.f32 alpha 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 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))
(*.f32 alpha alpha)
alpha
(fma.f32 alpha alpha #s(literal 1 binary32))
#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 (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

localize157.0ms (1.9%)

Memory
10.9MiB live, 315.1MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
✓accuracy100.0%
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))
✓accuracy100.0%
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 cosTheta cosTheta)
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
Samples
87.0ms256×0invalid
Compiler

Compiled 612 to 45 computations (92.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 61.0ms
ival-mult: 32.0ms (52.8% of total)
ival-div: 15.0ms (24.7% of total)
ival-add: 6.0ms (9.9% of total)
ival-log: 3.0ms (4.9% of total)
ival-sub: 2.0ms (3.3% of total)
ival-pi: 1.0ms (1.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series139.0ms (1.7%)

Memory
-2.6MiB live, 286.2MiB allocated
Counts
23 → 324
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 #s(literal 1 binary32) (fma.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 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))>
#<alt (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))>
#<alt (fma.f32 alpha alpha #s(literal -1 binary32))>
#<alt (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))>
#<alt (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))>
#<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 (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 #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))))>
#<alt (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))>
#<alt (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))>
#<alt (/.f32 (/.f32 (-.f32 (*.f32 (*.f32 (*.f32 alpha 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))))>
#<alt (/.f32 (-.f32 (*.f32 (*.f32 (*.f32 alpha 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))))>
#<alt (-.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32)))>
#<alt (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))>
#<alt (PI.f32)>
#<alt (log.f32 (*.f32 alpha alpha))>
#<alt (*.f32 cosTheta cosTheta)>
#<alt (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))>
#<alt (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)>
#<alt (*.f32 (PI.f32) (log.f32 (*.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))>
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#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 4)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 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)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 3)))))) (+ (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 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 (- (* -1 (pow alpha 2)) 1)>
#<alt (- (* (pow alpha 2) (- (pow alpha 2) 1)) 1)>
#<alt (- (* (pow alpha 2) (- (* (pow alpha 2) (+ 1 (pow alpha 2))) 1)) 1)>
#<alt (pow alpha 6)>
#<alt (* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 6) (- (+ 1 (/ 1 (pow alpha 2))) (/ 1 (pow alpha 4))))>
#<alt (* (pow alpha 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 4))) (/ 1 (pow alpha 2)))))>
#<alt (pow alpha 6)>
#<alt (* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 6) (- (+ 1 (/ 1 (pow alpha 2))) (/ 1 (pow alpha 4))))>
#<alt (* (pow alpha 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 4))) (/ 1 (pow alpha 2)))))>
#<alt (pow alpha 4)>
#<alt (* (pow alpha 4) (+ 1 (pow alpha 2)))>
#<alt (* (pow alpha 4) (+ 1 (pow alpha 2)))>
#<alt (* (pow alpha 4) (+ 1 (pow alpha 2)))>
#<alt (pow alpha 6)>
#<alt (* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 6)>
#<alt (* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))>
#<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 (* (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))>
#<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 (* -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 (* 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))))>
Calls

93 calls:

TimeVariablePointExpression
12.0ms
cosTheta
@0
(* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))))
10.0ms
alpha
@inf
(* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))
10.0ms
alpha
@inf
(* (PI) (log (* alpha alpha)))
8.0ms
alpha
@-inf
(log (* alpha alpha))
8.0ms
alpha
@0
(log (* alpha alpha))

rewrite19.0ms (0.2%)

Memory
-10.7MiB live, 28.2MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
34×lower-*.f64
28×lift-*.f32
22×lift-/.f32
22×lower-/.f64
12×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040305
078305
Stop Event
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
23 → 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 #s(literal 1 binary32) (fma.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 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 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 (*.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 #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 #s(literal 1 binary32) (/.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 (*.f32 (*.f32 (*.f32 alpha 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 (*.f32 (*.f32 alpha 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 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 cosTheta cosTheta)
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
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 #s(literal 1 binary32) (fma.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 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 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 (*.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 #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 #s(literal 1 binary32) (/.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 (*.f32 (*.f32 (*.f32 alpha 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 (*.f32 (*.f32 alpha 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 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 cosTheta cosTheta)
(*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))

simplify469.0ms (5.8%)

Memory
24.7MiB live, 625.9MiB allocated
Algorithm
1×egg-herbie
Rules
5 922×lower-fma.f64
5 922×lower-fma.f32
5 802×lower-*.f64
5 802×lower-*.f32
3 516×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048810655
1161210345
2709410324
081019800
Stop Event
1×iter limit
1×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))))))))
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(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (/ (pow alpha 4) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 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)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 3)))))) (+ (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 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))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 4)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 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)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 3)))))) (+ (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 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))
-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 alpha 2)) 1)
(- (* (pow alpha 2) (- (pow alpha 2) 1)) 1)
(- (* (pow alpha 2) (- (* (pow alpha 2) (+ 1 (pow alpha 2))) 1)) 1)
(pow alpha 6)
(* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 6) (- (+ 1 (/ 1 (pow alpha 2))) (/ 1 (pow alpha 4))))
(* (pow alpha 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 4))) (/ 1 (pow alpha 2)))))
(pow alpha 6)
(* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 6) (- (+ 1 (/ 1 (pow alpha 2))) (/ 1 (pow alpha 4))))
(* (pow alpha 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 4))) (/ 1 (pow alpha 2)))))
(pow alpha 4)
(* (pow alpha 4) (+ 1 (pow alpha 2)))
(* (pow alpha 4) (+ 1 (pow alpha 2)))
(* (pow alpha 4) (+ 1 (pow alpha 2)))
(pow alpha 6)
(* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))
(pow alpha 6)
(* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))
(* 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)
(* (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))
(* -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)))
(* -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))
(* 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))))
Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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) (fma.f32 (neg.f32 (*.f32 alpha alpha)) (*.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 (*.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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) (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha (*.f32 alpha (*.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (neg.f32 (*.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 (*.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(/ -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 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.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 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha (*.f32 alpha (*.f32 alpha 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))))))))
(- (+ (/ 1/2 (* (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 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.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 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 alpha alpha) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))))) (fma.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.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 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 alpha (*.f32 alpha (*.f32 alpha 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 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))))))))
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(* -1 (pow cosTheta 2))
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(* -1 cosTheta)
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(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
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(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
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(* cosTheta (- (pow alpha 2) 1))
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(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 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)))

eval52.0ms (0.6%)

Memory
10.9MiB live, 125.7MiB allocated
Compiler

Compiled 25 276 to 657 computations (97.4% saved)

prune51.0ms (0.6%)

Memory
-5.3MiB live, 106.9MiB allocated
Pruning

31 alts after pruning (31 fresh and 0 done)

PrunedKeptTotal
New64820668
Fresh91120
Picked505
Done000
Total66231693
Accuracy
99.9%
Counts
693 → 31
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.9%
(fma.f32 (*.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
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))))
95.6%
(/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
98.4%
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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))))
▶-0.0%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
▶98.6%
(/.f32 (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 (fma.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))))))
96.1%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶85.9%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #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))))
98.3%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32)) (-.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha 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))))
98.3%
(/.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))))
80.4%
(/.f32 (/.f32 (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (*.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))))
98.3%
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (neg.f32 (*.f32 alpha 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 (*.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))))
97.3%
(/.f32 (/.f32 (*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))))) (*.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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (*.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))))
▶97.1%
(/.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 #s(literal -1 binary32) cosTheta) cosTheta))))
80.4%
(/.f32 (/.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 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.3%
(/.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))))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (*.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (neg.f32 (log.f32 alpha))) (/.f32 (PI.f32) (*.f32 alpha alpha)) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))))
98.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (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))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
97.7%
(/.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 #s(literal -1 binary32) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
97.6%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
50.3%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.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))))))
96.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
98.3%
(/.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))))
98.3%
(/.f32 (*.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))))
63.8%
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
63.9%
(/.f32 #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))))
63.9%
(/.f32 #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 1 940 to 1 016 computations (47.6% saved)

simplify10.0ms (0.1%)

Memory
16.7MiB live, 16.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
041442
081442
Stop Event
1×iter limit
1×iter limit
1×unsound
1×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 (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))) (fma.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))
(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
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))
(*.f32 cosTheta (neg.f32 cosTheta))
cosTheta
(neg.f32 cosTheta)
(PI.f32)
(/.f32 (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))))
(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 #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 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (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))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))
(*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta)
(*.f32 #s(literal -1 binary32) cosTheta)
cosTheta
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #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 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(*.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))
#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
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.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))) (fma.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))
(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
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))
(*.f32 cosTheta (neg.f32 cosTheta))
cosTheta
(neg.f32 cosTheta)
(PI.f32)
(/.f32 (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))))
(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 #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 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (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))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))
(*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta)
(*.f32 #s(literal -1 binary32) cosTheta)
cosTheta
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #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 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(*.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))
#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

localize147.0ms (1.8%)

Memory
-41.8MiB live, 286.4MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(*.f32 #s(literal -1 binary32) cosTheta)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
✓accuracy100.0%
(*.f32 cosTheta (neg.f32 cosTheta))
✓accuracy100.0%
(neg.f32 cosTheta)
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 cosTheta cosTheta)
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
Samples
81.0ms256×0invalid
Compiler

Compiled 483 to 47 computations (90.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 60.0ms
ival-mult: 30.0ms (50.3% of total)
ival-div: 14.0ms (23.5% of total)
ival-add: 8.0ms (13.4% of total)
ival-log: 3.0ms (5% of total)
ival-sub: 2.0ms (3.4% of total)
ival-pi: 1.0ms (1.7% of total)
ival-neg: 1.0ms (1.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series120.0ms (1.5%)

Memory
33.0MiB live, 269.9MiB allocated
Counts
23 → 300
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 (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))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))>
#<alt (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))>
#<alt (fma.f32 alpha alpha #s(literal -1 binary32))>
#<alt (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))>
#<alt (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))>
#<alt (/.f32 (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 (PI.f32) (log.f32 (*.f32 alpha alpha)))>
#<alt (/.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 #s(literal -1 binary32) cosTheta) cosTheta))))>
#<alt (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))>
#<alt (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))>
#<alt (/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #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))))>
#<alt (/.f32 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))>
#<alt (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32))>
#<alt (PI.f32)>
#<alt (log.f32 (*.f32 alpha alpha))>
#<alt (*.f32 cosTheta cosTheta)>
#<alt (neg.f32 cosTheta)>
#<alt (*.f32 cosTheta (neg.f32 cosTheta))>
#<alt (*.f32 #s(literal -1 binary32) cosTheta)>
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))))>
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#<alt -1>
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#<alt (* 2 (log alpha))>
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#<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 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
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#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
Calls

84 calls:

TimeVariablePointExpression
10.0ms
alpha
@0
(log (* alpha alpha))
8.0ms
alpha
@-inf
(log (* alpha alpha))
8.0ms
alpha
@-inf
(* (PI) (log (* alpha alpha)))
7.0ms
alpha
@0
(* (PI) (log (* alpha alpha)))
7.0ms
alpha
@inf
(* (PI) (log (* alpha alpha)))

rewrite17.0ms (0.2%)

Memory
-14.3MiB live, 23.4MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
38×lower-*.f64
30×lift-*.f32
18×lift-/.f32
18×lower-/.f64
16×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
041243
081243
Stop Event
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
23 → 25
Calls
Call 1
Inputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.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))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
(/.f32 (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 (PI.f32) (log.f32 (*.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 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (/.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 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #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 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 cosTheta cosTheta)
(neg.f32 cosTheta)
(*.f32 cosTheta (neg.f32 cosTheta))
(*.f32 #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 (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))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
(/.f32 (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 (PI.f32) (log.f32 (*.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 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (/.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 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #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 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(+.f32 (*.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal -1 binary32))
(fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 cosTheta cosTheta)
(neg.f32 cosTheta)
(*.f32 cosTheta (neg.f32 cosTheta))
(*.f32 #s(literal -1 binary32) cosTheta)

simplify397.0ms (4.9%)

Memory
-3.5MiB live, 667.8MiB allocated
Algorithm
1×egg-herbie
Rules
5 638×lower-*.f64
5 638×lower-*.f32
5 498×lower-fma.f64
5 498×lower-fma.f32
3 668×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04969099
115898784
267388729
080938336
Stop Event
1×iter limit
1×node limit
Counts
300 → 300
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)))))
(/ (- (/ 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))
-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))))
(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) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 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))))
(/ -1/2 (* (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)))))
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(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (- (* (pow alpha 2) (- (pow alpha 2) 1)) 1) (pow (- (pow alpha 2) 1) 3))) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2))))) (* -1 (/ (* (- (* (pow alpha 2) (- (pow alpha 2) 1)) 1) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2))))))) (/ (* (- (* (pow alpha 2) (- (pow alpha 2) 1)) 1) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2)))))) (/ (* (pow alpha 2) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2)))))
(/ (- (* (pow alpha 2) (- (pow alpha 2) 1)) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1)))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2)))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 4)))))) (+ (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2)))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 3)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1)))))) (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 3)))))))))) (pow cosTheta 2))
(/ (- (* (pow alpha 2) (- (pow alpha 2) 1)) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1)))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2)))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 4)))))) (+ (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (pow alpha 2)) 2)))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 2))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 3)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (- (pow alpha 2) 1)))))) (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 (pow alpha 2)) 2) (pow (- (pow alpha 2) 1) 3)))))))))) (pow cosTheta 2))
-1
(- (pow alpha 2) 1)
(- (* (pow alpha 2) (+ 1 (* -1 (pow alpha 4)))) 1)
(- (* (pow alpha 2) (+ 1 (* (pow alpha 4) (- (* 2 (pow alpha 2)) 1)))) 1)
1
(- 1 (* 3 (/ 1 (pow alpha 2))))
(- (+ 1 (/ 4 (pow alpha 4))) (* 3 (/ 1 (pow alpha 2))))
(- (+ 1 (/ 4 (pow alpha 4))) (+ (* 3 (/ 1 (pow alpha 2))) (* 5 (/ 1 (pow alpha 6)))))
1
(- 1 (* 3 (/ 1 (pow alpha 2))))
(- (+ 1 (/ 4 (pow alpha 4))) (* 3 (/ 1 (pow alpha 2))))
(- (+ 1 (/ 4 (pow alpha 4))) (+ (* 3 (/ 1 (pow alpha 2))) (* 5 (/ 1 (pow alpha 6)))))
-1
(- (* -1 (pow alpha 2)) 1)
(- (* (pow alpha 2) (- (pow alpha 2) 1)) 1)
(- (* (pow alpha 2) (- (pow alpha 2) 1)) 1)
(pow alpha 4)
(* (pow alpha 4) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 4) (+ 1 (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2)))))
(* (pow alpha 4) (+ 1 (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2)))))
(pow alpha 4)
(* (pow alpha 4) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 4) (+ 1 (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2)))))
(* (pow alpha 4) (+ 1 (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2)))))
(* 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 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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) (fma.f32 (*.f32 alpha (neg.f32 alpha)) (*.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 (*.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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) (fma.f32 (*.f32 alpha alpha) (fma.f32 (neg.f32 (*.f32 cosTheta cosTheta)) (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (*.f32 alpha (*.f32 alpha (pow.f32 cosTheta #s(literal 4 binary32))))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(/ -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 alpha alpha) (*.f32 (*.f32 cosTheta cosTheta) (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))))))))
(-.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (*.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 (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))) (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 cosTheta (*.f32 cosTheta (*.f32 (*.f32 alpha alpha) (*.f32 alpha 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))))))
(-.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 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 (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))) (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 alpha alpha) (*.f32 (*.f32 cosTheta cosTheta) (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)))))) (fma.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 (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))) (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 cosTheta (*.f32 cosTheta (*.f32 (*.f32 alpha alpha) (*.f32 alpha 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 (PI.f32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.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 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (*.f32 alpha (*.f32 alpha (*.f32 cosTheta cosTheta))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (*.f32 alpha (*.f32 alpha (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (PI.f32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.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 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (neg.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (pow.f32 cosTheta #s(literal 4 binary32))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (PI.f32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 cosTheta cosTheta))))) (*.f32 cosTheta (*.f32 cosTheta (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (*.f32 alpha (*.f32 alpha (*.f32 cosTheta cosTheta)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (*.f32 alpha (*.f32 alpha (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (PI.f32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.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))))))
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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 (* -1 (pow alpha 4)))) 1)
(fma.f32 (*.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))
(- (* (pow alpha 2) (+ 1 (* (pow alpha 4) (- (* 2 (pow alpha 2)) 1)))) 1)
(fma.f32 (*.f32 alpha alpha) (fma.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 #s(literal 2 binary32) (*.f32 alpha alpha) #s(literal -1 binary32)) #s(literal 1 binary32)) #s(literal -1 binary32))
1
#s(literal 1 binary32)
(- 1 (* 3 (/ 1 (pow alpha 2))))
(+.f32 #s(literal 1 binary32) (/.f32 #s(literal -3 binary32) (*.f32 alpha alpha)))
(- (+ 1 (/ 4 (pow alpha 4))) (* 3 (/ 1 (pow alpha 2))))
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(- (+ 1 (/ 4 (pow alpha 4))) (+ (* 3 (/ 1 (pow alpha 2))) (* 5 (/ 1 (pow alpha 6)))))
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1
#s(literal 1 binary32)
(- 1 (* 3 (/ 1 (pow alpha 2))))
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(- (+ 1 (/ 4 (pow alpha 4))) (* 3 (/ 1 (pow alpha 2))))
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(- (+ 1 (/ 4 (pow alpha 4))) (+ (* 3 (/ 1 (pow alpha 2))) (* 5 (/ 1 (pow alpha 6)))))
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-1
#s(literal -1 binary32)
(- (* -1 (pow alpha 2)) 1)
(fma.f32 alpha (neg.f32 alpha) #s(literal -1 binary32))
(- (* (pow alpha 2) (- (pow alpha 2) 1)) 1)
(fma.f32 alpha (*.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal -1 binary32))
(- (* (pow alpha 2) (- (pow alpha 2) 1)) 1)
(fma.f32 alpha (*.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal -1 binary32))
(pow alpha 4)
(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))
(* (pow alpha 4) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 4) (+ 1 (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2)))))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 alpha alpha))))
(* (pow alpha 4) (+ 1 (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2)))))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 alpha alpha))))
(pow alpha 4)
(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))
(* (pow alpha 4) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 4) (+ 1 (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2)))))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 alpha alpha))))
(* (pow alpha 4) (+ 1 (* -1 (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2)))))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha 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))
(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 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)

eval59.0ms (0.7%)

Memory
7.8MiB live, 83.4MiB allocated
Compiler

Compiled 19 629 to 636 computations (96.8% saved)

prune70.0ms (0.9%)

Memory
33.6MiB live, 107.5MiB allocated
Pruning

30 alts after pruning (30 fresh and 0 done)

PrunedKeptTotal
New55316569
Fresh121426
Picked505
Done000
Total57030600
Accuracy
99.9%
Counts
600 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.5%
(fma.f32 alpha (*.f32 alpha (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
▶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))))
95.6%
(/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
98.4%
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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))))
84.0%
(/.f32 (fma.f32 alpha (*.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
98.1%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (*.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (*.f32 (neg.f32 (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))))
▶98.7%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
98.6%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
98.6%
(/.f32 (fma.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))))))
97.7%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
96.1%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
98.3%
(/.f32 (/.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32)) (-.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha 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))))
98.3%
(/.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))))
80.4%
(/.f32 (/.f32 (fma.f32 alpha (neg.f32 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))))
98.3%
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (neg.f32 (*.f32 alpha 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 (*.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))))
85.5%
(/.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 alpha alpha)))) (*.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))))
80.1%
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (neg.f32 alpha) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
97.1%
(/.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 (neg.f32 cosTheta) cosTheta))))
98.3%
(/.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))))
96.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
98.3%
(/.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))))
98.3%
(/.f32 (*.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 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
97.3%
(/.f32 (*.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(literal -1 binary32) cosTheta) cosTheta))))
63.8%
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
▶-0.0%
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
63.9%
(/.f32 #s(literal -1 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
▶63.9%
(/.f32 #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))))
97.0%
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (fma.f32 cosTheta cosTheta #s(literal 1 binary32)))
97.2%
(*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))))
Compiler

Compiled 1 786 to 950 computations (46.8% saved)

simplify15.0ms (0.2%)

Memory
-46.7MiB live, 14.0MiB allocated
Algorithm
1×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 alpha #s(literal -1 binary32)))
✓cost-diff0
(/.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))))
✓cost-diff0
(/.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))))
✓cost-diff0
(*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)
✓cost-diff0
(+.f32 alpha #s(literal -1 binary32))
✓cost-diff0
(fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
✓cost-diff0
(/.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))))
✓cost-diff0
(PI.f32)
✓cost-diff0
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
✓cost-diff0
(*.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(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
(fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))
✓cost-diff0
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
✓cost-diff0
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
✓cost-diff0
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
✓cost-diff0
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓cost-diff0
(*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (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
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
Rules
36×lower-*.f64
28×lift-*.f32
18×lower-+.f64
14×lift-/.f32
14×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042495
082495
Stop Event
1×iter limit
1×iter limit
1×unsound
1×iter limit
Calls
Call 1
Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 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)
(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 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))
(*.f32 cosTheta (neg.f32 cosTheta))
cosTheta
(neg.f32 cosTheta)
(PI.f32)
(/.f32 #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(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 alpha alpha)
alpha
(+.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))
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))))
(fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(+.f32 alpha #s(literal -1 binary32))
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 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.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 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 (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 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.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 alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))
(fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) 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 (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 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 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)
(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 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))
(*.f32 cosTheta (neg.f32 cosTheta))
cosTheta
(neg.f32 cosTheta)
(PI.f32)
(/.f32 #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(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 alpha alpha)
alpha
(+.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))
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))))
(fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(+.f32 alpha #s(literal -1 binary32))
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 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.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 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 (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 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.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 alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))
(fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) 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 (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

localize147.0ms (1.8%)

Memory
25.3MiB live, 294.2MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
✓accuracy100.0%
(*.f32 cosTheta (neg.f32 cosTheta))
✓accuracy100.0%
(neg.f32 cosTheta)
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
✓accuracy100.0%
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓accuracy100.0%
(log.f32 alpha)
✓accuracy6.3%
(PI.f32)
Samples
80.0ms256×0invalid
Compiler

Compiled 523 to 48 computations (90.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 57.0ms
ival-mult: 25.0ms (43.9% of total)
ival-div: 12.0ms (21.1% of total)
ival-add: 10.0ms (17.6% of total)
ival-log: 5.0ms (8.8% of total)
ival-sub: 2.0ms (3.5% of total)
ival-pi: 1.0ms (1.8% of total)
ival-neg: 1.0ms (1.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series242.0ms (3%)

Memory
-23.8MiB live, 461.0MiB allocated
Counts
26 → 336
Calls
Call 1
Inputs
#<alt (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))>
#<alt (fma.f32 alpha alpha #s(literal -1 binary32))>
#<alt (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))>
#<alt (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))>
#<alt (/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))>
#<alt (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))>
#<alt (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))>
#<alt (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))>
#<alt (/.f32 #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 (*.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 (PI.f32) (log.f32 (*.f32 alpha alpha)))>
#<alt (PI.f32)>
#<alt (/.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))))>
#<alt (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))>
#<alt (+.f32 alpha #s(literal -1 binary32))>
#<alt (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)>
#<alt (/.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))))>
#<alt (/.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))))>
#<alt (*.f32 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))>
#<alt (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))>
#<alt (log.f32 alpha)>
#<alt (*.f32 (log.f32 alpha) #s(literal 2 binary32))>
#<alt (neg.f32 cosTheta)>
#<alt (*.f32 cosTheta (neg.f32 cosTheta))>
#<alt (log.f32 (*.f32 alpha alpha))>
#<alt (*.f32 alpha alpha)>
Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (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 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (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 (/ (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)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (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 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))>
#<alt (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))>
#<alt (- (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))>
#<alt (- (+ (* -1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))>
#<alt (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))>
#<alt (+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log alpha)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))>
#<alt (+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log alpha)))))))>
#<alt (+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log alpha)))) (* 1/2 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log alpha)))))))))>
#<alt (/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha))))>
#<alt (/ (- (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1/2 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))) (* 1/2 (/ 1 (* (PI) (log alpha))))) (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (* 1/2 (/ 1 (* (pow cosTheta 6) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))>
#<alt (/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha))))>
#<alt (/ (- (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1/2 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))) (* 1/2 (/ 1 (* (PI) (log alpha))))) (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (* 1/2 (/ 1 (* (pow cosTheta 6) (* (PI) (* (log alpha) (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 (* 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) (* -1 (log (/ -1 alpha))))))))>
#<alt (* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))>
#<alt (+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))>
#<alt (+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))>
#<alt (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))>
#<alt (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (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) (* -1 (log (/ -1 alpha))))))>
#<alt (* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))>
#<alt (* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))>
#<alt (* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))>
#<alt (PI)>
#<alt (+ (PI) (* -1 (* (pow cosTheta 2) (PI))))>
#<alt (+ (PI) (* -1 (* (pow cosTheta 2) (PI))))>
#<alt (+ (PI) (* -1 (* (pow cosTheta 2) (PI))))>
#<alt (* -1 (* (pow cosTheta 2) (PI)))>
#<alt (* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))>
#<alt (* -1 (* (pow cosTheta 2) (PI)))>
#<alt (* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
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#<alt (* alpha (- alpha 1))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (/ (* alpha (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (* -1 (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 (- (* alpha (- (* alpha (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (* -1 (pow cosTheta 2)))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (* -1 (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 (- (* alpha (- (* alpha (- (+ (* -1 (* alpha (+ (* -1/2 (/ (+ 1 (+ (* -2 (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))))))) (+ (* 1/2 (/ (* (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (* -1 (pow cosTheta 2)))) (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (/ (* (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (* -1 (pow cosTheta 2)))) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (* -1 (pow cosTheta 2)))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (+ 1 (* -1 (pow cosTheta 2))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (* -1 (pow cosTheta 2)))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (+ 1 (* -1 (pow cosTheta 2)))) (* -1 (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 (/ (- (* 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 5))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 5) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ 1/2 (* (pow alpha 5) (* (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 (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 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))>
#<alt (+ (* -1 (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 2))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 3))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 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) 4))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 3)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (/ (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (/ (+ 1 (pow alpha 3)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (/ (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 6))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (* (pow cosTheta 4) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))))) (pow cosTheta 2))>
#<alt (/ (+ 1 (pow alpha 3)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (/ (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 6))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (* (pow cosTheta 4) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))))) (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)>
#<alt (- (* (pow alpha 2) (+ 1 (* -1 alpha))) 1)>
#<alt (- (* (pow alpha 2) (+ 1 (* alpha (- (pow alpha 2) 1)))) 1)>
#<alt (pow alpha 5)>
#<alt (* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 5)))))>
#<alt (pow alpha 5)>
#<alt (* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))>
#<alt (* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 3))))))>
#<alt (* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- 1 (/ 1 (pow alpha 2))) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))>
#<alt 1>
#<alt (+ 1 (pow alpha 3))>
#<alt (+ 1 (pow alpha 3))>
#<alt (+ 1 (pow alpha 3))>
#<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 (* (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 (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) (* -1 (log (/ -1 alpha)))))>
#<alt (* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* -1 (pow cosTheta 2))>
#<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 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)>
Calls

90 calls:

TimeVariablePointExpression
26.0ms
alpha
@0
(* (log alpha) 2)
22.0ms
cosTheta
@0
(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
12.0ms
alpha
@-inf
(* (PI) (* (log alpha) 2))
9.0ms
alpha
@inf
(* (PI) (log (* alpha alpha)))
9.0ms
alpha
@0
(* (PI) (* (log alpha) 2))

rewrite23.0ms (0.3%)

Memory
5.7MiB live, 45.8MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
36×lower-*.f64
28×lift-*.f32
18×lower-+.f64
14×lift-/.f32
14×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042272
082272
Stop Event
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
26 → 30
Calls
Call 1
Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
(fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))
(/.f32 #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 (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)
(/.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))))
(fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(+.f32 alpha #s(literal -1 binary32))
(*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)
(/.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 (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 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(log.f32 alpha)
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(neg.f32 cosTheta)
(*.f32 cosTheta (neg.f32 cosTheta))
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
Outputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (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))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
(+.f32 (*.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32)) (PI.f32))
(fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))
(/.f32 #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 (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)
(/.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 (*.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(+.f32 alpha #s(literal -1 binary32))
(*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)
(/.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 (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 (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32)) (fma.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))
(log.f32 alpha)
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(neg.f32 cosTheta)
(*.f32 cosTheta (neg.f32 cosTheta))
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)

simplify383.0ms (4.7%)

Memory
13.6MiB live, 610.3MiB allocated
Algorithm
1×egg-herbie
Rules
8 066×lower-*.f64
8 066×lower-*.f32
6 834×lower-fma.f64
6 834×lower-fma.f32
3 248×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06479793
122059341
083708951
Stop Event
1×iter limit
1×node limit
Counts
336 → 334
Calls
Call 1
Inputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (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 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (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 (/ (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)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (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 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))
(- (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))
(- (+ (* -1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))
(* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))
(+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log alpha)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))
(+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log alpha)))))))
(+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log alpha)))) (* 1/2 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log alpha)))))))))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha))))
(/ (- (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))
(/ (- (+ (/ 1/2 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))) (* 1/2 (/ 1 (* (PI) (log alpha))))) (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (* 1/2 (/ 1 (* (pow cosTheta 6) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha))))
(/ (- (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))
(/ (- (+ (/ 1/2 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))) (* 1/2 (/ 1 (* (PI) (log alpha))))) (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (* 1/2 (/ 1 (* (pow cosTheta 6) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))))))) (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))))
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
(* 2 (* (PI) (log alpha)))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (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) (* -1 (log (/ -1 alpha))))))
(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(PI)
(+ (PI) (* -1 (* (pow cosTheta 2) (PI))))
(+ (PI) (* -1 (* (pow cosTheta 2) (PI))))
(+ (PI) (* -1 (* (pow cosTheta 2) (PI))))
(* -1 (* (pow cosTheta 2) (PI)))
(* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))
(* -1 (* (pow cosTheta 2) (PI)))
(* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* -1 (PI)) (/ (PI) (pow cosTheta 2))))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* 1/2 (/ (* (pow alpha 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 (/ (* (pow alpha 2) (pow cosTheta 4)) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (* -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) (- (* (pow alpha 2) (- (* 1/2 (/ (* (pow alpha 2) (pow cosTheta 6)) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 4))))) (* 1/2 (/ (pow cosTheta 4) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))) (* -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 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))))))) (pow alpha 2))
(/ (- (+ (* 1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (pow alpha 2))
(/ (- (+ (* -1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 3) (* (pow alpha 6) (* (pow cosTheta 8) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))))) (pow alpha 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))))))) (pow alpha 2))
(/ (- (+ (* 1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (pow alpha 2))
(/ (- (+ (* -1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 3) (* (pow alpha 6) (* (pow cosTheta 8) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))))) (pow alpha 2))
(/ -1 (* (PI) (log (pow alpha 2))))
(- (/ (* (pow cosTheta 2) (- (pow alpha 2) 1)) (* (PI) (log (pow alpha 2)))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (* (pow cosTheta 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)))))) (* -1 (/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(/ -1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/ -1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (pow cosTheta 2))
(/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
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(+ (* -1 (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 2))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))
(+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 3))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))
(+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 4))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 3)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (/ (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))
(/ (+ 1 (pow alpha 3)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))
(/ (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 6))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (* (pow cosTheta 4) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))))) (pow cosTheta 2))
(/ (+ 1 (pow alpha 3)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))
(/ (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 6))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (* (pow cosTheta 4) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))))) (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 2) 1)
(- (* (pow alpha 2) (+ 1 (* -1 alpha))) 1)
(- (* (pow alpha 2) (+ 1 (* alpha (- (pow alpha 2) 1)))) 1)
(pow alpha 5)
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (/ 1 (pow alpha 2))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 5)))))
(pow alpha 5)
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 3))))))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- 1 (/ 1 (pow alpha 2))) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
1
(+ 1 (pow alpha 3))
(+ 1 (pow alpha 3))
(+ 1 (pow alpha 3))
(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)
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(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))))
(* 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) (* -1 (log (/ -1 alpha)))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* 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 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)
Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))))
(- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (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 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32)))))
(- (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (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 (/ (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 #s(literal 1/2 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32)))) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (/.f32 (*.f32 (*.f32 #s(literal -1/2 binary32) (*.f32 alpha (*.f32 alpha (*.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32)))) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.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 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32)))))
(- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 alpha (*.f32 alpha (fma.f32 alpha (*.f32 alpha (fma.f32 #s(literal -1/2 binary32) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32)))) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (/.f32 (*.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 alpha (*.f32 alpha (pow.f32 cosTheta #s(literal 4 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32)))) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))) (*.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))))) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32)))) (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32))) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (fma.f32 (*.f32 cosTheta cosTheta) (neg.f32 (PI.f32)) (PI.f32)))))
(/ -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 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (neg.f32 (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))))) (*.f32 alpha alpha)) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))))
(- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(fma.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (neg.f32 (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))))) (*.f32 alpha alpha)) (fma.f32 (fma.f32 #s(literal -1/2 binary32) (neg.f32 (*.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (neg.f32 (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))))) (*.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))))
(- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(fma.f32 #s(literal 1/2 binary32) (fma.f32 (*.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (neg.f32 (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))))) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (neg.f32 (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))))) (*.f32 alpha alpha))) (fma.f32 (fma.f32 #s(literal -1/2 binary32) (neg.f32 (*.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 (fma.f32 cosTheta cosTheta #s(literal -1 binary32)) (neg.f32 (*.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))))) (*.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))) (/.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) (* -1 (log (/ -1 alpha)))))))
(/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
(- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))
(+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
(- (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))
(+.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (*.f32 (*.f32 (pow.f32 alpha #s(literal 4 binary32)) (*.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
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(* 2 (* (PI) (log alpha)))
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(- (* (pow alpha 2) (+ 1 (* -1 alpha))) 1)
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(*.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (pow.f32 alpha #s(literal 5 binary32)))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (/ 1 (pow alpha 2))))
(*.f32 (pow.f32 alpha #s(literal 5 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 5)))))
(*.f32 (pow.f32 alpha #s(literal 5 binary32)) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32)))))
(pow alpha 5)
(pow.f32 alpha #s(literal 5 binary32))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(*.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) #s(literal -1 binary32)) (neg.f32 (pow.f32 alpha #s(literal 5 binary32))))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 3))))))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha alpha))))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32))))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- 1 (/ 1 (pow alpha 2))) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
(*.f32 (+.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32)) (neg.f32 (pow.f32 alpha #s(literal 5 binary32))))
1
#s(literal 1 binary32)
(+ 1 (pow alpha 3))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(+ 1 (pow alpha 3))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(+ 1 (pow alpha 3))
(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))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(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))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))
(* (pow alpha 3) (+ 1 (/ 1 (pow alpha 3))))
(fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 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) (* -1 (log (/ -1 alpha)))))
(*.f32 #s(literal 2 binary32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(*.f32 #s(literal 2 binary32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(*.f32 #s(literal 2 binary32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(*.f32 #s(literal 2 binary32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* 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))
(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)

eval48.0ms (0.6%)

Memory
-0.7MiB live, 114.7MiB allocated
Compiler

Compiled 21 786 to 747 computations (96.6% saved)

prune67.0ms (0.8%)

Memory
5.7MiB live, 167.8MiB allocated
Pruning

33 alts after pruning (31 fresh and 2 done)

PrunedKeptTotal
New57513588
Fresh71825
Picked325
Done000
Total58533618
Accuracy
99.9%
Counts
618 → 33
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.6%
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (*.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (*.f32 (PI.f32) #s(literal 2 binary32))))
96.1%
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
95.6%
(/.f32 (fma.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
98.2%
(/.f32 (fma.f32 (neg.f32 (fma.f32 alpha (/.f32 #s(literal 1 binary32) alpha) (neg.f32 alpha))) #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))))
98.4%
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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))))
96.1%
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
84.0%
(/.f32 (fma.f32 alpha (*.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
98.1%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (*.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (*.f32 (neg.f32 (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))))
✓98.7%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
98.6%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
98.6%
(/.f32 (fma.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))))))
97.7%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
96.1%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
96.2%
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
96.1%
(/.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
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))))
98.2%
(/.f32 (/.f32 (fma.f32 alpha (*.f32 alpha (fma.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1 binary32))) #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 (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 (PI.f32) (log.f32 (*.f32 alpha alpha))))
85.5%
(/.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 alpha alpha)))) (*.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))))
80.1%
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (neg.f32 alpha) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
97.1%
(/.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 (neg.f32 cosTheta) cosTheta))))
96.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
95.4%
(/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (PI.f32) (*.f32 (*.f32 (log.f32 (*.f32 alpha alpha)) (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))
98.3%
(/.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))))
98.3%
(/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
97.3%
(/.f32 (*.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(literal -1 binary32) cosTheta) cosTheta))))
63.8%
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
-0.0%
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
63.9%
(/.f32 #s(literal -1 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
✓63.9%
(/.f32 #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))))
63.9%
(/.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (fma.f32 (PI.f32) (/.f32 (*.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (neg.f32 (log.f32 alpha))) (*.f32 alpha alpha)) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))))))
63.0%
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
97.0%
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (fma.f32 cosTheta cosTheta #s(literal 1 binary32)))
Compiler

Compiled 2 924 to 773 computations (73.6% saved)

regimes90.0ms (1.1%)

Memory
8.1MiB live, 162.3MiB allocated
Counts
75 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(literal 1 binary32)))
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (fma.f32 cosTheta cosTheta #s(literal 1 binary32)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 #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(literal -1 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 #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 (*.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 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (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 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (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 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (*.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (*.f32 (PI.f32) #s(literal 2 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.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 (+.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 #s(literal 1 binary32) (fma.f32 alpha (neg.f32 alpha) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha (*.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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 #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 (neg.f32 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 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (PI.f32) (*.f32 (*.f32 (log.f32 (*.f32 alpha alpha)) (+.f32 alpha #s(literal 1 binary32))) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))
(/.f32 (/.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 (-.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 #s(literal 1 binary32) (fma.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
(/.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 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (*.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(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 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.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 (*.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 (*.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 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (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))) (/.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(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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (*.f32 (*.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 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #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 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (neg.f32 (fma.f32 alpha (/.f32 #s(literal 1 binary32) alpha) (neg.f32 alpha))) #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 (/.f32 (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (*.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 (fma.f32 alpha (neg.f32 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 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha #s(literal -1 binary32)) #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 (fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (+.f32 (fma.f32 alpha alpha #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 (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 (fma.f32 alpha (*.f32 alpha (fma.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1 binary32))) #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 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha 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 alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32)) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 (fma.f32 alpha 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 (/.f32 (-.f32 (*.f32 (*.f32 (*.f32 alpha 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 (fma.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32)) (-.f32 (fma.f32 (*.f32 alpha alpha) (*.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha 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 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (neg.f32 (*.f32 alpha 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 alpha) (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 alpha alpha)))) (*.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))))
(fma.f32 alpha (*.f32 alpha (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.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 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (fma.f32 (PI.f32) (/.f32 (*.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (neg.f32 (log.f32 alpha))) (*.f32 alpha alpha)) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha))))))))
(*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (*.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (*.f32 (neg.f32 (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha))) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (*.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (neg.f32 (log.f32 alpha))) (/.f32 (PI.f32) (*.f32 alpha alpha)) (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))))))
(/.f32 (/.f32 (-.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (*.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha (*.f32 alpha (*.f32 alpha alpha)) (fma.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 (*.f32 (pow.f32 alpha #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))))) (*.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))))
(fma.f32 (*.f32 alpha alpha) (fma.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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))
(fma.f32 (*.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (*.f32 cosTheta cosTheta) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 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 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
Calls

4 calls:

22.0ms
cosTheta
22.0ms
(/.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))))
22.0ms
alpha
21.0ms
(*.f32 alpha alpha)
Results
AccuracySegmentsBranch
98.7%1cosTheta
98.7%1alpha
98.7%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))))
98.7%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes35.0ms (0.4%)

Memory
-28.2MiB live, 64.9MiB allocated
Counts
23 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(literal 1 binary32)))
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (fma.f32 cosTheta cosTheta #s(literal 1 binary32)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 #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(literal -1 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 #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 (*.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 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
Outputs
(/.f32 (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:

12.0ms
cosTheta
8.0ms
(/.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))))
7.0ms
(*.f32 alpha alpha)
7.0ms
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)

regimes29.0ms (0.4%)

Memory
25.8MiB live, 63.6MiB allocated
Counts
21 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(literal 1 binary32)))
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (fma.f32 cosTheta cosTheta #s(literal 1 binary32)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 #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(literal -1 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 #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 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
Calls

4 calls:

8.0ms
(/.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))))
7.0ms
(*.f32 alpha alpha)
7.0ms
alpha
6.0ms
cosTheta
Results
AccuracySegmentsBranch
97.7%1cosTheta
97.7%1alpha
97.7%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))))
97.7%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes22.0ms (0.3%)

Memory
3.9MiB live, 41.5MiB allocated
Counts
14 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(literal 1 binary32)))
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (fma.f32 cosTheta cosTheta #s(literal 1 binary32)))
Outputs
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (fma.f32 cosTheta cosTheta #s(literal 1 binary32)))
Calls

4 calls:

7.0ms
cosTheta
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
(*.f32 alpha alpha)
5.0ms
alpha
Results
AccuracySegmentsBranch
97.0%1alpha
97.0%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))))
97.0%1(*.f32 alpha alpha)
97.0%1cosTheta
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes37.0ms (0.5%)

Memory
-17.1MiB live, 20.2MiB allocated
Counts
13 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.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))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(literal 1 binary32)))
Outputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
Calls

4 calls:

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))))
4.0ms
cosTheta
4.0ms
alpha
4.0ms
(*.f32 alpha alpha)
Results
AccuracySegmentsBranch
96.2%1cosTheta
96.2%1alpha
96.2%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))))
96.2%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes11.0ms (0.1%)

Memory
12.2MiB live, 12.2MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
Outputs
(/.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
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))))
3.0ms
(*.f32 alpha alpha)
3.0ms
alpha
3.0ms
cosTheta
Results
AccuracySegmentsBranch
96.1%1cosTheta
96.1%1alpha
96.1%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))))
96.1%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes10.0ms (0.1%)

Memory
10.5MiB live, 10.5MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
Outputs
(/.f32 #s(literal -1 binary32) (*.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
63.0%1cosTheta
63.0%1alpha
63.0%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))))
63.0%1(*.f32 alpha alpha)
Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes28.0ms (0.3%)

Memory
-22.8MiB live, 20.6MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
4 → 1
Calls
Call 1
Inputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (neg.f32 cosTheta)) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
Outputs
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
Calls

4 calls:

21.0ms
(/.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%1cosTheta
-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)
Compiler

Compiled 37 to 20 computations (45.9% saved)

simplify6.0ms (0.1%)

Memory
8.7MiB live, 8.7MiB allocated
Algorithm
1×egg-herbie
Rules
22×*-commutative_binary32
2×1-exp_binary64
2×1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039111
152111
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (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 (*.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 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (fma.f32 cosTheta cosTheta #s(literal 1 binary32)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
Outputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (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 (*.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 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32))))
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (fma.f32 cosTheta cosTheta #s(literal 1 binary32)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (fma.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(literal -1 binary32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))

soundness941.0ms (11.6%)

Memory
33.2MiB live, 1 051.0MiB allocated
Rules
8 466×lower-fma.f64
8 466×lower-fma.f32
8 066×lower-*.f64
8 066×lower-*.f32
6 834×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06479793
122059341
083708951
04969099
115898784
267388729
080938336
01972350
15822290
222312197
087302075
01365
02365
19865
276863
0844655
048810655
1161210345
2709410324
081019800
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 736 to 362 computations (50.8% saved)

preprocess449.0ms (5.5%)

Memory
-37.0MiB live, 131.6MiB allocated
Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 554 to 272 computations (50.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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