GTR1 distribution

Time bar (total: 8.7s)

analyze155.0ms (1.8%)

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 41 to 22 computations (46.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 82.0ms
ival-log: 38.0ms (46.6% of total)
ival-mult: 14.0ms (17.2% of total)
ival-<=: 9.0ms (11% of total)
...c/correct-round.rkt:119:19: 7.0ms (8.6% of total)
ival-pi: 3.0ms (3.7% of total)
ival-div: 3.0ms (3.7% of total)
ival-add: 3.0ms (3.7% of total)
ival-sub: 3.0ms (3.7% of total)
ival-and: 1.0ms (1.2% of total)
const: 1.0ms (1.2% of total)
backward-pass: 0.0ms (0% of total)

sample2.1s (24.6%)

Results
1.8s8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.2s
ival-mult: 384.0ms (33.2% of total)
...c/correct-round.rkt:119:19: 217.0ms (18.7% of total)
ival-<=: 180.0ms (15.5% of total)
ival-log: 116.0ms (10% of total)
ival-div: 84.0ms (7.3% of total)
ival-pi: 47.0ms (4.1% of total)
ival-add: 47.0ms (4.1% of total)
ival-sub: 42.0ms (3.6% of total)
ival-and: 27.0ms (2.3% of total)
const: 11.0ms (0.9% of total)
backward-pass: 3.0ms (0.3% of total)
Bogosity

preprocess358.0ms (4.1%)

Algorithm
2×egg-herbie
Rules
2506×*-lowering-*.f32
2506×*-lowering-*.f64
1886×fnmadd-define
1768×fma-lowering-fma.f32
1768×fma-lowering-fma.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
040138
1172128
2682126
33796126
01322
14321
215821
368021
4288221
5602221
0803121
Stop Event
1×iter limit
1×node limit
1×node limit
Calls
Call 1
Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
Outputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) 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 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
Call 2
Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta)))))
(/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta))))
(neg (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta))))))
(neg (/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta)))))
(/ (- (* cosTheta cosTheta) 1) (* (* (PI) (log (* cosTheta cosTheta))) (+ 1 (* (* (- (* cosTheta cosTheta) 1) alpha) alpha))))
Outputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (fmsub alpha alpha 1) (* (log (* alpha alpha)) (* (PI) (fma (fmsub alpha alpha 1) (* cosTheta cosTheta) 1))))
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta)))))
(/ (fmsub alpha alpha 1) (* (log (* alpha alpha)) (* (PI) (fma (fmsub alpha alpha 1) (* cosTheta cosTheta) 1))))
(/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta))))
(/ (fmsub alpha alpha 1) (* (log (* alpha alpha)) (* (PI) (fma (fmsub alpha alpha 1) (* cosTheta cosTheta) 1))))
(neg (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta))))))
(/ (fnmsub alpha alpha -1) (* (log (* alpha alpha)) (* (PI) (fma (fmsub alpha alpha 1) (* cosTheta cosTheta) 1))))
(neg (/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta)))))
(/ (fnmsub alpha alpha -1) (* (log (* alpha alpha)) (* (PI) (fma (fmsub alpha alpha 1) (* cosTheta cosTheta) 1))))
(/ (- (* cosTheta cosTheta) 1) (* (* (PI) (log (* cosTheta cosTheta))) (+ 1 (* (* (- (* cosTheta cosTheta) 1) alpha) alpha))))
(/ (fmsub cosTheta cosTheta 1) (* (log (* cosTheta cosTheta)) (fma (* (PI) alpha) (fmsub alpha (* cosTheta cosTheta) alpha) (PI))))
Symmetry

(abs cosTheta)

(abs alpha)

explain232.0ms (2.7%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
00-0-(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
00-0-(*.f32 alpha alpha)
00-0-(log.f32 (*.f32 alpha alpha))
00-0-(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
00-0-(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
00-0-(*.f32 (*.f32 (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 (*.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-alpha
00-0-cosTheta
00-0-(PI.f32)
00-0-#s(literal 1 binary32)
00-0-(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
Results
154.0ms512×0valid
Compiler

Compiled 214 to 41 computations (80.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 111.0ms
ival-mult: 90.0ms (81.4% of total)
ival-log: 7.0ms (6.3% of total)
ival-div: 4.0ms (3.6% of total)
ival-sub: 3.0ms (2.7% of total)
ival-add: 3.0ms (2.7% of total)
ival-pi: 2.0ms (1.8% of total)
const: 1.0ms (0.9% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 26 to 14 computations (46.2% saved)

prune1.0ms (0%)

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)

simplify175.0ms (2%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓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 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 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
Rules
2506×*-lowering-*.f32
2506×*-lowering-*.f64
1886×fnmadd-define
1768×fma-lowering-fma.f32
1768×fma-lowering-fma.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01384
14381
215881
368081
4288281
5602281
0803181
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(- (* alpha alpha) 1)
(* alpha alpha)
alpha
1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
cosTheta
Outputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) 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 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
(- (* alpha alpha) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(* alpha alpha)
(*.f32 alpha alpha)
alpha
1
#s(literal 1 binary32)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
(* (PI) (log (* alpha alpha)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(* (- (* alpha alpha) 1) cosTheta)
(*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)
cosTheta

localize73.0ms (0.8%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
✓accuracy99.4%
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓accuracy99.1%
(/.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))))
✓accuracy99.0%
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
Results
52.0ms256×0valid
Compiler

Compiled 94 to 14 computations (85.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 38.0ms
ival-pi: 19.0ms (50.5% of total)
ival-mult: 9.0ms (23.9% of total)
ival-log: 5.0ms (13.3% of total)
ival-div: 2.0ms (5.3% of total)
ival-sub: 1.0ms (2.7% of total)
ival-add: 1.0ms (2.7% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series135.0ms (1.6%)

Counts
7 → 132
Calls
Call 1
Inputs
#<alt (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (- (* alpha alpha) 1)>
#<alt (* alpha alpha)>
#<alt (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))>
#<alt (* (PI) (log (* alpha alpha)))>
#<alt (* (- (* alpha alpha) 1) cosTheta)>
#<alt (* (* (- (* alpha alpha) 1) cosTheta) 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))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))>
#<alt (* 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
44.0ms
alpha
@0
(* (PI) (log (* alpha alpha)))
36.0ms
alpha
@inf
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
18.0ms
alpha
@inf
(* (- (* alpha alpha) 1) cosTheta)
10.0ms
alpha
@inf
(* (PI) (log (* alpha alpha)))
8.0ms
alpha
@0
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))

rewrite439.0ms (5%)

Algorithm
1×batch-egg-rewrite
Rules
5018×*-lowering-*.f32
5018×*-lowering-*.f64
3984×/-lowering-/.f32
3984×/-lowering-/.f64
1616×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01366
19464
279461
0859861
Stop Event
1×iter limit
1×node limit
Counts
7 → 529
Calls
Call 1
Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(- (* alpha alpha) 1)
(* alpha alpha)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(* (- (* alpha alpha) 1) cosTheta)
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
Outputs
(neg.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))))))
(neg.f32 (*.f32 #s(literal 1 binary32) (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))))))
(neg.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))))
(neg.f32 (/.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))))
(neg.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
(exp.f32 (*.f32 (log.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))) #s(literal -1 binary32)))
(+.f32 (/.f32 (/.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))))
(+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))) (/.f32 (/.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
(+.f32 (fma.f32 alpha (/.f32 alpha (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))) (neg.f32 (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)))) (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))) #s(literal 1 binary32) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32))))
(+.f32 (fma.f32 (*.f32 alpha alpha) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) (neg.f32 (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)))) (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))) #s(literal 1 binary32) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32))))
(+.f32 (fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))) (neg.f32 (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)))) (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))) #s(literal 1 binary32) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32))))
(+.f32 (fma.f32 (/.f32 alpha (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 alpha (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) (neg.f32 (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)))) (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))) #s(literal 1 binary32) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32))))
(+.f32 (fma.f32 (/.f32 alpha (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) (/.f32 alpha (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (neg.f32 (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)))) (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))) #s(literal 1 binary32) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32))))
(+.f32 (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) (*.f32 alpha alpha)) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal -1 binary32)))
(+.f32 (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal -1 binary32)) (*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) (*.f32 alpha alpha)))
(+.f32 (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))) #s(literal 1 binary32)) (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (+.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32)))))
(+.f32 (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (+.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32)))) (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))) #s(literal 1 binary32)))
(+.f32 (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))) #s(literal 1 binary32)) (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
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(/.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 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta))
(*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)
(*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 cosTheta #s(literal 1 binary32)))
(*.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))
(*.f32 (+.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 cosTheta (+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))))
(*.f32 (*.f32 cosTheta (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
(*.f32 (*.f32 (+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32)) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))))
(*.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
(*.f32 (/.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (/.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) #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)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
(/.f32 (*.f32 cosTheta cosTheta) (/.f32 #s(literal -1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(/.f32 (*.f32 (+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
(/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
(/.f32 (neg.f32 (*.f32 (+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) (neg.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))))
(/.f32 (neg.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))) (-.f32 #s(literal 0 binary32) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
(*.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))
(*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta))
(*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) cosTheta)
(*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) #s(literal 1 binary32))
(*.f32 (+.f32 alpha #s(literal 1 binary32)) (*.f32 (+.f32 alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))
(*.f32 (*.f32 (+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))))
(*.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))

simplify300.0ms (3.4%)

Algorithm
1×egg-herbie
Rules
5852×*-lowering-*.f32
5852×*-lowering-*.f64
2538×/-lowering-/.f32
2538×/-lowering-/.f64
2264×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02132627
17102409
228822383
086342383
Stop Event
1×iter limit
1×node limit
Counts
132 → 132
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))))
(* 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
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(+.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 (log.f32 alpha) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (PI.f32)))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
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(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (/.f32 (/.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (*.f32 (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))) (/.f32 (/.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
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-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(- (pow alpha 2) 1)
(+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(- (pow alpha 2) 1)
(+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(pow alpha 2)
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(pow alpha 2)
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(*.f32 alpha alpha)
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(*.f32 alpha alpha)
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(*.f32 alpha alpha)
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(*.f32 alpha alpha)
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(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
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(*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32)))
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(*.f32 #s(literal 2 binary32) (+.f32 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (*.f32 (*.f32 alpha alpha) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
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(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(*.f32 #s(literal 2 binary32) (+.f32 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (*.f32 (*.f32 alpha alpha) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(*.f32 (*.f32 (*.f32 cosTheta cosTheta) (neg.f32 (*.f32 (PI.f32) (log.f32 alpha)))) (*.f32 (*.f32 alpha alpha) #s(literal -2 binary32)))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (-.f32 (neg.f32 (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (-.f32 (neg.f32 (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (-.f32 (neg.f32 (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 cosTheta cosTheta))) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (+.f32 (*.f32 (PI.f32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 cosTheta cosTheta))) (/.f32 (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (*.f32 alpha 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)))))
(*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (+.f32 (*.f32 (PI.f32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 cosTheta cosTheta))) (/.f32 (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (*.f32 alpha 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)))))
(*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (+.f32 (*.f32 (PI.f32) (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 cosTheta cosTheta))) (/.f32 (*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (*.f32 alpha alpha)))))
(* (PI) (log (pow alpha 2)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(+.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(+.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(+.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(*.f32 (*.f32 cosTheta cosTheta) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (+.f32 (*.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (+.f32 (*.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (+.f32 (*.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(*.f32 (*.f32 cosTheta cosTheta) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (+.f32 (*.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (+.f32 (*.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (+.f32 (*.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta)))))
(* 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))))
(neg.f32 (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(neg.f32 (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(neg.f32 (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(neg.f32 (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) #s(literal -2 binary32)))
(* -1 cosTheta)
(neg.f32 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow alpha 2) cosTheta)
(*.f32 alpha (*.f32 alpha cosTheta))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 alpha (*.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 alpha (*.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 alpha (*.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* (pow alpha 2) cosTheta)
(*.f32 alpha (*.f32 alpha cosTheta))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 alpha (*.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 alpha (*.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(*.f32 alpha (*.f32 alpha (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* -1 (pow cosTheta 2))
(-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
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(* (pow alpha 2) (pow cosTheta 2))
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(*.f32 (*.f32 alpha alpha) (*.f32 (+.f32 cosTheta (/.f32 cosTheta alpha)) (-.f32 cosTheta (/.f32 cosTheta alpha))))
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(*.f32 (*.f32 alpha alpha) (*.f32 (+.f32 cosTheta (/.f32 cosTheta alpha)) (-.f32 cosTheta (/.f32 cosTheta alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 (*.f32 alpha alpha) (*.f32 (+.f32 cosTheta (/.f32 cosTheta alpha)) (-.f32 cosTheta (/.f32 cosTheta alpha))))
(* (pow alpha 2) (pow cosTheta 2))
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(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 (*.f32 alpha alpha) (*.f32 (+.f32 cosTheta (/.f32 cosTheta alpha)) (-.f32 cosTheta (/.f32 cosTheta alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 (*.f32 alpha alpha) (*.f32 (+.f32 cosTheta (/.f32 cosTheta alpha)) (-.f32 cosTheta (/.f32 cosTheta alpha))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(*.f32 (*.f32 alpha alpha) (*.f32 (+.f32 cosTheta (/.f32 cosTheta alpha)) (-.f32 cosTheta (/.f32 cosTheta alpha))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
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(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(*.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))

eval82.0ms (0.9%)

Compiler

Compiled 33065 to 2431 computations (92.6% saved)

prune122.0ms (1.4%)

Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New76024784
Fresh000
Picked011
Done000
Total76025785
Accuracy
99.9%
Counts
785 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.2%
(/.f32 (/.f32 (-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶98.5%
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.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))))
▶-0.0%
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
98.5%
(/.f32 (/.f32 (+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32)) (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.5%
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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))))
96.2%
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
98.4%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal 1 binary32)) (+.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))))
98.0%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 (*.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))))
98.1%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (/.f32 #s(literal 1 binary32) (/.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))))
67.2%
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 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 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶98.3%
(/.f32 (-.f32 (*.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))))
47.7%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (+.f32 (*.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (-.f32 (neg.f32 (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
96.3%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶98.2%
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 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))))
98.4%
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (*.f32 (+.f32 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))))
98.5%
(/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.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))))
98.2%
(/.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))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
1.8%
(/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
67.2%
(/.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))))
98.1%
(+.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 (log.f32 alpha) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (PI.f32)))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
Compiler

Compiled 1612 to 841 computations (47.8% saved)

simplify33.0ms (0.4%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
✓cost-diff0
(-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
✓cost-diff0
(/.f32 (-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
✓cost-diff0
(/.f32 (/.f32 (-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.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-diff0
(+.f32 alpha #s(literal 1 binary32))
✓cost-diff0
(*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha)
✓cost-diff0
(+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32)))
✓cost-diff0
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 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))))
✓cost-diff0
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta)))
✓cost-diff0
(*.f32 alpha alpha)
✓cost-diff0
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓cost-diff0
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
✓cost-diff0
(*.f32 alpha alpha)
✓cost-diff0
(-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
✓cost-diff0
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
✓cost-diff0
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
✓cost-diff0
(*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))
✓cost-diff0
(-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))
✓cost-diff0
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
✓cost-diff0
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.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))))
Rules
32×*-lowering-*.f32
32×*-lowering-*.f64
18×/-lowering-/.f32
18×/-lowering-/.f64
12×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044622
Stop Event
1×iter limit
1×iter limit
1×unsound
Calls
Call 1
Inputs
(/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha)))
(- 1 (* alpha (* alpha (* alpha alpha))))
1
(* alpha (* alpha (* alpha alpha)))
alpha
(* alpha (* alpha alpha))
(* alpha alpha)
(- -1 (* alpha alpha))
-1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* cosTheta (* cosTheta (- 1 (* alpha alpha))))))
(/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))
(- 1 (* alpha alpha))
1
(* alpha alpha)
alpha
(* (PI) (/ 0 0))
(PI)
(/ 0 0)
0
(+ -1 (* cosTheta (* cosTheta (- 1 (* alpha alpha)))))
-1
(* cosTheta (* cosTheta (- 1 (* alpha alpha))))
cosTheta
(* cosTheta (- 1 (* alpha alpha)))
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta))))
(- (* alpha alpha) 1)
(* alpha alpha)
alpha
1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (neg cosTheta) cosTheta))
(* (neg cosTheta) cosTheta)
(neg cosTheta)
cosTheta
(/ (+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1))
(* (+ alpha 1) alpha)
(+ alpha 1)
alpha
1
(* (+ alpha 1) -1)
-1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(* alpha alpha)
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))
(- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1))
(* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))
(* alpha (* alpha (* alpha alpha)))
alpha
(* alpha (* alpha alpha))
(* alpha alpha)
(+ (* alpha alpha) 1)
1
(* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
Outputs
(/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.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))))
(/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha)))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(- 1 (* alpha (* alpha (* alpha alpha))))
(-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))
1
#s(literal 1 binary32)
(* alpha (* alpha (* alpha alpha)))
(*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))
alpha
(* alpha (* alpha alpha))
(*.f32 alpha (*.f32 alpha alpha))
(* alpha alpha)
(*.f32 alpha alpha)
(- -1 (* alpha alpha))
(-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
-1
#s(literal -1 binary32)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) 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)))
(* (PI) (log (* alpha alpha)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(- (* alpha alpha) 1)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* cosTheta (* cosTheta (- 1 (* alpha alpha))))))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
(/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(- 1 (* alpha alpha))
(-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
1
#s(literal 1 binary32)
(* alpha alpha)
(*.f32 alpha alpha)
alpha
(* (PI) (/ 0 0))
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(PI)
(PI.f32)
(/ 0 0)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
0
#s(literal 0 binary32)
(+ -1 (* cosTheta (* cosTheta (- 1 (* alpha alpha)))))
(+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
-1
#s(literal -1 binary32)
(* cosTheta (* cosTheta (- 1 (* alpha alpha))))
(*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
cosTheta
(* cosTheta (- 1 (* alpha alpha)))
(*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg 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 (neg.f32 cosTheta) cosTheta))))
(- (* alpha alpha) 1)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(* alpha alpha)
(*.f32 alpha alpha)
alpha
1
#s(literal 1 binary32)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta)))
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(+ 1 (* (neg cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))
(* (neg cosTheta) cosTheta)
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg cosTheta)
(neg.f32 cosTheta)
cosTheta
(/ (+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 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))))
(+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1))
(+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32)))
(* (+ alpha 1) alpha)
(*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha)
(+ alpha 1)
(+.f32 alpha #s(literal 1 binary32))
alpha
1
#s(literal 1 binary32)
(* (+ alpha 1) -1)
(*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))
-1
#s(literal -1 binary32)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) 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)))
(* (PI) (log (* alpha alpha)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(* alpha alpha)
(*.f32 alpha alpha)
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(- (* alpha alpha) 1)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (/.f32 (-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.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))))
(/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))
(/.f32 (-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
(- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1))
(-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
(* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
(* alpha (* alpha (* alpha alpha)))
(*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))
alpha
(* alpha (* alpha alpha))
(*.f32 alpha (*.f32 alpha alpha))
(* alpha alpha)
(*.f32 alpha alpha)
(+ (* alpha alpha) 1)
(+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
1
#s(literal 1 binary32)
(* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))
(*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) 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)))
(* (PI) (log (* alpha alpha)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(- (* alpha alpha) 1)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta

localize270.0ms (3.1%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f32 alpha (*.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 alpha alpha)
✓accuracy100.0%
(neg.f32 cosTheta)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
✓accuracy100.0%
(*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 alpha (*.f32 alpha alpha))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
Results
186.0ms256×0invalid
Compiler

Compiled 625 to 45 computations (92.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 65.0ms
ival-mult: 32.0ms (49% of total)
ival-div: 13.0ms (19.9% of total)
ival-add: 7.0ms (10.7% of total)
ival-sub: 6.0ms (9.2% of total)
ival-log: 4.0ms (6.1% of total)
ival-pi: 1.0ms (1.5% of total)
const: 1.0ms (1.5% of total)
ival-neg: 1.0ms (1.5% of total)
backward-pass: 0.0ms (0% of total)

series54.0ms (0.6%)

Counts
26 → 360
Calls
Call 1
Inputs
#<alt (/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha)))>
#<alt (- 1 (* alpha (* alpha (* alpha alpha))))>
#<alt (* alpha (* alpha (* alpha alpha)))>
#<alt (/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* cosTheta (* cosTheta (- 1 (* alpha alpha))))))>
#<alt (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))>
#<alt (- 1 (* alpha alpha))>
#<alt (* alpha alpha)>
#<alt (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta))))>
#<alt (- (* alpha alpha) 1)>
#<alt (* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta)))>
#<alt (/ (+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1))>
#<alt (* (+ alpha 1) alpha)>
#<alt (+ alpha 1)>
#<alt (/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))>
#<alt (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1))>
#<alt (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))>
#<alt (PI)>
#<alt (log (* alpha alpha))>
#<alt (* alpha (* alpha alpha))>
#<alt (* cosTheta (* cosTheta (- 1 (* alpha alpha))))>
#<alt (* cosTheta (- 1 (* alpha alpha)))>
#<alt (neg cosTheta)>
#<alt (* (PI) (log (* alpha alpha)))>
Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* (pow alpha 2) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (+ (* 1/2 (/ 1 (* (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 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* (pow alpha 2) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (+ (* 1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* (pow alpha 2) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (+ (* 1/2 (/ 1 (* (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) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))))))))) (* 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 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))) (+ (* 1/2 (/ 1 (* (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 2)))) (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))) (+ (* 1/2 (/ 1 (* (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 2)))) (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
#<alt (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))>
#<alt (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (pow cosTheta 2) (* (- 1 (pow alpha 4)) (- (pow alpha 2) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))>
#<alt (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* -1 (/ (* (pow cosTheta 2) (* (- 1 (pow alpha 4)) (pow (- (pow alpha 2) 1) 2))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (- 1 (pow alpha 4)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))))>
#<alt (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* (pow cosTheta 2) (+ (* -1 (/ (* (- 1 (pow alpha 4)) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (pow cosTheta 2) (* (- 1 (pow alpha 4)) (pow (- (pow alpha 2) 1) 3))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))) (/ (* (- 1 (pow alpha 4)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))))>
#<alt (* -1 (/ (- 1 (pow alpha 4)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2)))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (+ (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (pow cosTheta 6)))))) (pow cosTheta 2))>
#<alt (* -1 (/ (- 1 (pow alpha 4)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2)))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (+ (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (pow cosTheta 6)))))) (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 (* -1 (pow alpha 4)))>
#<alt (+ 1 (* -1 (pow alpha 4)))>
#<alt (+ 1 (* -1 (pow alpha 4)))>
#<alt (* -1 (pow alpha 4))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* -1 (pow alpha 4))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt 1>
#<alt (+ 1 (* -1 (pow alpha 2)))>
#<alt (+ 1 (* -1 (pow alpha 2)))>
#<alt (+ 1 (* -1 (pow alpha 2)))>
#<alt (* -1 (pow alpha 2))>
#<alt (* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))>
#<alt (* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))>
#<alt (* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))>
#<alt (* -1 (pow alpha 2))>
#<alt (* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))>
#<alt (* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))>
#<alt (* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))>
#<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 (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (/ (pow alpha 2) (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* 1/2 (/ (pow alpha 2) (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* 1/2 (/ (pow alpha 2) (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (* -1/2 (/ (pow alpha 2) (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))))>
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#<alt (* (pow alpha 2) (+ (* -1 (pow cosTheta 2)) (/ (pow cosTheta 2) (pow alpha 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (pow cosTheta 2)) (/ (pow cosTheta 2) (pow alpha 2))))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt (* cosTheta (- 1 (pow alpha 2)))>
#<alt cosTheta>
#<alt (+ cosTheta (* -1 (* (pow alpha 2) cosTheta)))>
#<alt (+ cosTheta (* -1 (* (pow alpha 2) cosTheta)))>
#<alt (+ cosTheta (* -1 (* (pow alpha 2) cosTheta)))>
#<alt (* -1 (* (pow alpha 2) cosTheta))>
#<alt (* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))>
#<alt (* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))>
#<alt (* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))>
#<alt (* -1 (* (pow alpha 2) cosTheta))>
#<alt (* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))>
#<alt (* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))>
#<alt (* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 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)>
#<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

99 calls:

TimeVariablePointExpression
5.0ms
alpha
@0
(/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
3.0ms
alpha
@inf
(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms
alpha
@inf
(log (* alpha alpha))
2.0ms
alpha
@inf
(/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms
alpha
@0
(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite18.0ms (0.2%)

Algorithm
1×batch-egg-rewrite
Rules
32×*-lowering-*.f32
32×*-lowering-*.f64
18×/-lowering-/.f32
18×/-lowering-/.f64
12×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044340
Stop Event
1×iter limit
1×iter limit
1×unsound
Counts
26 → 26
Calls
Call 1
Inputs
(/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha)))
(- 1 (* alpha (* alpha (* alpha alpha))))
(* alpha (* alpha (* alpha alpha)))
(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* cosTheta (* cosTheta (- 1 (* alpha alpha))))))
(/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))
(- 1 (* alpha alpha))
(* alpha alpha)
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta))))
(- (* alpha alpha) 1)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta)))
(/ (+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1))
(* (+ alpha 1) alpha)
(+ alpha 1)
(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1)))
(- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1))
(* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))
(PI)
(log (* alpha alpha))
(* alpha (* alpha alpha))
(* cosTheta (* cosTheta (- 1 (* alpha alpha))))
(* cosTheta (- 1 (* alpha alpha)))
(neg cosTheta)
(* (PI) (log (* alpha alpha)))
Outputs
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.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 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))
(*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(*.f32 alpha alpha)
(/.f32 (-.f32 (*.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 (*.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 (+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 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 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.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 (-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.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 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
(-.f32 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha (*.f32 alpha alpha))
(*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(neg.f32 cosTheta)
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))

simplify406.0ms (4.6%)

Algorithm
1×egg-herbie
Rules
4782×*-lowering-*.f32
4782×*-lowering-*.f64
4578×+-lowering-+.f64
4578×+-lowering-+.f32
2092×/-lowering-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
072210769
127229432
086139432
Stop Event
1×iter limit
1×node limit
Counts
360 → 360
Calls
Call 1
Inputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* (pow alpha 2) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (+ (* 1/2 (/ 1 (* (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 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* (pow alpha 2) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (+ (* 1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* (pow alpha 2) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (+ (* 1/2 (/ 1 (* (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) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(- (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (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 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (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 cosTheta 4) (* (PI) (log (/ 1 alpha))))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(- (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (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 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (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 cosTheta 4) (* (PI) (log (/ -1 alpha))))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))
(+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (pow cosTheta 2) (* (- 1 (pow alpha 4)) (- (pow alpha 2) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))
(+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* -1 (/ (* (pow cosTheta 2) (* (- 1 (pow alpha 4)) (pow (- (pow alpha 2) 1) 2))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (- 1 (pow alpha 4)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))))
(+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* (pow cosTheta 2) (+ (* -1 (/ (* (- 1 (pow alpha 4)) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (pow cosTheta 2) (* (- 1 (pow alpha 4)) (pow (- (pow alpha 2) 1) 3))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))) (/ (* (- 1 (pow alpha 4)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))))
(* -1 (/ (- 1 (pow alpha 4)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2)))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (+ (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (pow cosTheta 6)))))) (pow cosTheta 2))
(* -1 (/ (- 1 (pow alpha 4)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2)))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (+ (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (pow cosTheta 6)))))) (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 (* -1 (pow alpha 4)))
(+ 1 (* -1 (pow alpha 4)))
(+ 1 (* -1 (pow alpha 4)))
(* -1 (pow alpha 4))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* -1 (pow alpha 4))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
1
(+ 1 (* -1 (pow alpha 2)))
(+ 1 (* -1 (pow alpha 2)))
(+ 1 (* -1 (pow alpha 2)))
(* -1 (pow alpha 2))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(* -1 (pow alpha 2))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 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)
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
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-1
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(- (pow alpha 2) 1)
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(pow alpha 2)
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
-1
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(- (* (pow alpha 2) (- (* (pow alpha 2) (+ 1 (pow alpha 2))) 1)) 1)
(pow alpha 6)
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(* (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))))
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(pow alpha 4)
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(* 2 (log alpha))
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(+ (* -1 (* (pow alpha 2) (pow cosTheta 2))) (pow cosTheta 2))
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(* -1 (* (pow alpha 2) (pow cosTheta 2)))
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(* cosTheta (- 1 (pow alpha 2)))
(* cosTheta (- 1 (pow alpha 2)))
(* cosTheta (- 1 (pow alpha 2)))
(* cosTheta (- 1 (pow alpha 2)))
(* cosTheta (- 1 (pow alpha 2)))
cosTheta
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(+ cosTheta (* -1 (* (pow alpha 2) cosTheta)))
(+ cosTheta (* -1 (* (pow alpha 2) cosTheta)))
(* -1 (* (pow alpha 2) cosTheta))
(* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))
(* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))
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(* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))
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(* -1 cosTheta)
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(* 2 (* (PI) (log alpha)))
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(* -2 (* (PI) (log (/ -1 alpha))))
Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
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#s(literal -1 binary32)
(- (pow alpha 2) 1)
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(- (pow alpha 2) 1)
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#s(literal -1 binary32)
(- (* -1 (pow alpha 2)) 1)
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(- (* (pow alpha 2) (- (pow alpha 2) 1)) 1)
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(- (* (pow alpha 2) (- (* (pow alpha 2) (+ 1 (pow alpha 2))) 1)) 1)
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(pow alpha 6)
(pow.f32 alpha #s(literal 6 binary32))
(* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))
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(pow alpha 6)
(pow.f32 alpha #s(literal 6 binary32))
(* (pow alpha 6) (+ 1 (/ 1 (pow alpha 2))))
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(pow alpha 4)
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(* (pow alpha 4) (+ 1 (pow alpha 2)))
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(pow alpha 6)
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(* 2 (log alpha))
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(* 2 (log alpha))
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(* 2 (log alpha))
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(pow alpha 3)
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(pow alpha 3)
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(* (pow cosTheta 2) (- 1 (pow alpha 2)))
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(* (pow cosTheta 2) (- 1 (pow alpha 2)))
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(* (pow cosTheta 2) (- 1 (pow alpha 2)))
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(* (pow cosTheta 2) (- 1 (pow alpha 2)))
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(* (pow cosTheta 2) (- 1 (pow alpha 2)))
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(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(+ (* -1 (* (pow alpha 2) (pow cosTheta 2))) (pow cosTheta 2))
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(+ (* -1 (* (pow alpha 2) (pow cosTheta 2))) (pow cosTheta 2))
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(+ (* -1 (* (pow alpha 2) (pow cosTheta 2))) (pow cosTheta 2))
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(* -1 (* (pow alpha 2) (pow cosTheta 2)))
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(* (pow alpha 2) (+ (* -1 (pow cosTheta 2)) (/ (pow cosTheta 2) (pow alpha 2))))
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(* -1 (* (pow alpha 2) (pow cosTheta 2)))
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(* cosTheta (- 1 (pow alpha 2)))
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(* cosTheta (- 1 (pow alpha 2)))
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(* cosTheta (- 1 (pow alpha 2)))
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(* cosTheta (- 1 (pow alpha 2)))
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(* cosTheta (- 1 (pow alpha 2)))
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(* cosTheta (- 1 (pow alpha 2)))
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(* cosTheta (- 1 (pow alpha 2)))
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(* cosTheta (- 1 (pow alpha 2)))
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(* cosTheta (- 1 (pow alpha 2)))
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(* cosTheta (- 1 (pow alpha 2)))
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cosTheta
(+ cosTheta (* -1 (* (pow alpha 2) cosTheta)))
(*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(+ cosTheta (* -1 (* (pow alpha 2) cosTheta)))
(*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(+ cosTheta (* -1 (* (pow alpha 2) cosTheta)))
(*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(* -1 (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))
(* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (-.f32 (/.f32 cosTheta (*.f32 alpha alpha)) cosTheta))
(* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (-.f32 (/.f32 cosTheta (*.f32 alpha alpha)) cosTheta))
(* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (-.f32 (/.f32 cosTheta (*.f32 alpha alpha)) cosTheta))
(* -1 (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))
(* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (-.f32 (/.f32 cosTheta (*.f32 alpha alpha)) cosTheta))
(* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (-.f32 (/.f32 cosTheta (*.f32 alpha alpha)) cosTheta))
(* (pow alpha 2) (+ (* -1 cosTheta) (/ cosTheta (pow alpha 2))))
(*.f32 (*.f32 alpha alpha) (-.f32 (/.f32 cosTheta (*.f32 alpha alpha)) 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)
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (log.f32 alpha))
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (log.f32 alpha))
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (log.f32 alpha))
(* 2 (* (PI) (log alpha)))
(*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (log.f32 alpha))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))
(*.f32 (*.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))

eval74.0ms (0.8%)

Compiler

Compiled 32184 to 837 computations (97.4% saved)

prune48.0ms (0.5%)

Pruning

27 alts after pruning (26 fresh and 1 done)

PrunedKeptTotal
New75017767
Fresh10919
Picked505
Done011
Total76527792
Accuracy
100.0%
Counts
792 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.2%
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.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))))
▶-0.0%
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
81.9%
(/.f32 (/.f32 (-.f32 #s(literal 0 binary32) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.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%
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
▶98.5%
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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))))
98.0%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 (*.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))))
98.1%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶95.9%
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
▶98.2%
(/.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #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))))
81.9%
(/.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))))
67.2%
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
98.3%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 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 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (-.f32 (neg.f32 (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
96.3%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶97.9%
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
98.4%
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (*.f32 (+.f32 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))))
98.1%
(/.f32 (+.f32 (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) alpha))) (*.f32 (+.f32 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))))
97.9%
(/.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 (neg.f32 cosTheta) cosTheta))))
1.8%
(/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
67.2%
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
96.8%
(-.f32 (*.f32 (/.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal -1 binary32) alpha)) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
98.1%
(+.f32 (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
97.2%
(*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
97.8%
(*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
96.1%
(neg.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
Compiler

Compiled 1522 to 843 computations (44.6% saved)

simplify11.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))
✓cost-diff0
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32)))
✓cost-diff0
(/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
✓cost-diff0
(/.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #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))))
✓cost-diff0
(+.f32 alpha #s(literal 1 binary32))
✓cost-diff0
(*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha)
✓cost-diff0
(+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32)))
✓cost-diff0
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
✓cost-diff0
(+.f32 alpha #s(literal 1 binary32))
✓cost-diff0
(*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha))
✓cost-diff0
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32))
✓cost-diff0
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
✓cost-diff0
(*.f32 alpha alpha)
✓cost-diff0
(-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
✓cost-diff0
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
✓cost-diff0
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
✓cost-diff0
(*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))
✓cost-diff0
(+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))))
✓cost-diff0
(/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))))
✓cost-diff0
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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))))
Rules
36×*-lowering-*.f32
36×*-lowering-*.f64
22×/-lowering-/.f32
22×/-lowering-/.f64
18×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050605
Stop Event
1×iter limit
1×iter limit
1×unsound
Calls
Call 1
Inputs
(/ (/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))))
(+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha)))))
-1
(* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))
(* alpha alpha)
alpha
(* alpha (* alpha (* alpha alpha)))
(* alpha (* alpha alpha))
(+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))
1
(- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))
(- 0 (* alpha alpha))
0
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* cosTheta cosTheta)))
(/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))
(- 1 (* alpha alpha))
1
(* alpha alpha)
alpha
(* (PI) (/ 0 0))
(PI)
(/ 0 0)
0
(+ -1 (* cosTheta cosTheta))
-1
(* cosTheta cosTheta)
cosTheta
(/ (/ (* (+ alpha 1) (+ -1 alpha)) (PI)) (log (* alpha alpha)))
(/ (* (+ alpha 1) (+ -1 alpha)) (PI))
(* (+ alpha 1) (+ -1 alpha))
(+ alpha 1)
alpha
1
(+ -1 alpha)
-1
(PI)
(log (* alpha alpha))
(* alpha alpha)
(/ (+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))
(+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1))
(* (+ alpha 1) alpha)
(+ alpha 1)
alpha
1
(* (+ alpha 1) -1)
-1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(* alpha alpha)
(+ 1 (* (* -1 cosTheta) cosTheta))
(* (* -1 cosTheta) cosTheta)
(* -1 cosTheta)
cosTheta
(/ (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha)))
(* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1))
(* (* alpha alpha) (* alpha alpha))
(* alpha alpha)
alpha
(+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)
(/ 1 (* (* alpha alpha) (* alpha alpha)))
1
-1
(- -1 (* alpha alpha))
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
Outputs
(/ (/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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))))
(/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))))
(/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))))
(+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha)))))
(+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))))
-1
#s(literal -1 binary32)
(* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))
(*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))
(* alpha alpha)
(*.f32 alpha alpha)
alpha
(* alpha (* alpha (* alpha alpha)))
(*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))
(* alpha (* alpha alpha))
(*.f32 alpha (*.f32 alpha alpha))
(+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))
(+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha))))
1
#s(literal 1 binary32)
(- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))
(-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))
(- 0 (* alpha alpha))
(-.f32 #s(literal 0 binary32) (*.f32 alpha alpha))
0
#s(literal 0 binary32)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) 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)))
(* (PI) (log (* alpha alpha)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(- (* alpha alpha) 1)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(- 1 (* alpha alpha))
(-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
1
#s(literal 1 binary32)
(* alpha alpha)
(*.f32 alpha alpha)
alpha
(* (PI) (/ 0 0))
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(PI)
(PI.f32)
(/ 0 0)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
0
#s(literal 0 binary32)
(+ -1 (* cosTheta cosTheta))
(+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta))
-1
#s(literal -1 binary32)
(* cosTheta cosTheta)
(*.f32 cosTheta cosTheta)
cosTheta
(/ (/ (* (+ alpha 1) (+ -1 alpha)) (PI)) (log (* alpha alpha)))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/ (* (+ alpha 1) (+ -1 alpha)) (PI))
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32))
(* (+ alpha 1) (+ -1 alpha))
(*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha))
(+ alpha 1)
(+.f32 alpha #s(literal 1 binary32))
alpha
1
#s(literal 1 binary32)
(+ -1 alpha)
(+.f32 #s(literal -1 binary32) alpha)
-1
#s(literal -1 binary32)
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(* alpha alpha)
(*.f32 alpha alpha)
(/ (+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1))
(+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32)))
(* (+ alpha 1) alpha)
(*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha)
(+ alpha 1)
(+.f32 alpha #s(literal 1 binary32))
alpha
1
#s(literal 1 binary32)
(* (+ alpha 1) -1)
(*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))
-1
#s(literal -1 binary32)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta)))
(*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(* alpha alpha)
(*.f32 alpha alpha)
(+ 1 (* (* -1 cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))
(* (* -1 cosTheta) cosTheta)
(*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta)
(* -1 cosTheta)
(*.f32 #s(literal -1 binary32) cosTheta)
cosTheta
(/ (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #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))))
(/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha)))
(/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32)))
(* (* alpha alpha) (* alpha alpha))
(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))
(* alpha alpha)
(*.f32 alpha alpha)
alpha
(+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)
(+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))
(/ 1 (* (* alpha alpha) (* alpha alpha)))
(/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)))
1
#s(literal 1 binary32)
-1
#s(literal -1 binary32)
(- -1 (* alpha alpha))
(-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) 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)))
(* (PI) (log (* alpha alpha)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(- (* alpha alpha) 1)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta

localize269.0ms (3.1%)

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 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
✓accuracy100.0%
(*.f32 cosTheta cosTheta)
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 alpha (*.f32 alpha alpha))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
Results
180.0ms256×0invalid
Compiler

Compiled 608 to 51 computations (91.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 123.0ms
ival-div: 49.0ms (40% of total)
ival-mult: 34.0ms (27.8% of total)
ival-pi: 17.0ms (13.9% of total)
ival-add: 11.0ms (9% of total)
ival-sub: 6.0ms (4.9% of total)
ival-log: 5.0ms (4.1% of total)
const: 1.0ms (0.8% of total)
backward-pass: 0.0ms (0% of total)

series35.0ms (0.4%)

Counts
26 → 300
Calls
Call 1
Inputs
#<alt (/ (/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))))>
#<alt (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha)))))>
#<alt (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))>
#<alt (/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* cosTheta cosTheta)))>
#<alt (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))>
#<alt (- 1 (* alpha alpha))>
#<alt (* alpha alpha)>
#<alt (/ (/ (* (+ alpha 1) (+ -1 alpha)) (PI)) (log (* alpha alpha)))>
#<alt (/ (* (+ alpha 1) (+ -1 alpha)) (PI))>
#<alt (* (+ alpha 1) (+ -1 alpha))>
#<alt (+ alpha 1)>
#<alt (/ (+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))>
#<alt (+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1))>
#<alt (* (+ alpha 1) alpha)>
#<alt (/ (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha)))>
#<alt (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1))>
#<alt (* (* alpha alpha) (* alpha alpha))>
#<alt (PI)>
#<alt (log (* alpha alpha))>
#<alt (* alpha (* alpha alpha))>
#<alt (* cosTheta cosTheta)>
#<alt (* (PI) (/ 0 0))>
#<alt (* -1 cosTheta)>
#<alt (* (PI) (log (* alpha alpha)))>
Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (* -1 (* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (* (pow alpha 2) (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (* -1 (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (pow alpha 4))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 6) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
#<alt (- (* -1 (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (pow alpha 4))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))>
#<alt (- (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 6) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))))))))>
#<alt (/ (- (pow alpha 6) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))>
#<alt (- (+ (* -1 (/ (* (pow cosTheta 2) (* (- (pow alpha 2) 1) (- (pow alpha 6) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (/ (pow alpha 6) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))>
#<alt (- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 6) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 6) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))) (/ (pow alpha 6) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))>
#<alt (- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 6) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (* -1 (/ (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 6) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 6) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))) (/ (pow alpha 6) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))>
#<alt (/ (- (pow alpha 6) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (/ (pow alpha 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ (pow alpha 6) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ (pow alpha 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ (pow alpha 6) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3)))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 6) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 4)))))) (+ (/ (pow alpha 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ (pow alpha 6) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3)))))) (+ (/ (pow alpha 6) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (/ (pow alpha 6) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 4)))))))))) (pow cosTheta 2))>
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#<alt (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (+ (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))))))) (pow cosTheta 2))>
#<alt (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (+ (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (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 (* -1 (pow alpha 4)))>
#<alt (+ 1 (* -1 (pow alpha 4)))>
#<alt (+ 1 (* -1 (pow alpha 4)))>
#<alt (* -1 (pow alpha 4))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* -1 (pow alpha 4))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<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 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<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)>
#<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

84 calls:

TimeVariablePointExpression
4.0ms
alpha
@inf
(/ (/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
3.0ms
alpha
@-inf
(/ (* (+ alpha 1) (+ -1 alpha)) (PI))
2.0ms
alpha
@0
(/ (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms
cosTheta
@inf
(/ (/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms
alpha
@0
(/ (/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite19.0ms (0.2%)

Algorithm
1×batch-egg-rewrite
Rules
36×*-lowering-*.f32
36×*-lowering-*.f64
22×/-lowering-/.f32
22×/-lowering-/.f64
18×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050334
Stop Event
1×iter limit
1×iter limit
1×unsound
Counts
26 → 26
Calls
Call 1
Inputs
(/ (/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))) (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))))
(+ -1 (* (* alpha alpha) (* alpha (* alpha (* alpha alpha)))))
(* (* alpha alpha) (* alpha (* alpha (* alpha alpha))))
(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* cosTheta cosTheta)))
(/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))
(- 1 (* alpha alpha))
(* alpha alpha)
(/ (/ (* (+ alpha 1) (+ -1 alpha)) (PI)) (log (* alpha alpha)))
(/ (* (+ alpha 1) (+ -1 alpha)) (PI))
(* (+ alpha 1) (+ -1 alpha))
(+ alpha 1)
(/ (+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))
(+ (* (+ alpha 1) alpha) (* (+ alpha 1) -1))
(* (+ alpha 1) alpha)
(/ (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha)))
(* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1))
(* (* alpha alpha) (* alpha alpha))
(PI)
(log (* alpha alpha))
(* alpha (* alpha alpha))
(* cosTheta cosTheta)
(* (PI) (/ 0 0))
(* -1 cosTheta)
(* (PI) (log (* alpha alpha)))
Outputs
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))))
(+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))))
(*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(*.f32 alpha alpha)
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32))
(*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha))
(+.f32 alpha #s(literal 1 binary32))
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32)))
(*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha)
(/.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #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 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32)))
(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha (*.f32 alpha alpha))
(*.f32 cosTheta cosTheta)
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(*.f32 #s(literal -1 binary32) cosTheta)
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))

simplify360.0ms (4.1%)

Algorithm
1×egg-herbie
Rules
6322×*-lowering-*.f32
6322×*-lowering-*.f64
3970×/-lowering-/.f32
3970×/-lowering-/.f64
2958×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05106991
119075932
095665932
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))))))
(- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (* -1 (* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (* (pow alpha 2) (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(- (* -1 (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (pow alpha 4))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 6) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(- (* -1 (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (pow alpha 4))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 6) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))))))))
(/ (- (pow alpha 6) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (* (- (pow alpha 2) 1) (- (pow alpha 6) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (/ (pow alpha 6) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 6) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 6) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))) (/ (pow alpha 6) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 6) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (* -1 (/ (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 6) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 6) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))) (/ (pow alpha 6) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))
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(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(- (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (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 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (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 cosTheta 4) (* (PI) (log (/ -1 alpha))))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))
(+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (pow alpha 4) (* (pow cosTheta 2) (* (- (/ 1 (pow alpha 4)) 1) (- (pow alpha 2) 1)))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))
(+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* -1 (/ (* (pow alpha 4) (* (pow cosTheta 2) (* (- (/ 1 (pow alpha 4)) 1) (pow (- (pow alpha 2) 1) 2)))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (pow alpha 4) (* (- (/ 1 (pow alpha 4)) 1) (- (pow alpha 2) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))))
(+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* (pow cosTheta 2) (+ (* -1 (/ (* (pow alpha 4) (* (- (/ 1 (pow alpha 4)) 1) (pow (- (pow alpha 2) 1) 2))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (pow alpha 4) (* (pow cosTheta 2) (* (- (/ 1 (pow alpha 4)) 1) (pow (- (pow alpha 2) 1) 3)))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))) (/ (* (pow alpha 4) (* (- (/ 1 (pow alpha 4)) 1) (- (pow alpha 2) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))))
(* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))
(/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (+ (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))))))) (pow cosTheta 2))
(* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))
(/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (+ (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (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 (* -1 (pow alpha 4)))
(+ 1 (* -1 (pow alpha 4)))
(+ 1 (* -1 (pow alpha 4)))
(* -1 (pow alpha 4))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* -1 (pow alpha 4))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(* 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 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(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)
(* 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 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(+.f32 (/.f32 (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (- (* -1 (* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(+.f32 (*.f32 (*.f32 alpha alpha) (neg.f32 (+.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.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 (*.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 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (- (* (pow alpha 2) (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(+.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (*.f32 (*.f32 alpha alpha) (-.f32 (*.f32 (*.f32 alpha alpha) (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (-.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.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 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 (*.f32 #s(literal -1/2 binary32) (*.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 (+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.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 (*.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 binary32) (*.f32 cosTheta cosTheta))))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.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 (*.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 binary32) (*.f32 cosTheta cosTheta))))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))) (*.f32 cosTheta cosTheta))
(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha)) (*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 cosTheta cosTheta)))
(- (* -1 (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (pow alpha 4))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (pow.f32 cosTheta #s(literal 6 binary32)))) (-.f32 #s(literal 0 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 cosTheta cosTheta)) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))))))))
(- (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 6) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))))))))
(-.f32 (-.f32 (+.f32 (/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 cosTheta cosTheta)) (pow.f32 alpha #s(literal 6 binary32))) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (pow.f32 cosTheta #s(literal 6 binary32)))) (*.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 6 binary32)))))) (/.f32 (*.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (*.f32 (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (pow.f32 alpha #s(literal 6 binary32)))))) (+.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (+.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (*.f32 (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (pow.f32 alpha #s(literal 4 binary32))))) (+.f32 (/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (pow.f32 cosTheta #s(literal 6 binary32))) (pow.f32 alpha #s(literal 4 binary32))) (+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 cosTheta cosTheta)) (/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (pow.f32 cosTheta #s(literal 6 binary32))) (pow.f32 alpha #s(literal 6 binary32))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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#s(literal 1 binary32)
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alpha
(* alpha (+ 1 (/ 1 alpha)))
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(* alpha (+ 1 (/ 1 alpha)))
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(* alpha (+ 1 (/ 1 alpha)))
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alpha
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(* alpha (+ 1 (/ 1 alpha)))
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(* alpha (+ 1 (/ 1 alpha)))
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(* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))))
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(* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))))
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(* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2)))))))))
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#s(literal -1 binary32)
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alpha
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(/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (pow cosTheta 2))
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(/ (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (+ (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))))))) (pow cosTheta 2))
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-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(- (pow alpha 2) 1)
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(pow alpha 2)
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 alpha (*.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(*.f32 alpha (*.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
1
#s(literal 1 binary32)
(+ 1 (* -1 (pow alpha 4)))
(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(+ 1 (* -1 (pow alpha 4)))
(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(+ 1 (* -1 (pow alpha 4)))
(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(* -1 (pow alpha 4))
(-.f32 #s(literal 0 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
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(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
(* -1 (pow alpha 4))
(-.f32 #s(literal 0 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
(pow alpha 4)
(pow.f32 alpha #s(literal 4 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 alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (-.f32 #s(literal 0 binary32) (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 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
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(pow alpha 3)
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(pow alpha 3)
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(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
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(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
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(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow 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)
(* 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 (PI.f32) (*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (PI.f32) (*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (PI.f32) (*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(*.f32 (PI.f32) (*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #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)))

eval71.0ms (0.8%)

Compiler

Compiled 24931 to 579 computations (97.7% saved)

prune37.0ms (0.4%)

Pruning

27 alts after pruning (25 fresh and 2 done)

PrunedKeptTotal
New62913642
Fresh91221
Picked415
Done011
Total64227669
Accuracy
100.0%
Counts
669 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.2%
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.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))))
▶96.2%
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
✓98.5%
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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))))
97.7%
(/.f32 (/.f32 (*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #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))))
98.0%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 (*.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))))
98.1%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
95.9%
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
▶98.2%
(/.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.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))))
95.9%
(/.f32 (/.f32 (*.f32 alpha (*.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
81.9%
(/.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))))
▶-0.0%
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
67.2%
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
▶87.1%
(/.f32 (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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))))
66.0%
(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 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 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
96.3%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
96.0%
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶95.9%
(/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))) (log.f32 (*.f32 alpha alpha)))
97.9%
(/.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 (neg.f32 cosTheta) cosTheta))))
97.8%
(/.f32 (*.f32 alpha (*.f32 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))))
67.2%
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
66.0%
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
96.7%
(+.f32 (/.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (*.f32 (/.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal -1 binary32) alpha)))
96.2%
(+.f32 (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
97.2%
(*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
96.1%
(neg.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
Compiler

Compiled 1306 to 766 computations (41.3% saved)

simplify11.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))
✓cost-diff0
(+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha))))
✓cost-diff0
(/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))))
✓cost-diff0
(/.f32 (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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))))
✓cost-diff0
(+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))
✓cost-diff0
(*.f32 alpha alpha)
✓cost-diff0
(*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha)))))
✓cost-diff0
(/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))) (log.f32 (*.f32 alpha alpha)))
✓cost-diff0
(*.f32 alpha alpha)
✓cost-diff0
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
✓cost-diff0
(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
✓cost-diff0
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
✓cost-diff0
(PI.f32)
✓cost-diff0
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
✓cost-diff0
(/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
✓cost-diff0
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
✓cost-diff0
(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))
✓cost-diff0
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32)))
✓cost-diff0
(/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
✓cost-diff0
(/.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.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))))
Rules
32×*-lowering-*.f32
32×*-lowering-*.f64
26×/-lowering-/.f32
26×/-lowering-/.f64
12×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048505
Stop Event
1×iter limit
1×iter limit
1×unsound
Calls
Call 1
Inputs
(/ (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha))) (* (* (PI) (* (log alpha) 2)) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha)))
(* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1))
(* (* alpha alpha) (* alpha alpha))
(* alpha alpha)
alpha
(+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)
(/ 1 (* (* alpha alpha) (* alpha alpha)))
1
-1
(- -1 (* alpha alpha))
(* (* (PI) (* (log alpha) 2)) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (* (log alpha) 2))
(PI)
(* (log alpha) 2)
(log alpha)
2
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
(/ (/ 1 (* (PI) (/ 0 0))) (+ -1 (* cosTheta cosTheta)))
(/ 1 (* (PI) (/ 0 0)))
1
(* (PI) (/ 0 0))
(PI)
(/ 0 0)
0
(+ -1 (* cosTheta cosTheta))
-1
(* cosTheta cosTheta)
cosTheta
(/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha)))
(/ (+ (* alpha alpha) -1) (PI))
(+ (* alpha alpha) -1)
(* alpha alpha)
alpha
-1
(PI)
(log (* alpha alpha))
(/ (* (* alpha alpha) (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha))))) (log (* alpha alpha)))
(* (* alpha alpha) (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha)))))
(* alpha alpha)
alpha
(+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha))))
(/ 1 (PI))
1
(PI)
(/ -1 (* (PI) (* alpha alpha)))
-1
(* (PI) (* alpha alpha))
(log (* alpha alpha))
(/ (/ -1 (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ -1 (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))))
-1
(+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))
1
(- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))
(* alpha (* alpha (* alpha alpha)))
alpha
(* alpha (* alpha alpha))
(* alpha alpha)
(- 0 (* alpha alpha))
0
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
Outputs
(/ (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha))) (* (* (PI) (* (log alpha) 2)) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.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))))
(/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha)))
(/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32)))
(* (* alpha alpha) (* alpha alpha))
(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))
(* alpha alpha)
(*.f32 alpha alpha)
alpha
(+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)
(+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))
(/ 1 (* (* alpha alpha) (* alpha alpha)))
(/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)))
1
#s(literal 1 binary32)
-1
#s(literal -1 binary32)
(- -1 (* alpha alpha))
(-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(* (* (PI) (* (log alpha) 2)) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(*.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)))
(* (PI) (* (log alpha) 2))
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(PI)
(PI.f32)
(* (log alpha) 2)
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(log alpha)
(log.f32 alpha)
2
#s(literal 2 binary32)
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(- (* alpha alpha) 1)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/ (/ 1 (* (PI) (/ 0 0))) (+ -1 (* cosTheta cosTheta)))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/ 1 (* (PI) (/ 0 0)))
(/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
1
#s(literal 1 binary32)
(* (PI) (/ 0 0))
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(PI)
(PI.f32)
(/ 0 0)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
0
#s(literal 0 binary32)
(+ -1 (* cosTheta cosTheta))
(+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta))
-1
#s(literal -1 binary32)
(* cosTheta cosTheta)
(*.f32 cosTheta cosTheta)
cosTheta
(/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/ (+ (* alpha alpha) -1) (PI))
(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
(+ (* alpha alpha) -1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(* alpha alpha)
(*.f32 alpha alpha)
alpha
-1
#s(literal -1 binary32)
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(/ (* (* alpha alpha) (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha))))) (log (* alpha alpha)))
(/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))) (log.f32 (*.f32 alpha alpha)))
(* (* alpha alpha) (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha)))))
(*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha)))))
(* alpha alpha)
(*.f32 alpha alpha)
alpha
(+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha))))
(+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))
(/ 1 (PI))
(/.f32 #s(literal 1 binary32) (PI.f32))
1
#s(literal 1 binary32)
(PI)
(PI.f32)
(/ -1 (* (PI) (* alpha alpha)))
(/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha)))
-1
#s(literal -1 binary32)
(* (PI) (* alpha alpha))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(/ (/ -1 (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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))))
(/ -1 (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))))
(/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))))
-1
#s(literal -1 binary32)
(+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))
(+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha))))
1
#s(literal 1 binary32)
(- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))
(-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))
(* alpha (* alpha (* alpha alpha)))
(*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))
alpha
(* alpha (* alpha alpha))
(*.f32 alpha (*.f32 alpha alpha))
(* alpha alpha)
(*.f32 alpha alpha)
(- 0 (* alpha alpha))
(-.f32 #s(literal 0 binary32) (*.f32 alpha alpha))
0
#s(literal 0 binary32)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) 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)))
(* (PI) (log (* alpha alpha)))
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(- (* alpha alpha) 1)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta

localize198.0ms (2.3%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f32 alpha (*.f32 alpha alpha))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (PI.f32) (*.f32 alpha alpha))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 (*.f32 alpha alpha))
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta))
✓accuracy100.0%
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
✓accuracy100.0%
(*.f32 cosTheta cosTheta)
✓accuracy6.3%
(PI.f32)
✓accuracy100.0%
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓accuracy100.0%
(*.f32 alpha alpha)
✓accuracy100.0%
(log.f32 alpha)
✓accuracy6.3%
(PI.f32)
Results
123.0ms256×0invalid
Compiler

Compiled 508 to 49 computations (90.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 73.0ms
ival-mult: 28.0ms (38.6% of total)
ival-div: 20.0ms (27.6% of total)
ival-log: 8.0ms (11% of total)
ival-add: 8.0ms (11% of total)
ival-sub: 7.0ms (9.7% of total)
ival-pi: 1.0ms (1.4% of total)
const: 1.0ms (1.4% of total)
backward-pass: 0.0ms (0% of total)

series84.0ms (1%)

Counts
26 → 288
Calls
Call 1
Inputs
#<alt (/ (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha))) (* (* (PI) (* (log alpha) 2)) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha)))>
#<alt (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1))>
#<alt (* (* alpha alpha) (* alpha alpha))>
#<alt (/ (/ 1 (* (PI) (/ 0 0))) (+ -1 (* cosTheta cosTheta)))>
#<alt (/ 1 (* (PI) (/ 0 0)))>
#<alt (* (PI) (/ 0 0))>
#<alt (PI)>
#<alt (/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha)))>
#<alt (/ (+ (* alpha alpha) -1) (PI))>
#<alt (+ (* alpha alpha) -1)>
#<alt (* alpha alpha)>
#<alt (/ (* (* alpha alpha) (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha))))) (log (* alpha alpha)))>
#<alt (* (* alpha alpha) (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha)))))>
#<alt (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha))))>
#<alt (/ (/ -1 (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ -1 (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))))>
#<alt (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))>
#<alt (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))>
#<alt (log alpha)>
#<alt (* (PI) (* (log alpha) 2))>
#<alt (* cosTheta cosTheta)>
#<alt (+ -1 (* cosTheta cosTheta))>
#<alt (log (* alpha alpha))>
#<alt (* (PI) (* alpha alpha))>
#<alt (* alpha (* alpha alpha))>
Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 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 (* (pow alpha 2) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (* 1/2 (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 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 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* 1/2 (* (pow alpha 2) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* -1 (/ (* (pow cosTheta 2) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* 1/2 (/ (+ (* -1 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))) (/ 1 (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (pow alpha 4))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* 1/2 (/ (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))) (/ 1 (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow cosTheta 2))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (pow alpha 6))) (+ (* 1/2 (/ (+ (* -1 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))) (/ 1 (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (pow alpha 4))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))>
#<alt (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))>
#<alt (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* -1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (+ (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (pow alpha 4))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))>
#<alt (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* -1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (+ (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (pow alpha 4))) (+ (* 1/2 (/ (+ (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (+ (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))) (pow cosTheta 2))) (pow alpha 6))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))))>
#<alt (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log alpha) (+ 1 (pow alpha 2))))))>
#<alt (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log alpha) (+ 1 (pow alpha 2)))))) (* 1/2 (/ (* (pow alpha 4) (* (pow cosTheta 2) (* (- (/ 1 (pow alpha 4)) 1) (- (pow alpha 2) 1)))) (* (PI) (* (log alpha) (+ 1 (pow alpha 2)))))))>
#<alt (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log alpha) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow alpha 4) (* (pow cosTheta 2) (* (- (/ 1 (pow alpha 4)) 1) (pow (- (pow alpha 2) 1) 2)))) (* (PI) (* (log alpha) (+ 1 (pow alpha 2)))))) (* 1/2 (/ (* (pow alpha 4) (* (- (/ 1 (pow alpha 4)) 1) (- (pow alpha 2) 1))) (* (PI) (* (log alpha) (+ 1 (pow alpha 2)))))))))>
#<alt (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log alpha) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* 1/2 (/ (* (pow alpha 4) (* (- (/ 1 (pow alpha 4)) 1) (- (pow alpha 2) 1))) (* (PI) (* (log alpha) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow alpha 4) (* (- (/ 1 (pow alpha 4)) 1) (pow (- (pow alpha 2) 1) 2))) (* (PI) (* (log alpha) (+ 1 (pow alpha 2)))))) (* 1/2 (/ (* (pow alpha 4) (* (pow cosTheta 2) (* (- (/ 1 (pow alpha 4)) 1) (pow (- (pow alpha 2) 1) 3)))) (* (PI) (* (log alpha) (+ 1 (pow alpha 2)))))))))))>
#<alt (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (* 1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (* 1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (+ (* 1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (* 1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 6) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))))))) (pow cosTheta 2))>
#<alt (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))>
#<alt (/ (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (* 1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (* 1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 4) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (+ (* 1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 2) (* (PI) (* (log alpha) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (* 1/2 (/ (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1)) (* (pow cosTheta 6) (* (PI) (* (log alpha) (* (+ 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 (* -1 (pow alpha 4)))>
#<alt (+ 1 (* -1 (pow alpha 4)))>
#<alt (+ 1 (* -1 (pow alpha 4)))>
#<alt (* -1 (pow alpha 4))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* -1 (pow alpha 4))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (pow alpha 4)>
#<alt (/ -1/2 (* (PI) (log alpha)))>
#<alt (- (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))>
#<alt (- (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))>
#<alt (- (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))>
#<alt (* -1/2 (/ (pow alpha 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ 1 alpha)))))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ 1 alpha)))))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ 1 alpha)))))))>
#<alt (* -1/2 (/ (pow alpha 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ -1 alpha)))))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ -1 alpha)))))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ -1 alpha)))))))>
#<alt (/ -1 (PI))>
#<alt (- (/ (pow alpha 2) (PI)) (/ 1 (PI)))>
#<alt (- (/ (pow alpha 2) (PI)) (/ 1 (PI)))>
#<alt (- (/ (pow alpha 2) (PI)) (/ 1 (PI)))>
#<alt (/ (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (/ (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<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 (/ -1/2 (* (PI) (log alpha)))>
#<alt (- (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))>
#<alt (- (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))>
#<alt (- (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))>
#<alt (* -1/2 (/ (pow alpha 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ 1 alpha)))))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ 1 alpha)))))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ 1 alpha)))))))>
#<alt (* -1/2 (/ (pow alpha 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ -1 alpha)))))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ -1 alpha)))))))>
#<alt (* (pow alpha 2) (- (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (PI) (log (/ -1 alpha)))))))>
#<alt (/ -1 (PI))>
#<alt (- (/ (pow alpha 2) (PI)) (/ 1 (PI)))>
#<alt (- (/ (pow alpha 2) (PI)) (/ 1 (PI)))>
#<alt (- (/ (pow alpha 2) (PI)) (/ 1 (PI)))>
#<alt (/ (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (/ (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))>
#<alt (/ -1 (* (pow alpha 2) (PI)))>
#<alt (/ (- (/ (pow alpha 2) (PI)) (/ 1 (PI))) (pow alpha 2))>
#<alt (/ (- (/ (pow alpha 2) (PI)) (/ 1 (PI))) (pow alpha 2))>
#<alt (/ (- (/ (pow alpha 2) (PI)) (/ 1 (PI))) (pow alpha 2))>
#<alt (/ 1 (PI))>
#<alt (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI))))>
#<alt (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI))))>
#<alt (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI))))>
#<alt (/ 1 (PI))>
#<alt (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI))))>
#<alt (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI))))>
#<alt (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI))))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (* -1 (* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (* (pow alpha 2) (- (* -1 (* (pow alpha 2) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))>
#<alt (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (pow alpha 6))>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 4))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (pow alpha 6))>
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (pow alpha 6))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))))) (pow alpha 6))>
#<alt (/ 1/2 (* (pow alpha 6) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))>
#<alt (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (pow alpha 6))>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (pow alpha 4))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (pow alpha 6))>
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (pow alpha 6))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))))) (pow alpha 6))>
#<alt (/ -1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))>
#<alt (- (/ (* (pow cosTheta 2) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))>
#<alt (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))>
#<alt (- (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))) (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))>
#<alt (/ -1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))))>
#<alt (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 4))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))>
#<alt (/ -1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))))>
#<alt (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 4))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (* (pow alpha 2) (+ 1 (* -1 (pow alpha 4)))) 1)>
#<alt (- (* (pow alpha 2) (+ 1 (* (pow alpha 4) (- (pow alpha 2) 1)))) 1)>
#<alt (/ -1 (pow alpha 4))>
#<alt (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 4))>
#<alt (/ (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 6)))) (pow alpha 4))>
#<alt (/ (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 8))) (+ 1 (/ 1 (pow alpha 6)))) (pow alpha 4))>
#<alt (/ -1 (pow alpha 4))>
#<alt (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 4))>
#<alt (/ (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 6)))) (pow alpha 4))>
#<alt (/ (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 8))) (+ 1 (/ 1 (pow alpha 6)))) (pow alpha 4))>
#<alt 1>
#<alt (+ 1 (pow alpha 2))>
#<alt (+ 1 (* (pow alpha 2) (+ 1 (pow alpha 2))))>
#<alt (+ 1 (* (pow alpha 2) (+ 1 (pow alpha 2))))>
#<alt (pow alpha 4)>
#<alt (* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 4) (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))))>
#<alt (* (pow alpha 4) (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))))>
#<alt (pow alpha 4)>
#<alt (* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 4) (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))))>
#<alt (* (pow alpha 4) (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (pow alpha 2)))>
#<alt (* (pow alpha 2) (+ 1 (pow alpha 2)))>
#<alt (* (pow alpha 2) (+ 1 (pow alpha 2)))>
#<alt (pow alpha 4)>
#<alt (* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 4)>
#<alt (* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))>
#<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 (* (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 (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt -1>
#<alt (- (pow cosTheta 2) 1)>
#<alt (- (pow cosTheta 2) 1)>
#<alt (- (pow cosTheta 2) 1)>
#<alt (pow cosTheta 2)>
#<alt (* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))>
#<alt (pow cosTheta 2)>
#<alt (* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))>
#<alt (* (pow cosTheta 2) (- 1 (/ 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) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (* (pow alpha 2) (PI))>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
#<alt (pow alpha 3)>
Calls

75 calls:

TimeVariablePointExpression
36.0ms
alpha
@-inf
(log alpha)
7.0ms
alpha
@inf
(log alpha)
6.0ms
alpha
@0
(log alpha)
3.0ms
alpha
@inf
(/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha)))
3.0ms
alpha
@-inf
(/ (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha))) (* (* (PI) (* (log alpha) 2)) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite21.0ms (0.2%)

Algorithm
1×batch-egg-rewrite
Rules
32×*-lowering-*.f32
32×*-lowering-*.f64
26×/-lowering-/.f32
26×/-lowering-/.f64
12×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048305
Stop Event
1×iter limit
1×iter limit
1×unsound
Counts
26 → 26
Calls
Call 1
Inputs
(/ (/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha))) (* (* (PI) (* (log alpha) 2)) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1)) (- -1 (* alpha alpha)))
(* (* (* alpha alpha) (* alpha alpha)) (+ (/ 1 (* (* alpha alpha) (* alpha alpha))) -1))
(* (* alpha alpha) (* alpha alpha))
(/ (/ 1 (* (PI) (/ 0 0))) (+ -1 (* cosTheta cosTheta)))
(/ 1 (* (PI) (/ 0 0)))
(* (PI) (/ 0 0))
(PI)
(/ (/ (+ (* alpha alpha) -1) (PI)) (log (* alpha alpha)))
(/ (+ (* alpha alpha) -1) (PI))
(+ (* alpha alpha) -1)
(* alpha alpha)
(/ (* (* alpha alpha) (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha))))) (log (* alpha alpha)))
(* (* alpha alpha) (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha)))))
(+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha))))
(/ (/ -1 (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ -1 (+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))))
(+ 1 (- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha))))
(- (* alpha (* alpha (* alpha alpha))) (- 0 (* alpha alpha)))
(log alpha)
(* (PI) (* (log alpha) 2))
(* cosTheta cosTheta)
(+ -1 (* cosTheta cosTheta))
(log (* alpha alpha))
(* (PI) (* alpha alpha))
(* alpha (* alpha alpha))
Outputs
(/.f32 (/.f32 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.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 (*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(*.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32)))
(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(PI.f32)
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(*.f32 alpha alpha)
(/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))) (log.f32 (*.f32 alpha alpha)))
(*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha)))))
(+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))
(/.f32 (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))))
(+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha))))
(-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha)))
(log.f32 alpha)
(*.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(*.f32 cosTheta cosTheta)
(+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta))
(log.f32 (*.f32 alpha alpha))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(*.f32 alpha (*.f32 alpha alpha))

simplify297.0ms (3.4%)

Algorithm
1×egg-herbie
Rules
6036×*-lowering-*.f32
6036×*-lowering-*.f64
2986×/-lowering-/.f32
2986×/-lowering-/.f64
2054×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04545907
116195128
082995128
Stop Event
1×iter limit
1×node limit
Counts
288 → 288
Calls
Call 1
Inputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* 1/2 (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
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(/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (pow alpha 6))
(/ (- (+ (* -1 (/ (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (pow alpha 4))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (pow alpha 6))
(/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (pow alpha 6))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))))) (pow alpha 6))
(/ -1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))
(- (/ (* (pow cosTheta 2) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))
(- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))) (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))
(- (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))) (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4))))))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (+ 1 (+ (pow alpha 2) (pow alpha 4)))))))
(/ -1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))))
(/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 4))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))
(/ -1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))))
(/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (pow (- (pow alpha 2) 1) 4))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ (pow alpha 2) (pow alpha 4))) (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) (- (pow alpha 2) 1)))) 1)
(/ -1 (pow alpha 4))
(/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 4))
(/ (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 6)))) (pow alpha 4))
(/ (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 8))) (+ 1 (/ 1 (pow alpha 6)))) (pow alpha 4))
(/ -1 (pow alpha 4))
(/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 4))
(/ (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 6)))) (pow alpha 4))
(/ (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 8))) (+ 1 (/ 1 (pow alpha 6)))) (pow alpha 4))
1
(+ 1 (pow alpha 2))
(+ 1 (* (pow alpha 2) (+ 1 (pow alpha 2))))
(+ 1 (* (pow alpha 2) (+ 1 (pow alpha 2))))
(pow alpha 4)
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 4) (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))))
(* (pow alpha 4) (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))))
(pow alpha 4)
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 4) (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))))
(* (pow alpha 4) (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (pow alpha 2)))
(* (pow alpha 2) (+ 1 (pow alpha 2)))
(* (pow alpha 2) (+ 1 (pow alpha 2)))
(pow alpha 4)
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(pow alpha 4)
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(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 (* (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))))))
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
-1
(- (pow cosTheta 2) 1)
(- (pow cosTheta 2) 1)
(- (pow cosTheta 2) 1)
(pow cosTheta 2)
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(pow cosTheta 2)
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(* (pow cosTheta 2) (- 1 (/ 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) (PI))
(* (pow alpha 2) (PI))
(* (pow alpha 2) (PI))
(* (pow alpha 2) (PI))
(* (pow alpha 2) (PI))
(* (pow alpha 2) (PI))
(* (pow alpha 2) (PI))
(* (pow alpha 2) (PI))
(* (pow alpha 2) (PI))
(* (pow alpha 2) (PI))
(* (pow alpha 2) (PI))
(* (pow alpha 2) (PI))
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(- (* 1/2 (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 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))))))))
(+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (*.f32 alpha alpha) (*.f32 #s(literal 1/2 binary32) (-.f32 (+.f32 (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))))))
(- (* (pow alpha 2) (+ (* 1/2 (* (pow alpha 2) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (* 1/2 (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 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))))))))
(+.f32 (*.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha)) (+.f32 (-.f32 (+.f32 (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (/.f32 (*.f32 #s(literal -1 binary32) (-.f32 (+.f32 (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (+ (* 1/2 (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* 1/2 (* (pow alpha 2) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* -1 (/ (* (pow cosTheta 2) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2)))))))) (* 1/2 (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (+ (/ 1 (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(+.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (*.f32 #s(literal 1/2 binary32) (-.f32 (+.f32 (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))) (*.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha)) (+.f32 (+.f32 (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (/.f32 (*.f32 #s(literal -1 binary32) (-.f32 (+.f32 (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (*.f32 alpha (*.f32 alpha (-.f32 (/.f32 (*.f32 #s(literal -1 binary32) (+.f32 (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (/.f32 (*.f32 #s(literal -1 binary32) (-.f32 (+.f32 (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (-.f32 (+.f32 (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (*.f32 (log.f32 alpha) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (/.f32 (*.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 (-.f32 #s(literal 0 binary32) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))) (*.f32 cosTheta cosTheta))
(- (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(-.f32 (/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 alpha alpha)) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))) (*.f32 cosTheta cosTheta)))
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(*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 4) (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(* (pow alpha 4) (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (+ 1 (pow alpha 2)))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(* (pow alpha 2) (+ 1 (pow alpha 2)))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(* (pow alpha 2) (+ 1 (pow alpha 2)))
(*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(pow alpha 4)
(*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(pow alpha 4)
(*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 4) (+ 1 (/ 1 (pow alpha 2))))
(*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* 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) (* -1 (log (/ -1 alpha))))))
(*.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (*.f32 (PI.f32) #s(literal 2 binary32)))
(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(*.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (*.f32 (PI.f32) #s(literal 2 binary32)))
(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(*.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (*.f32 (PI.f32) #s(literal 2 binary32)))
(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(*.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (*.f32 (PI.f32) #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
#s(literal -1 binary32)
(- (pow cosTheta 2) 1)
(+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta))
(- (pow cosTheta 2) 1)
(+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta))
(- (pow cosTheta 2) 1)
(+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta))
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (- 1 (/ 1 (pow cosTheta 2))))
(*.f32 cosTheta (*.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.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) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(* (pow alpha 2) (PI))
(*.f32 (PI.f32) (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))
(pow alpha 3)
(*.f32 alpha (*.f32 alpha alpha))

eval39.0ms (0.4%)

Compiler

Compiled 18812 to 497 computations (97.4% saved)

prune44.0ms (0.5%)

Pruning

28 alts after pruning (25 fresh and 3 done)

PrunedKeptTotal
New5337540
Fresh21820
Picked415
Done022
Total53928567
Accuracy
100.0%
Counts
567 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.2%
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.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))))
96.2%
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓96.2%
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
✓98.5%
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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))))
97.7%
(/.f32 (/.f32 (*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #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))))
98.0%
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 (*.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))))
95.9%
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
95.8%
(/.f32 (/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
95.9%
(/.f32 (/.f32 (*.f32 alpha (*.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
-0.0%
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))
67.2%
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
66.0%
(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
98.2%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 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 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
96.3%
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
96.0%
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
65.9%
(/.f32 (*.f32 (*.f32 alpha alpha) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha)))) (log.f32 (*.f32 alpha alpha)))
95.9%
(/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
98.2%
(/.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))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
97.9%
(/.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 (neg.f32 cosTheta) cosTheta))))
97.8%
(/.f32 (*.f32 alpha (*.f32 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))))
67.2%
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
66.0%
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
84.8%
(/.f32 #s(literal -1 binary32) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))) (PI.f32))))
96.7%
(+.f32 (/.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (*.f32 (/.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal -1 binary32) alpha)))
96.2%
(+.f32 (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
97.2%
(*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
96.1%
(neg.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
Compiler

Compiled 2262 to 635 computations (71.9% saved)

regimes75.0ms (0.9%)

Counts
62 → 1
Calls
Call 1
Inputs
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 (*.f32 (*.f32 alpha alpha) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha)))) (log.f32 (*.f32 alpha alpha)))
(*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (/.f32 (*.f32 alpha (*.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))) (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))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal -1 binary32) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))) (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 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))) (log.f32 (*.f32 alpha alpha)))
(/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(neg.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(/.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 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 (neg.f32 cosTheta) cosTheta))))
(/.f32 (*.f32 alpha (*.f32 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 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.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 #s(literal 1 binary32) (/.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) (+.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) (+.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))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (+.f32 (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (*.f32 (+.f32 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 (+.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (*.f32 (+.f32 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 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.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 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) alpha))) (*.f32 (+.f32 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 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) (-.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 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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 #s(literal 0 binary32) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.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 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #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 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (*.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 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha alpha)) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))) #s(literal -1 binary32)) (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.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 #s(literal -1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (-.f32 #s(literal 0 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 (*.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (+.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 (+.f32 (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 alpha alpha) (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))))) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) #s(literal 1 binary32)) (+.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 #s(literal 1/2 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(+.f32 (/.f32 (*.f32 #s(literal 1/2 binary32) (*.f32 alpha alpha)) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (PI.f32) (+.f32 (*.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (/.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
(+.f32 (/.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (*.f32 (/.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal -1 binary32) alpha)))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 alpha alpha) (*.f32 #s(literal -2 binary32) (-.f32 (neg.f32 (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
(*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(-.f32 (*.f32 (/.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal -1 binary32) alpha)) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (/.f32 (*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) #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) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (/.f32 (*.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (*.f32 (log.f32 alpha) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (PI.f32)))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 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))))
Calls

4 calls:

18.0ms
alpha
17.0ms
(*.f32 alpha alpha)
17.0ms
(/.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))))
17.0ms
cosTheta
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)

regimes28.0ms (0.3%)

Counts
28 → 1
Calls
Call 1
Inputs
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 (*.f32 (*.f32 alpha alpha) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha)))) (log.f32 (*.f32 alpha alpha)))
(*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (/.f32 (*.f32 alpha (*.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))) (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))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal -1 binary32) (*.f32 (log.f32 (*.f32 alpha alpha)) (*.f32 (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))) (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 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))) (log.f32 (*.f32 alpha alpha)))
(/.f32 (*.f32 (*.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha))))) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(neg.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
Calls

3 calls:

10.0ms
cosTheta
8.0ms
(*.f32 alpha alpha)
8.0ms
alpha
Results
AccuracySegmentsBranch
98.3%1cosTheta
98.3%1alpha
98.3%1(*.f32 alpha alpha)
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes22.0ms (0.2%)

Counts
19 → 1
Calls
Call 1
Inputs
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 (*.f32 (*.f32 alpha alpha) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha)))) (log.f32 (*.f32 alpha alpha)))
(*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
Calls

3 calls:

9.0ms
alpha
6.0ms
(*.f32 alpha alpha)
6.0ms
cosTheta
Results
AccuracySegmentsBranch
98.2%1cosTheta
98.2%1alpha
98.2%1(*.f32 alpha alpha)
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes19.0ms (0.2%)

Counts
18 → 1
Calls
Call 1
Inputs
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 (*.f32 (*.f32 alpha alpha) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha)))) (log.f32 (*.f32 alpha alpha)))
(*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
Outputs
(*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
Calls

3 calls:

7.0ms
(*.f32 alpha alpha)
6.0ms
alpha
5.0ms
cosTheta
Results
AccuracySegmentsBranch
97.2%1cosTheta
97.2%1alpha
97.2%1(*.f32 alpha alpha)
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes18.0ms (0.2%)

Counts
17 → 1
Calls
Call 1
Inputs
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 (/.f32 (*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal -1 binary32) alpha)) (PI.f32)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(/.f32 (*.f32 (*.f32 alpha alpha) (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (*.f32 alpha alpha)))) (log.f32 (*.f32 alpha alpha)))
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
Calls

3 calls:

7.0ms
(*.f32 alpha alpha)
5.0ms
alpha
5.0ms
cosTheta
Results
AccuracySegmentsBranch
96.3%1alpha
96.3%1(*.f32 alpha alpha)
96.3%1cosTheta
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes12.0ms (0.1%)

Counts
8 → 1
Calls
Call 1
Inputs
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
Outputs
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
Calls

3 calls:

5.0ms
cosTheta
3.0ms
(*.f32 alpha alpha)
3.0ms
alpha
Results
AccuracySegmentsBranch
67.2%1cosTheta
67.2%1alpha
67.2%1(*.f32 alpha alpha)
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes9.0ms (0.1%)

Counts
7 → 1
Calls
Call 1
Inputs
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 #s(literal 1/2 binary32) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
Outputs
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
Calls

3 calls:

3.0ms
(*.f32 alpha alpha)
3.0ms
cosTheta
3.0ms
alpha
Results
AccuracySegmentsBranch
66.0%1alpha
66.0%1(*.f32 alpha alpha)
66.0%1cosTheta
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes11.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

3 calls:

7.0ms
alpha
2.0ms
(*.f32 alpha alpha)
2.0ms
cosTheta
Results
AccuracySegmentsBranch
-0.0%1alpha
-0.0%1(*.f32 alpha alpha)
-0.0%1cosTheta
Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify9.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
30×*-commutative_binary32
14×+-commutative_binary32
10×sub-neg_binary32
6×neg-sub0_binary32
6×neg-mul-1_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040117
164117
273117
381117
483117
Stop Event
1×saturated
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 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
(*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))
Outputs
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.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 cosTheta (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.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))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (log.f32 alpha)) (*.f32 (PI.f32) #s(literal 2 binary32))))
(*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (*.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))

soundness1.9s (21.4%)

Rules
6322×*-lowering-*.f32
6322×*-lowering-*.f64
6036×*-lowering-*.f32
6036×*-lowering-*.f64
5852×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01366
19464
279461
0859861
02132627
17102409
228822383
086342383
04545907
116195128
082995128
072210769
127229432
086139432
05106991
119075932
095665932
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 370 to 207 computations (44.1% saved)

preprocess43.0ms (0.5%)

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 914 to 440 computations (51.9% saved)

end0.0ms (0%)

Profiling

Loading profile data...