HairBSDF, Mp, lower

Time bar (total: 18.7s)

analyze800.0ms (4.3%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%3%97%0%0%0%0
0%0%3%97%0%0%0%1
0%0%3%97%0%0%0%2
0%0%3%97%0%0%0%3
0%0%3%97%0%0%0%4
0%0%3%97%0%0%0%5
0%0%1.5%97%0%1.5%0%6
0%0%1.5%97%0%1.5%0%7
0%0%1.5%97%0%1.5%0%8
0%0%1.5%97%0%1.5%0%9
0%0%1.5%97%0%1.5%0%10
50%0.7%0.7%97%0%1.5%0%11
50%0.7%0.7%97%0%1.5%0%12
Compiler

Compiled 69 to 51 computations (26.1% saved)

sample3.2s (17.3%)

Results
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Bogosity

preprocess671.0ms (3.6%)

Algorithm
egg-herbie
Rules
795×exp-diff
750×times-frac
457×fma-neg
330×fma-define
276×associate-+l-
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1044(-4.142242104876459e-8 -2.7428979636612723e-24 -3.8496139892677906e-31 2.3381455548290408e-21 4.319063862112671e-8)39(-0.10279592871665955 -0.025210902094841003 -3.4767951413564746e-31 9.80960590535318e-11 2.179217517550569e-8)(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
901(-7.162906924893353e-19 1.3384777371841372e-28 5.304026474282003e-26 1.7025089391609072e-6 0.03722643479704857)26(-6.778990382372285e-7 1.0737883324893466e-35 -3.548109235614849e-36 7.606163853779435e-5 2.5666577533385092e-20)(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
45(2.1490089041131103e-39 3.588250099069608e-14 -4.9616840857217263e-17 -6.132203143176153e-32 0.0070293862372636795)4(8.763006460873676e-14 0.011338040232658386 2.484009892353281e-34 3.593793115531828e-23 0.012353457510471344)(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
00-0-cosTheta_O
00-0-(*.f32 2 v)
00-0-(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
00-0-(log.f32 (/.f32 1 (*.f32 2 v)))
00-0-(/.f32 1 v)
00-0-(*.f32 cosTheta_i cosTheta_O)
00-0-(*.f32 sinTheta_i sinTheta_O)
00-0-(+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)
00-0-sinTheta_O
00-0-v
00-0-(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
00-0-cosTheta_i
00-0-sinTheta_i
00-0-(/.f32 1 (*.f32 2 v))
00-0-2
00-0-6931/10000
00-0-1
00-0-(-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01732130
14851898
214481854
357471854
Stop Event
node limit
Calls
Call 1
Inputs
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 (neg.f32 cosTheta_i) cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i (neg.f32 cosTheta_O)) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) (neg.f32 v)) (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v))) (/.f32 1 (neg.f32 v))) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 (neg.f32 v))))))
(neg.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 (neg.f32 cosTheta_i) cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
(neg.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i (neg.f32 cosTheta_O)) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
(neg.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
(neg.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
(neg.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) (neg.f32 v)) (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v))) (/.f32 1 (neg.f32 v))) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 (neg.f32 v)))))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 sinTheta_i cosTheta_O) v) (/.f32 (*.f32 cosTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 sinTheta_O cosTheta_O) v) (/.f32 (*.f32 sinTheta_i cosTheta_i) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 v cosTheta_O) cosTheta_i) (/.f32 (*.f32 sinTheta_i sinTheta_O) cosTheta_i)) (/.f32 1 cosTheta_i)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 cosTheta_i)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i sinTheta_i) v) (/.f32 (*.f32 cosTheta_O sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i sinTheta_O) v) (/.f32 (*.f32 sinTheta_i cosTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i v) cosTheta_O) (/.f32 (*.f32 sinTheta_i sinTheta_O) cosTheta_O)) (/.f32 1 cosTheta_O)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 cosTheta_O)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) sinTheta_i) (/.f32 (*.f32 v sinTheta_O) sinTheta_i)) (/.f32 1 sinTheta_i)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 sinTheta_i)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) sinTheta_O) (/.f32 (*.f32 sinTheta_i v) sinTheta_O)) (/.f32 1 sinTheta_O)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 sinTheta_O)))))
Outputs
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))) 6931/10000)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))) 6931/10000)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 (neg.f32 cosTheta_i) cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v)) (-.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)) 6931/10000))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (-.f32 6931/10000 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (-.f32 6931/10000 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i (neg.f32 cosTheta_O)) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v)) (-.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)) 6931/10000))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (-.f32 6931/10000 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (-.f32 6931/10000 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v) (/.f32 1 v))))))
(*.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
(*.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 -1 v))))) (/.f32 1/2 v))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v) (/.f32 1 v))))))
(*.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
(*.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 -1 v))))) (/.f32 1/2 v))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) (neg.f32 v)) (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v))) (/.f32 1 (neg.f32 v))) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 (neg.f32 v))))))
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O (neg.f32 v))) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O (neg.f32 v))) (/.f32 1 (neg.f32 v)))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 (neg.f32 v))))))
(*.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (*.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))) (/.f32 -1/2 v))
(*.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (/.f32 -1/2 v))
(*.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 -1/2 v))
(neg.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 (neg.f32 cosTheta_i) cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
(neg.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v)))))))
(*.f32 (exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v)) (-.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)) 6931/10000))) (/.f32 -1/2 v))
(*.f32 (exp.f32 (-.f32 (-.f32 6931/10000 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 -1/2 v))
(*.f32 (exp.f32 (-.f32 (-.f32 6931/10000 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 -1/2 v))
(neg.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i (neg.f32 cosTheta_O)) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
(neg.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v)))))))
(*.f32 (exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v)) (-.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)) 6931/10000))) (/.f32 -1/2 v))
(*.f32 (exp.f32 (-.f32 (-.f32 6931/10000 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 -1/2 v))
(*.f32 (exp.f32 (-.f32 (-.f32 6931/10000 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 -1/2 v))
(neg.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
(neg.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v) (/.f32 1 v)))))))
(*.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 -1/2 v))
(*.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 -1 v))))) (/.f32 -1/2 v))
(neg.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
(neg.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v) (/.f32 1 v)))))))
(*.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 -1/2 v))
(*.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 -1 v))))) (/.f32 -1/2 v))
(neg.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) (neg.f32 v)) (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v))) (/.f32 1 (neg.f32 v))) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 (neg.f32 v)))))))
(neg.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O (neg.f32 v))) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O (neg.f32 v))) (/.f32 1 (neg.f32 v)))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 (neg.f32 v)))))))
(*.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (*.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))) (neg.f32 (/.f32 -1/2 v)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 (neg.f32 cosTheta_O) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 6931/10000 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))) 6931/10000)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 sinTheta_i cosTheta_O) v) (/.f32 (*.f32 cosTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 sinTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 cosTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (*.f32 cosTheta_O (/.f32 sinTheta_i v))) (fma.f32 cosTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 sinTheta_i v)) (+.f32 (fma.f32 cosTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_O (/.f32 sinTheta_i v)) (fma.f32 cosTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 sinTheta_O cosTheta_O) v) (/.f32 (*.f32 sinTheta_i cosTheta_i) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_O (/.f32 sinTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 cosTheta_i v)) (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 sinTheta_O v)) (-.f32 (fma.f32 cosTheta_i (/.f32 sinTheta_i v) (/.f32 1 v)) 6931/10000))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_O (/.f32 sinTheta_O v)) (fma.f32 cosTheta_i (/.f32 sinTheta_i v) (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_O (/.f32 sinTheta_O v) (neg.f32 (fma.f32 sinTheta_i (/.f32 cosTheta_i v) (/.f32 1 v)))))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 v cosTheta_O) cosTheta_i) (/.f32 (*.f32 sinTheta_i sinTheta_O) cosTheta_i)) (/.f32 1 cosTheta_i)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 cosTheta_i)))))
(exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O v) cosTheta_i) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O cosTheta_i)) (/.f32 1 cosTheta_i))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 cosTheta_i)))))
(*.f32 (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 v cosTheta_i)) (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O cosTheta_i) (/.f32 1 cosTheta_i)) 6931/10000))) (/.f32 1/2 cosTheta_i))
(*.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (*.f32 v (/.f32 cosTheta_O cosTheta_i)) (fma.f32 sinTheta_i (/.f32 sinTheta_O cosTheta_i) (/.f32 1 cosTheta_i))))) (/.f32 1/2 cosTheta_i))
(*.f32 (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i cosTheta_i) (/.f32 1 cosTheta_i)) -6931/10000))) (/.f32 1/2 cosTheta_i))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i sinTheta_i) v) (/.f32 (*.f32 cosTheta_O sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 sinTheta_i (/.f32 cosTheta_i v)) (+.f32 (*.f32 cosTheta_O (/.f32 sinTheta_O v)) (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 sinTheta_i v)) (-.f32 (fma.f32 sinTheta_O (/.f32 cosTheta_O v) (/.f32 1 v)) 6931/10000))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 sinTheta_i v)) (fma.f32 sinTheta_O (/.f32 cosTheta_O v) (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 sinTheta_i v) (fma.f32 cosTheta_O (/.f32 sinTheta_O (neg.f32 v)) (/.f32 -1 v))))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i sinTheta_O) v) (/.f32 (*.f32 sinTheta_i cosTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 sinTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 sinTheta_O v)) (fma.f32 sinTheta_i (/.f32 cosTheta_O v) (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 sinTheta_O v) (fma.f32 sinTheta_i (/.f32 (neg.f32 cosTheta_O) v) (/.f32 -1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 sinTheta_O v) (fma.f32 (neg.f32 sinTheta_i) (/.f32 cosTheta_O v) (/.f32 -1 v))))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i v) cosTheta_O) (/.f32 (*.f32 sinTheta_i sinTheta_O) cosTheta_O)) (/.f32 1 cosTheta_O)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 cosTheta_O)))))
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O cosTheta_O)) (/.f32 1 cosTheta_O))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 cosTheta_O)))))
(*.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (*.f32 cosTheta_i (/.f32 v cosTheta_O))) (fma.f32 sinTheta_i (/.f32 sinTheta_O cosTheta_O) (/.f32 1 cosTheta_O)))) (/.f32 1/2 cosTheta_O))
(*.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i cosTheta_O) (/.f32 1 cosTheta_O))))) (/.f32 1/2 cosTheta_O))
(*.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_i (/.f32 sinTheta_O cosTheta_O) (/.f32 1 cosTheta_O))))) (/.f32 1/2 cosTheta_O))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))) 6931/10000)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) sinTheta_i) (/.f32 (*.f32 v sinTheta_O) sinTheta_i)) (/.f32 1 sinTheta_i)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 sinTheta_i)))))
(exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) sinTheta_i) (+.f32 (/.f32 (*.f32 v sinTheta_O) sinTheta_i) (/.f32 1 sinTheta_i))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 sinTheta_i)))))
(*.f32 (exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O sinTheta_i)) (-.f32 (fma.f32 v (/.f32 sinTheta_O sinTheta_i) (/.f32 1 sinTheta_i)) 6931/10000))) (/.f32 1/2 sinTheta_i))
(*.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O sinTheta_i) (fma.f32 v (/.f32 sinTheta_O (neg.f32 sinTheta_i)) (/.f32 -1 sinTheta_i))))) (/.f32 1/2 sinTheta_i))
(*.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O sinTheta_i)) (fma.f32 v (/.f32 sinTheta_O sinTheta_i) (/.f32 1 sinTheta_i))))) (/.f32 1/2 sinTheta_i))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) sinTheta_O) (/.f32 (*.f32 sinTheta_i v) sinTheta_O)) (/.f32 1 sinTheta_O)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 sinTheta_O)))))
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O sinTheta_O)) (+.f32 (*.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 sinTheta_O))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 sinTheta_O)))))
(*.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (*.f32 cosTheta_i (/.f32 cosTheta_O sinTheta_O))) (fma.f32 sinTheta_i (/.f32 v sinTheta_O) (/.f32 1 sinTheta_O)))) (/.f32 1/2 sinTheta_O))
(*.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O sinTheta_O)) (fma.f32 v (/.f32 sinTheta_i sinTheta_O) (/.f32 1 sinTheta_O))))) (/.f32 1/2 sinTheta_O))
(*.f32 (exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O sinTheta_O)) (fma.f32 v (/.f32 sinTheta_i sinTheta_O) (+.f32 (/.f32 1 sinTheta_O) -6931/10000)))) (/.f32 1/2 sinTheta_O))
Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 308 to 138 computations (55.2% saved)

eval1.0ms (0%)

Compiler

Compiled 91 to 53 computations (41.8% saved)

prune2.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
99.7%
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
99.6%
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
Compiler

Compiled 54 to 38 computations (29.6% saved)

localize527.0ms (2.8%)

Localize:

Found 8 expressions with local error:

NewAccuracyProgram
100.0%
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
99.9%
(+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)
99.7%
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000))
99.4%
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
99.8%
(+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
99.6%
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
99.4%
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
99.3%
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
Compiler

Compiled 216 to 90 computations (58.3% saved)

series176.0ms (0.9%)

Counts
8 → 408
Calls

102 calls:

TimeVariablePointExpression
43.0ms
sinTheta_i
@-inf
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
8.0ms
cosTheta_i
@0
(+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
7.0ms
v
@-inf
(+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
3.0ms
cosTheta_O
@inf
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
3.0ms
cosTheta_i
@0
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

rewrite377.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
562×log1p-expm1-u
229×expm1-log1p-u
218×add-exp-log
217×add-log-exp
216×add-cube-cbrt
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
035465
1518432
27461432
Stop Event
node limit
Counts
8 → 268
Calls
Call 1
Inputs
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000))
(+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
Outputs
(-.f32 (exp.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 1)
(/.f32 sinTheta_i (/.f32 v sinTheta_O))
(/.f32 1 (/.f32 v (*.f32 sinTheta_i sinTheta_O)))
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(/.f32 (neg.f32 (*.f32 sinTheta_i sinTheta_O)) (neg.f32 v))
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) (neg.f32 v))
(/.f32 (*.f32 (neg.f32 sinTheta_O) sinTheta_i) (neg.f32 v))
(/.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) 1) v)
(/.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))
(/.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (sqrt.f32 v)) (sqrt.f32 v))
(pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)
(pow.f32 (cbrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 3)
(pow.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 2)
(sqrt.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 2))
(log.f32 (pow.f32 (exp.f32 (/.f32 sinTheta_O v)) sinTheta_i))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))
(cbrt.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3))
(expm1.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(log1p.f32 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(exp.f32 (log.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(exp.f32 (*.f32 (log.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 1))
(-.f32 (exp.f32 (log1p.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)))) 1)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 1 (/.f32 v (*.f32 cosTheta_i cosTheta_O)))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 (neg.f32 (*.f32 cosTheta_i cosTheta_O)) (neg.f32 v))
(/.f32 (*.f32 cosTheta_i (neg.f32 cosTheta_O)) (neg.f32 v))
(/.f32 (*.f32 (neg.f32 cosTheta_O) cosTheta_i) (neg.f32 v))
(/.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) 1) v)
(/.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))
(/.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) (sqrt.f32 v)) (sqrt.f32 v))
(pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 1)
(pow.f32 (cbrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 3)
(pow.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 2)
(sqrt.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 2))
(log.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)))))
(cbrt.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 3))
(expm1.f32 (log1p.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(log1p.f32 (expm1.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(exp.f32 (log.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(exp.f32 (*.f32 (log.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 1))
(-.f32 (exp.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)))) 1)
(*.f32 1 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))
(*.f32 1/2 (*.f32 (/.f32 1 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
(*.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 1)
(*.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) (/.f32 1/2 v))
(*.f32 (exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) 2) (*.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (/.f32 1/2 v)))
(*.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))) (pow.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))) 2))
(*.f32 (pow.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))) 2) (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))))
(*.f32 (pow.f32 (cbrt.f32 (/.f32 1/2 v)) 2) (*.f32 (cbrt.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
(*.f32 (sqrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (*.f32 (sqrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (/.f32 1/2 v)))
(*.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))) (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))))
(*.f32 (sqrt.f32 (/.f32 1/2 v)) (*.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
(*.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (/.f32 1 v))
(*.f32 (/.f32 1/2 (pow.f32 (cbrt.f32 v) 2)) (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) (cbrt.f32 v)))
(*.f32 (/.f32 1/2 (sqrt.f32 v)) (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) (sqrt.f32 v)))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))) (exp.f32 6931/10000))
(*.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) 2)) (cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
(*.f32 (*.f32 (/.f32 1/2 v) (sqrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) (sqrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
(*.f32 (*.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) (pow.f32 (cbrt.f32 (/.f32 1/2 v)) 2)) (cbrt.f32 (/.f32 1/2 v)))
(*.f32 (*.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) (sqrt.f32 (/.f32 1/2 v))) (sqrt.f32 (/.f32 1/2 v)))
(/.f32 1 (/.f32 v (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))))
(/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) (*.f32 v 2))
(/.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)) (exp.f32 (-.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000) (log.f32 (/.f32 1/2 v)))))
(/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) v)
(/.f32 (neg.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) (neg.f32 v))
(/.f32 (*.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) -1/2) (neg.f32 v))
(/.f32 (*.f32 -1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (neg.f32 v))
(/.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) 1) v)
(/.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))
(/.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (sqrt.f32 v)) (sqrt.f32 v))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 1)
(pow.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))) 3)
(pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))) 2)
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 2)) (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(pow.f32 (exp.f32 (sqrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (sqrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(sqrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 2))
(log.f32 (pow.f32 (exp.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (/.f32 1/2 v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)))))
(cbrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3))
(cbrt.f32 (*.f32 (pow.f32 (/.f32 1/2 v) 3) (pow.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 3)))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 3) (pow.f32 (/.f32 1/2 v) 3)))
(expm1.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))))
(log1p.f32 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))))
(-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000) (log.f32 (/.f32 1/2 v))))
(-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(-.f32 (exp.f32 (log1p.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) 1)
(-.f32 (log.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) (log.f32 v))
(-.f32 (/.f32 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 2) (-.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (/.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) (-.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
(-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)) (/.f32 1 v))
(-.f32 (+.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000) (log.f32 1/2)) (log.f32 v))
(*.f32 1 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(*.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1)
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(*.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
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(fma.f32 1 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)
(fma.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) 6931/10000)
(fma.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000)))
(fma.f32 (sqrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) (sqrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) 6931/10000)
(fma.f32 (sqrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000)))
(-.f32 (exp.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)))) 1)
(/.f32 1 (/.f32 v (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))))
(/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) (*.f32 v 2))
(/.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)) (exp.f32 (-.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000) (log.f32 (/.f32 1/2 v)))))
(/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) v)
(/.f32 (neg.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) (neg.f32 v))
(/.f32 (*.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) -1/2) (neg.f32 v))
(/.f32 (*.f32 -1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (neg.f32 v))
(/.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) 1) v)
(/.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))
(/.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (sqrt.f32 v)) (sqrt.f32 v))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 1)
(pow.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))) 3)
(pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))) 2)
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 2)) (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(pow.f32 (exp.f32 (sqrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (sqrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(sqrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 2))
(log.f32 (pow.f32 (exp.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (/.f32 1/2 v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)))))
(cbrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3))
(cbrt.f32 (*.f32 (pow.f32 (/.f32 1/2 v) 3) (pow.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 3)))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 3) (pow.f32 (/.f32 1/2 v) 3)))
(expm1.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))))
(log1p.f32 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))))
(exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))

simplify582.0ms (3.1%)

Algorithm
egg-herbie
Rules
436×associate-*r*
372×associate-*l*
328×fma-define
298×exp-prod
296×*-commutative
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
077755922
1204852595
2758552595
Stop Event
node limit
Counts
676 → 469
Calls
Call 1
Inputs
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v)))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))) (+.f32 (*.f32 1/6 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v)))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))) (+.f32 (*.f32 1/6 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
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(/.f32 1 (/.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) -6931/10000) (+.f32 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 2) -48038761/100000000)))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 3)) (+.f32 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 2) (-.f32 48038761/100000000 (*.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 3)) (+.f32 48038761/100000000 (-.f32 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 2) (*.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
(/.f32 (+.f32 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 2) -48038761/100000000) (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) -6931/10000))
(/.f32 (neg.f32 (+.f32 332956652491/1000000000000 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 3))) (neg.f32 (+.f32 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 2) (-.f32 48038761/100000000 (*.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))))
(/.f32 (neg.f32 (+.f32 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 2) -48038761/100000000)) (neg.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) -6931/10000)))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) (pow.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000) 3)) (+.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (+.f32 (*.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000) (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000)) (*.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000)))))
(/.f32 (-.f32 48038761/100000000 (pow.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 2)) (-.f32 6931/10000 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (*.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000) (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000))) (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000)))
(pow.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000) 1)
(pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 3)
(pow.f32 (pow.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000) 3) 1/3)
(pow.f32 (sqrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 2)
(sqrt.f32 (pow.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000) 2))
(log.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
(cbrt.f32 (pow.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000) 3))
(expm1.f32 (log1p.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
(log1p.f32 (expm1.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
(exp.f32 (log.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
(exp.f32 (*.f32 (log.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 1))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000)))
(fma.f32 (/.f32 cosTheta_O v) cosTheta_i (neg.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000)))
(fma.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (neg.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000)))
(fma.f32 1 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)
(fma.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) 6931/10000)
(fma.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000)))
(fma.f32 (sqrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) (sqrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) 6931/10000)
(fma.f32 (sqrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000)))
(-.f32 (exp.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)))) 1)
(/.f32 1 (/.f32 v (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))))
(/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) (*.f32 v 2))
(/.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)) (exp.f32 (-.f32 (+.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) -6931/10000) (log.f32 (/.f32 1/2 v)))))
(/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) v)
(/.f32 (neg.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) (neg.f32 v))
(/.f32 (*.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) -1/2) (neg.f32 v))
(/.f32 (*.f32 -1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (neg.f32 v))
(/.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) 1) v)
(/.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))
(/.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (sqrt.f32 v)) (sqrt.f32 v))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 1)
(pow.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))) 3)
(pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))) 2)
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 2)) (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(pow.f32 (exp.f32 (sqrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (sqrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(sqrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 2))
(log.f32 (pow.f32 (exp.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))) (/.f32 1/2 v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)))))
(cbrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3))
(cbrt.f32 (*.f32 (pow.f32 (/.f32 1/2 v) 3) (pow.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 3)))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 3) (pow.f32 (/.f32 1/2 v) 3)))
(expm1.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))))
(log1p.f32 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))))
(exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
Outputs
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
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(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))
(cbrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3))
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))
(cbrt.f32 (*.f32 (pow.f32 (/.f32 1/2 v) 3) (pow.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 3)))
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 3) (pow.f32 (/.f32 1/2 v) 3)))
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))
(expm1.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))))
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))
(log1p.f32 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v))))
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))
(exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))

eval302.0ms (1.6%)

Compiler

Compiled 18418 to 10292 computations (44.1% saved)

prune103.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New48314497
Fresh000
Picked202
Done000
Total48514499
Accuracy
99.9%
Counts
499 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.9%
(pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3) 1/3)
99.6%
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
99.5%
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 2)) (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
99.6%
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
99.7%
(*.f32 (/.f32 1/2 v) (*.f32 (exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) (exp.f32 6931/10000)))
99.7%
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
4.7%
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
99.7%
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))) (exp.f32 6931/10000))
4.7%
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
99.4%
(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3))
97.5%
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v))
10.6%
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
99.6%
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
10.6%
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
Compiler

Compiled 632 to 468 computations (25.9% saved)

localize739.0ms (3.9%)

Localize:

Found 16 expressions with local error:

NewAccuracyProgram
99.9%
(-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))
99.8%
(-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
99.8%
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
88.2%
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)
99.8%
(+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
99.8%
(-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v))
99.6%
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
99.2%
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
100.0%
(*.f32 (neg.f32 sinTheta_i) sinTheta_O)
99.9%
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
72.7%
(/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v)
99.1%
(/.f32 (exp.f32 6931/10000) v)
99.9%
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))))
99.9%
(-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))
99.7%
(exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))
88.2%
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)
Compiler

Compiled 323 to 147 computations (54.5% saved)

series154.0ms (0.8%)

Counts
16 → 648
Calls

165 calls:

TimeVariablePointExpression
12.0ms
sinTheta_O
@inf
(*.f32 (neg.f32 sinTheta_i) sinTheta_O)
5.0ms
v
@0
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))))
3.0ms
cosTheta_i
@inf
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
2.0ms
v
@inf
(/.f32 (exp.f32 6931/10000) v)
2.0ms
v
@-inf
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)

rewrite181.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
352×log1p-expm1-u
352×expm1-log1p-u
349×add-exp-log
347×add-log-exp
345×add-cube-cbrt
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
043651
1766639
Stop Event
node limit
Counts
16 → 365
Calls
Call 1
Inputs
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)
(exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))
(-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))))
(/.f32 (exp.f32 6931/10000) v)
(/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v)
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
(*.f32 (neg.f32 sinTheta_i) sinTheta_O)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
(-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v))
(+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
(-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))
Outputs
(-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(-.f32 (exp.f32 (log1p.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v))) 1)
(*.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) (/.f32 1 v))
(*.f32 1 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v))
(*.f32 (pow.f32 (cbrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)) 2) (cbrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)))
(*.f32 (sqrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)) (sqrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)))
(pow.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) 1)
(pow.f32 (cbrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)) 3)
(pow.f32 (sqrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)) 2)
(pow.f32 (pow.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) 3) 1/3)
(pow.f32 (/.f32 v (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) -1)
(log.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)))
(log.f32 (+.f32 1 (expm1.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v))))
(cbrt.f32 (pow.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) 3))
(expm1.f32 (log1p.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)))
(log1p.f32 (expm1.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)))
(exp.f32 (log.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)))
(exp.f32 (*.f32 (log.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)) 1))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(fma.f32 1 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(fma.f32 (/.f32 cosTheta_i v) cosTheta_O (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(fma.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) 2) (cbrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(fma.f32 (sqrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (sqrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)))) 1)
(*.f32 1 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)))
(*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)) (exp.f32 (neg.f32 (/.f32 1 v))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))) 2) (cbrt.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))) (sqrt.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))))
(/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)) (exp.f32 (/.f32 1 v)))
(pow.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) 1)
(pow.f32 (E.f32) (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))
(pow.f32 (cbrt.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))) 3)
(pow.f32 (pow.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))) 2)
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) 2)) (cbrt.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)))
(pow.f32 (exp.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))) (sqrt.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)))
(log.f32 (exp.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)))))
(cbrt.f32 (pow.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) 3))
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))))
(log1p.f32 (expm1.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))))
(+.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(+.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(+.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (*.f32 sinTheta_i sinTheta_O)))
(+.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) (fma.f32 (neg.f32 (sqrt.f32 (*.f32 sinTheta_i sinTheta_O))) (sqrt.f32 (*.f32 sinTheta_i sinTheta_O)) (*.f32 sinTheta_i sinTheta_O)))
(+.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1))) (fma.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) 1 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1)))
(+.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O))) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2) (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2))))
(+.f32 (fma.f32 cosTheta_O cosTheta_i (neg.f32 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1))) (fma.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) 1 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1)))
(+.f32 (fma.f32 cosTheta_O cosTheta_i (neg.f32 (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O))) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2) (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2))))
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(*.f32 (sqrt.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) (sqrt.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(*.f32 (pow.f32 1 (+.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (+.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (cbrt.f32 (E.f32)) (+.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(*.f32 (pow.f32 (sqrt.f32 (E.f32)) (+.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (sqrt.f32 (E.f32)) (+.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)) (/.f32 (exp.f32 (-.f32 (/.f32 1 v) 6931/10000)) (/.f32 1/2 v)))
(log.f32 (exp.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))))
(cbrt.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 3))
(expm1.f32 (log1p.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(log1p.f32 (expm1.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(+.f32 (/.f32 1 v) (neg.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(+.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (fma.f32 (neg.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(+.f32 (fma.f32 1 (/.f32 1 v) (neg.f32 (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1))) (fma.f32 (neg.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1 (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1)))
(+.f32 (fma.f32 1 (/.f32 1 v) (neg.f32 (*.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2) (*.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2))))
(+.f32 (fma.f32 (cbrt.f32 (pow.f32 v -2)) (/.f32 1 (cbrt.f32 v)) (neg.f32 (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1))) (fma.f32 (neg.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1 (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1)))
(+.f32 (fma.f32 (cbrt.f32 (pow.f32 v -2)) (/.f32 1 (cbrt.f32 v)) (neg.f32 (*.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2) (*.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2))))
(+.f32 (fma.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 1 (sqrt.f32 v)) (neg.f32 (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1))) (fma.f32 (neg.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1 (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1)))
(+.f32 (fma.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 1 (sqrt.f32 v)) (neg.f32 (*.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2) (*.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2))))
(*.f32 1 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(*.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2) (cbrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(*.f32 (sqrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (sqrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(/.f32 (-.f32 (pow.f32 v -3) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)) (+.f32 (pow.f32 v -2) (+.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) (*.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(/.f32 (-.f32 (pow.f32 v -2) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)) (+.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(pow.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1)
(pow.f32 (cbrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)
(pow.f32 (pow.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3) 1/3)
(pow.f32 (sqrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)
(log.f32 (/.f32 (exp.f32 (-.f32 (/.f32 1 v) 6931/10000)) (/.f32 1/2 v)))
(log.f32 (+.f32 1 (expm1.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(cbrt.f32 (pow.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))
(expm1.f32 (log1p.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(log1p.f32 (expm1.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(exp.f32 (log.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(exp.f32 (*.f32 (log.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1))
(fma.f32 1 (/.f32 1 v) (neg.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(fma.f32 (cbrt.f32 (pow.f32 v -2)) (/.f32 1 (cbrt.f32 v)) (neg.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(fma.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 1 (sqrt.f32 v)) (neg.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(+.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(+.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(+.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (*.f32 sinTheta_i sinTheta_O)))
(+.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) (fma.f32 (neg.f32 (sqrt.f32 (*.f32 sinTheta_i sinTheta_O))) (sqrt.f32 (*.f32 sinTheta_i sinTheta_O)) (*.f32 sinTheta_i sinTheta_O)))
(+.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1))) (fma.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) 1 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1)))
(+.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O))) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2) (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2))))
(+.f32 (fma.f32 cosTheta_O cosTheta_i (neg.f32 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1))) (fma.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) 1 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1)))
(+.f32 (fma.f32 cosTheta_O cosTheta_i (neg.f32 (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O))) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2) (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2))))
(+.f32 (fma.f32 1 (*.f32 cosTheta_i cosTheta_O) (neg.f32 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1))) (fma.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) 1 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1)))
(+.f32 (fma.f32 1 (*.f32 cosTheta_i cosTheta_O) (neg.f32 (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O))) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2) (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2))))
(+.f32 (fma.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) 2) (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) (neg.f32 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1))) (fma.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) 1 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1)))
(+.f32 (fma.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) 2) (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) (neg.f32 (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O))) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2) (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2))))
(+.f32 (fma.f32 (sqrt.f32 (*.f32 cosTheta_i cosTheta_O)) (sqrt.f32 (*.f32 cosTheta_i cosTheta_O)) (neg.f32 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1))) (fma.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) 1 (*.f32 (*.f32 sinTheta_i sinTheta_O) 1)))
(+.f32 (fma.f32 (sqrt.f32 (*.f32 cosTheta_i cosTheta_O)) (sqrt.f32 (*.f32 cosTheta_i cosTheta_O)) (neg.f32 (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O))) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2) (*.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i sinTheta_O)) 2))))
(*.f32 1 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)))
(*.f32 (pow.f32 (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 2) (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(*.f32 (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i cosTheta_O) 2) (pow.f32 (*.f32 sinTheta_i sinTheta_O) 2)) (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i sinTheta_O)))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i cosTheta_O) 3) (pow.f32 (*.f32 sinTheta_i sinTheta_O) 3)) (+.f32 (pow.f32 (*.f32 cosTheta_i cosTheta_O) 2) (+.f32 (pow.f32 (*.f32 sinTheta_i sinTheta_O) 2) (*.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)))))
(pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1)
(pow.f32 (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 3)
(pow.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 3) 1/3)
(pow.f32 (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 2)
(log.f32 (exp.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(log.f32 (+.f32 1 (expm1.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)))))
(cbrt.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 3))
(expm1.f32 (log1p.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(log1p.f32 (expm1.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(exp.f32 (log.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(exp.f32 (*.f32 (log.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 1))
(fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(fma.f32 1 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(fma.f32 1 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(fma.f32 (pow.f32 (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 2) (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(fma.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) 2) (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(fma.f32 (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(fma.f32 (sqrt.f32 (*.f32 cosTheta_i cosTheta_O)) (sqrt.f32 (*.f32 cosTheta_i cosTheta_O)) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))

simplify536.0ms (2.9%)

Algorithm
egg-herbie
Rules
506×associate-*r*
468×fma-define
465×associate-*l*
256×associate-+r+
241×associate-+l+
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
096955135
1234651169
Stop Event
node limit
Counts
1013 → 606
Calls
Call 1
Inputs
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
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(exp.f32 (*.f32 (log.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)) 1))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(fma.f32 1 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(fma.f32 (/.f32 cosTheta_i v) cosTheta_O (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(fma.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) 2) (cbrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
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(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)))) 1)
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(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
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(*.f32 (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i cosTheta_O) 2) (pow.f32 (*.f32 sinTheta_i sinTheta_O) 2)) (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i sinTheta_O)))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i cosTheta_O) 3) (pow.f32 (*.f32 sinTheta_i sinTheta_O) 3)) (+.f32 (pow.f32 (*.f32 cosTheta_i cosTheta_O) 2) (+.f32 (pow.f32 (*.f32 sinTheta_i sinTheta_O) 2) (*.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)))))
(pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1)
(pow.f32 (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 3)
(pow.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 3) 1/3)
(pow.f32 (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 2)
(log.f32 (exp.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(log.f32 (+.f32 1 (expm1.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)))))
(cbrt.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 3))
(expm1.f32 (log1p.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(log1p.f32 (expm1.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(exp.f32 (log.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(exp.f32 (*.f32 (log.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 1))
(fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(fma.f32 1 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(fma.f32 1 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(fma.f32 (pow.f32 (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 2) (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(fma.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) 2) (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(fma.f32 (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(fma.f32 (sqrt.f32 (*.f32 cosTheta_i cosTheta_O)) (sqrt.f32 (*.f32 cosTheta_i cosTheta_O)) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
Outputs
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(+.f32 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)
(exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (+.f32 (/.f32 -1 v) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))
(exp.f32 (*.f32 (/.f32 1 v) (neg.f32 (fma.f32 sinTheta_O sinTheta_i 1))))
(+.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v))
(+.f32 (exp.f32 (+.f32 (/.f32 -1 v) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))) (*.f32 cosTheta_O (/.f32 (*.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 -1 v) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))) v)))
(fma.f32 cosTheta_O (*.f32 cosTheta_i (/.f32 (exp.f32 (*.f32 (/.f32 1 v) (neg.f32 (fma.f32 sinTheta_O sinTheta_i 1)))) v)) (exp.f32 (*.f32 (/.f32 1 v) (neg.f32 (fma.f32 sinTheta_O sinTheta_i 1)))))
(+.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v)))
(+.f32 (exp.f32 (+.f32 (/.f32 -1 v) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))) (fma.f32 1/2 (/.f32 (*.f32 (*.f32 (pow.f32 cosTheta_O 2) (pow.f32 cosTheta_i 2)) (exp.f32 (+.f32 (/.f32 -1 v) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))) (pow.f32 v 2)) (*.f32 cosTheta_O (/.f32 (*.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 -1 v) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))) v))))
(+.f32 (exp.f32 (*.f32 (/.f32 1 v) (neg.f32 (fma.f32 sinTheta_O sinTheta_i 1)))) (fma.f32 1/2 (/.f32 (*.f32 (exp.f32 (*.f32 (/.f32 1 v) (neg.f32 (fma.f32 sinTheta_O sinTheta_i 1)))) (pow.f32 (*.f32 cosTheta_O cosTheta_i) 2)) (pow.f32 v 2)) (*.f32 cosTheta_O (*.f32 cosTheta_i (/.f32 (exp.f32 (*.f32 (/.f32 1 v) (neg.f32 (fma.f32 sinTheta_O sinTheta_i 1)))) v)))))
(+.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))) (+.f32 (*.f32 1/6 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v))))
(+.f32 (exp.f32 (+.f32 (/.f32 -1 v) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))) (fma.f32 1/6 (*.f32 (pow.f32 cosTheta_O 3) (/.f32 (*.f32 (exp.f32 (+.f32 (/.f32 -1 v) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))) (pow.f32 cosTheta_i 3)) (pow.f32 v 3))) (fma.f32 1/2 (/.f32 (*.f32 (*.f32 (pow.f32 cosTheta_O 2) (pow.f32 cosTheta_i 2)) (exp.f32 (+.f32 (/.f32 -1 v) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))) (pow.f32 v 2)) (*.f32 cosTheta_O (/.f32 (*.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 -1 v) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))) v)))))
(+.f32 (exp.f32 (*.f32 (/.f32 1 v) (neg.f32 (fma.f32 sinTheta_O sinTheta_i 1)))) (fma.f32 1/6 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (exp.f32 (*.f32 (/.f32 1 v) (neg.f32 (fma.f32 sinTheta_O sinTheta_i 1)))) (pow.f32 (/.f32 cosTheta_i v) 3))) (fma.f32 1/2 (/.f32 (*.f32 (exp.f32 (*.f32 (/.f32 1 v) (neg.f32 (fma.f32 sinTheta_O sinTheta_i 1)))) (pow.f32 (*.f32 cosTheta_O cosTheta_i) 2)) (pow.f32 v 2)) (*.f32 cosTheta_O (*.f32 cosTheta_i (/.f32 (exp.f32 (*.f32 (/.f32 1 v) (neg.f32 (fma.f32 sinTheta_O sinTheta_i 1)))) v))))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_O (/.f32 sinTheta_i v))))
(exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_O cosTheta_i -1) (*.f32 sinTheta_O sinTheta_i)) v))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_O (/.f32 sinTheta_i v))))
(exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_O cosTheta_i -1) (*.f32 sinTheta_O sinTheta_i)) v))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_O (/.f32 sinTheta_i v))))
(exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_O cosTheta_i -1) (*.f32 sinTheta_O sinTheta_i)) v))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_O (/.f32 sinTheta_i v))))
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(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i cosTheta_O) 2) (pow.f32 (*.f32 sinTheta_i sinTheta_O) 2)) (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i sinTheta_O)))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_O cosTheta_i) 2) (pow.f32 (*.f32 sinTheta_O sinTheta_i) 2)) (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O sinTheta_i)))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_O cosTheta_i) 2) (pow.f32 (*.f32 sinTheta_O sinTheta_i) 2)) (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O sinTheta_i)))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i cosTheta_O) 3) (pow.f32 (*.f32 sinTheta_i sinTheta_O) 3)) (+.f32 (pow.f32 (*.f32 cosTheta_i cosTheta_O) 2) (+.f32 (pow.f32 (*.f32 sinTheta_i sinTheta_O) 2) (*.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)))))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_O cosTheta_i) 3) (pow.f32 (*.f32 sinTheta_O sinTheta_i) 3)) (+.f32 (pow.f32 (*.f32 cosTheta_O cosTheta_i) 2) (+.f32 (pow.f32 (*.f32 sinTheta_O sinTheta_i) 2) (*.f32 (*.f32 sinTheta_O sinTheta_i) (*.f32 cosTheta_O cosTheta_i)))))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_O cosTheta_i) 3) (pow.f32 (*.f32 sinTheta_O sinTheta_i) 3)) (+.f32 (pow.f32 (*.f32 cosTheta_O cosTheta_i) 2) (*.f32 (*.f32 sinTheta_O sinTheta_i) (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O sinTheta_i)))))
(pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1)
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(pow.f32 (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 3)
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(pow.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 3) 1/3)
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(pow.f32 (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 2)
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(log.f32 (exp.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(log.f32 (+.f32 1 (expm1.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)))))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(cbrt.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 3))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(expm1.f32 (log1p.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(expm1.f32 (log1p.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))))
(log1p.f32 (expm1.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(exp.f32 (log.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(exp.f32 (*.f32 (log.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 1))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(fma.f32 1 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(fma.f32 1 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(+.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (*.f32 sinTheta_O sinTheta_i)))
(+.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) (*.f32 (*.f32 sinTheta_O sinTheta_i) 0))
(fma.f32 (pow.f32 (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) 2) (cbrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(+.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (*.f32 sinTheta_O sinTheta_i)))
(+.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) (*.f32 (*.f32 sinTheta_O sinTheta_i) 0))
(fma.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) 2) (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))
(fma.f32 (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (sqrt.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_i sinTheta_O)))
(+.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (*.f32 sinTheta_O sinTheta_i)))
(+.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) (*.f32 (*.f32 sinTheta_O sinTheta_i) 0))
(fma.f32 (sqrt.f32 (*.f32 cosTheta_i cosTheta_O)) (sqrt.f32 (*.f32 cosTheta_i cosTheta_O)) (*.f32 sinTheta_O (neg.f32 sinTheta_i)))
(-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))

eval363.0ms (1.9%)

Compiler

Compiled 20389 to 12277 computations (39.8% saved)

prune143.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New67514689
Fresh639
Picked505
Done000
Total68617703
Accuracy
99.9%
Counts
703 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.9%
(pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3) 1/3)
99.6%
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 (sqrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)))
99.5%
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 (cbrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)))
99.6%
(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))) 3)
99.6%
(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))
6.2%
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
6.2%
(+.f32 1 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
6.2%
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
97.9%
(*.f32 (pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v)) 3) 1/3) (exp.f32 6931/10000))
99.7%
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
99.6%
(*.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))) (exp.f32 6931/10000))
99.7%
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) (exp.f32 6931/10000))
99.7%
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 1 v))))
99.4%
(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3))
97.5%
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
99.6%
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
10.6%
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
Compiler

Compiled 728 to 564 computations (22.5% saved)

localize739.0ms (3.9%)

Localize:

Found 16 expressions with local error:

NewAccuracyProgram
99.6%
(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3))
99.5%
(cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
97.7%
(pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
88.2%
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)
100.0%
(/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)
99.9%
(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)))
99.9%
(-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))
99.7%
(pow.f32 (E.f32) (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))
100.0%
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
99.7%
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
100.0%
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
99.3%
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
100.0%
(-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))
99.9%
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
99.7%
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))
76.2%
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
Compiler

Compiled 366 to 162 computations (55.7% saved)

series222.0ms (1.2%)

Counts
14 → 443
Calls

162 calls:

TimeVariablePointExpression
11.0ms
v
@-inf
(pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
8.0ms
sinTheta_i
@0
(pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
7.0ms
cosTheta_i
@0
(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3))
7.0ms
sinTheta_O
@0
(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3))
6.0ms
v
@inf
(pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)

rewrite149.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
358×log1p-expm1-u
358×expm1-log1p-u
350×add-exp-log
349×add-log-exp
349×add-cube-cbrt
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
047609
1855577
Stop Event
node limit
Counts
14 → 333
Calls
Call 1
Inputs
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
(-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))
(*.f32 sinTheta_O (/.f32 sinTheta_i v))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
(pow.f32 (E.f32) (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))
(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)))
(/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)
(pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
(cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3))
Outputs
(-.f32 (exp.f32 (log1p.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))) 1)
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 (*.f32 cosTheta_O cosTheta_i) (/.f32 1 v))
(*.f32 1 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(*.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) 2) (cbrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))))
(*.f32 (sqrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (sqrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))))
(pow.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) 1)
(pow.f32 (cbrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) 3)
(pow.f32 (pow.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) 2)
(pow.f32 (/.f32 v (*.f32 cosTheta_O cosTheta_i)) -1)
(log.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))))
(cbrt.f32 (pow.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) 3))
(expm1.f32 (log1p.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))))
(log1p.f32 (expm1.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))))
(exp.f32 (log.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))))
(exp.f32 (*.f32 (log.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) 1))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1)
(*.f32 1 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))
(*.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)) (exp.f32 (neg.f32 (/.f32 1 v))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 2) (cbrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) (sqrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(/.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)) (exp.f32 (/.f32 1 v)))
(pow.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 1)
(pow.f32 (E.f32) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))
(pow.f32 (exp.f32 (fma.f32 cosTheta_O cosTheta_i -1)) (/.f32 1 v))
(pow.f32 (cbrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 3)
(pow.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 2)
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 2)) (cbrt.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))
(pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) (sqrt.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))
(log.f32 (exp.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 3))
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(log1p.f32 (expm1.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 1/2 v)))) 1)
(/.f32 (*.f32 1/2 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) v)
(pow.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 1/2 v)) 1)
(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 1/2 v))) 3)
(pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 1/2 v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 1/2 v))) 2)
(log.f32 (pow.f32 (exp.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) (/.f32 1/2 v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 1/2 v)))))
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(pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 2)
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (sqrt.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(log.f32 (exp.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))))
(cbrt.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 3))
(expm1.f32 (log1p.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(log1p.f32 (expm1.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))

simplify590.0ms (3.1%)

Algorithm
egg-herbie
Rules
561×distribute-rgt-in
560×distribute-lft-in
491×times-frac
409×*-commutative
333×+-commutative
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01458231928275355
14441231928273962
Stop Event
node limit
Counts
776 → 664
Calls
Call 1
Inputs
(exp.f32 (neg.f32 (/.f32 1 v)))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v)))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (+.f32 (*.f32 1/6 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v))))
(exp.f32 (neg.f32 (/.f32 1 v)))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v)))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (+.f32 (*.f32 1/6 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v))))
1
(-.f32 (+.f32 1 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
(-.f32 (+.f32 1 (+.f32 (*.f32 1/2 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 2) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
(-.f32 (+.f32 1 (+.f32 (*.f32 1/6 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 3) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 2) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))) (/.f32 1 v))
1
(+.f32 1 (*.f32 -1 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) v)))
(+.f32 1 (+.f32 (*.f32 -1 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) v)) (*.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 2) (pow.f32 v 2)))))
(+.f32 1 (+.f32 (*.f32 -1 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) v)) (+.f32 (*.f32 -1/6 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 3) (pow.f32 v 3))) (*.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 2) (pow.f32 v 2))))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(/.f32 1/2 v)
(+.f32 (*.f32 1/2 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (*.f32 1/4 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 2) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v))))
(+.f32 (*.f32 1/12 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 3) (pow.f32 v 4))) (+.f32 (*.f32 1/4 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 2) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))))
(/.f32 1/2 v)
(+.f32 (*.f32 -1/2 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (*.f32 -1/2 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) (pow.f32 v 2))) (+.f32 (*.f32 1/4 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 2) (pow.f32 v 3))) (*.f32 1/2 (/.f32 1 v))))
(+.f32 (*.f32 -1/2 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) (pow.f32 v 2))) (+.f32 (*.f32 -1/12 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 3) (pow.f32 v 4))) (+.f32 (*.f32 1/4 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 2) (pow.f32 v 3))) (*.f32 1/2 (/.f32 1 v)))))
(*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v))
(+.f32 (*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v)) (*.f32 1/2 (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))))
(+.f32 (*.f32 1/4 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v)) (*.f32 1/2 (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2)))))
(+.f32 (*.f32 1/12 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 4))) (+.f32 (*.f32 1/4 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v)) (*.f32 1/2 (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v))
(+.f32 (*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v)) (*.f32 1/2 (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))))
(+.f32 (*.f32 1/4 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v)) (*.f32 1/2 (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2)))))
(+.f32 (*.f32 1/12 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 4))) (+.f32 (*.f32 1/4 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v)) (*.f32 1/2 (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(/.f32 -1 v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 -1 v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
(*.f32 -1 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) v))
(*.f32 -1 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) v))
(*.f32 -1 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) v))
(*.f32 -1 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) v))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
1
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
1
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
1
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
1
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(exp.f32 (/.f32 -1 v))
(+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (/.f32 -1 v)))) v))
(+.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (/.f32 -1 v)))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (/.f32 -1 v)))) v)))
(+.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (*.f32 1/6 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (/.f32 -1 v)))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (/.f32 -1 v)))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (/.f32 -1 v)))) v))))
(exp.f32 (/.f32 -1 v))
(+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (/.f32 -1 v)))) v))
(+.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (/.f32 -1 v)))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (/.f32 -1 v)))) v)))
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1
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1
1
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1
1
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(pow.f32 (exp.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2))
(pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 1)
(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 3)
(pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 2)
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (sqrt.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(log.f32 (exp.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))))
(cbrt.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 3))
(expm1.f32 (log1p.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(log1p.f32 (expm1.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
Outputs
(exp.f32 (neg.f32 (/.f32 1 v)))
(exp.f32 (/.f32 -1 v))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v))
(+.f32 (exp.f32 (/.f32 -1 v)) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) v)))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v)))
(+.f32 (exp.f32 (/.f32 -1 v)) (fma.f32 1/2 (*.f32 (pow.f32 cosTheta_O 2) (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_i 2)) (pow.f32 v 2))) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) v))))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (+.f32 (*.f32 1/6 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v))))
(+.f32 (exp.f32 (/.f32 -1 v)) (fma.f32 1/6 (*.f32 (pow.f32 cosTheta_O 3) (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_i 3)) (pow.f32 v 3))) (fma.f32 1/2 (*.f32 (pow.f32 cosTheta_O 2) (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_i 2)) (pow.f32 v 2))) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) v)))))
(exp.f32 (neg.f32 (/.f32 1 v)))
(exp.f32 (/.f32 -1 v))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v))
(+.f32 (exp.f32 (/.f32 -1 v)) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) v)))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v)))
(+.f32 (exp.f32 (/.f32 -1 v)) (fma.f32 1/2 (*.f32 (pow.f32 cosTheta_O 2) (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_i 2)) (pow.f32 v 2))) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) v))))
(+.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (+.f32 (*.f32 1/6 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) v))))
(+.f32 (exp.f32 (/.f32 -1 v)) (fma.f32 1/6 (*.f32 (pow.f32 cosTheta_O 3) (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_i 3)) (pow.f32 v 3))) (fma.f32 1/2 (*.f32 (pow.f32 cosTheta_O 2) (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_i 2)) (pow.f32 v 2))) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) v)))))
1
(-.f32 (+.f32 1 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
(+.f32 1 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))
(-.f32 (+.f32 1 (+.f32 (*.f32 1/2 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 2) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
(+.f32 1 (-.f32 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_O cosTheta_i -1) 2) (pow.f32 v 2)) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
(+.f32 1 (+.f32 (fma.f32 1/2 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 2) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 -1 v)))
(-.f32 (+.f32 1 (+.f32 (*.f32 1/6 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 3) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 2) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))) (/.f32 1 v))
(+.f32 1 (-.f32 (fma.f32 1/6 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 3) (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_O cosTheta_i -1) 2) (pow.f32 v 2)) (*.f32 cosTheta_O (/.f32 cosTheta_i v)))) (/.f32 1 v)))
(+.f32 1 (+.f32 (fma.f32 1/6 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 3) (fma.f32 1/2 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 2) (*.f32 cosTheta_O (/.f32 cosTheta_i v)))) (/.f32 -1 v)))
1
(+.f32 1 (*.f32 -1 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) v)))
(+.f32 1 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))
(+.f32 1 (+.f32 (*.f32 -1 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) v)) (*.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 2) (pow.f32 v 2)))))
(+.f32 1 (fma.f32 -1 (/.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) v) (/.f32 (*.f32 1/2 (pow.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) 2)) (pow.f32 v 2))))
(+.f32 (+.f32 1 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 (*.f32 1/2 (pow.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) 2)) (pow.f32 v 2)))
(+.f32 1 (+.f32 (*.f32 -1 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) v)) (+.f32 (*.f32 -1/6 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 3) (pow.f32 v 3))) (*.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 2) (pow.f32 v 2))))))
(+.f32 1 (fma.f32 -1 (/.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) v) (fma.f32 -1/6 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) 3) (pow.f32 v 3)) (/.f32 (*.f32 1/2 (pow.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) 2)) (pow.f32 v 2)))))
(+.f32 (+.f32 1 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (fma.f32 -1/6 (/.f32 (pow.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) 3) (pow.f32 v 3)) (/.f32 (*.f32 1/2 (pow.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) 2)) (pow.f32 v 2))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) v))
(/.f32 1/2 v)
(+.f32 (*.f32 1/2 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 1/2 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) (pow.f32 v 2)) (/.f32 1/2 v))
(+.f32 (*.f32 1/4 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 2) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v))))
(fma.f32 1/4 (/.f32 (pow.f32 (fma.f32 cosTheta_O cosTheta_i -1) 2) (pow.f32 v 3)) (fma.f32 1/2 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) (pow.f32 v 2)) (/.f32 1/2 v)))
(+.f32 (*.f32 1/12 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 3) (pow.f32 v 4))) (+.f32 (*.f32 1/4 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) 2) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))))
(fma.f32 1/12 (/.f32 (pow.f32 (fma.f32 cosTheta_O cosTheta_i -1) 3) (pow.f32 v 4)) (fma.f32 1/4 (/.f32 (pow.f32 (fma.f32 cosTheta_O cosTheta_i -1) 2) (pow.f32 v 3)) (fma.f32 1/2 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) (pow.f32 v 2)) (/.f32 1/2 v))))
(/.f32 1/2 v)
(+.f32 (*.f32 -1/2 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) (pow.f32 v 2)) (/.f32 1/2 v))
(fma.f32 -1/2 (/.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) (pow.f32 v 2)) (/.f32 1/2 v))
(+.f32 (*.f32 -1/2 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) (pow.f32 v 2))) (+.f32 (*.f32 1/4 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 2) (pow.f32 v 3))) (*.f32 1/2 (/.f32 1 v))))
(fma.f32 -1/2 (/.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) (pow.f32 v 2)) (fma.f32 1/4 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) 2) (pow.f32 v 3)) (/.f32 1/2 v)))
(fma.f32 -1/2 (/.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) (pow.f32 v 2)) (fma.f32 1/4 (/.f32 (pow.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) 2) (pow.f32 v 3)) (/.f32 1/2 v)))
(+.f32 (*.f32 -1/2 (/.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) (pow.f32 v 2))) (+.f32 (*.f32 -1/12 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 3) (pow.f32 v 4))) (+.f32 (*.f32 1/4 (/.f32 (pow.f32 (+.f32 1 (*.f32 -1 (*.f32 cosTheta_O cosTheta_i))) 2) (pow.f32 v 3))) (*.f32 1/2 (/.f32 1 v)))))
(fma.f32 -1/2 (/.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) (pow.f32 v 2)) (fma.f32 -1/12 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) 3) (pow.f32 v 4)) (fma.f32 1/4 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_O cosTheta_i))) 2) (pow.f32 v 3)) (/.f32 1/2 v))))
(fma.f32 -1/2 (/.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) (pow.f32 v 2)) (fma.f32 -1/12 (/.f32 (pow.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) 3) (pow.f32 v 4)) (fma.f32 1/4 (/.f32 (pow.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) 2) (pow.f32 v 3)) (/.f32 1/2 v))))
(*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v))
(/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v)
(+.f32 (*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v)) (*.f32 1/2 (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))))
(*.f32 1/2 (+.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) (pow.f32 v 2)))))
(+.f32 (*.f32 1/4 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v)) (*.f32 1/2 (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2)))))
(fma.f32 1/4 (*.f32 (pow.f32 cosTheta_O 2) (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_i 2)) (pow.f32 v 3))) (*.f32 1/2 (+.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) (pow.f32 v 2))))))
(fma.f32 1/4 (*.f32 (pow.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) 2) (/.f32 (exp.f32 (/.f32 -1 v)) v)) (*.f32 1/2 (+.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) (pow.f32 v 2))))))
(+.f32 (*.f32 1/12 (/.f32 (*.f32 (pow.f32 cosTheta_O 3) (*.f32 (pow.f32 cosTheta_i 3) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 4))) (+.f32 (*.f32 1/4 (/.f32 (*.f32 (pow.f32 cosTheta_O 2) (*.f32 (pow.f32 cosTheta_i 2) (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (*.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v)) (*.f32 1/2 (/.f32 (*.f32 cosTheta_O (*.f32 cosTheta_i (exp.f32 (neg.f32 (/.f32 1 v))))) (pow.f32 v 2))))))
(fma.f32 1/12 (*.f32 (pow.f32 cosTheta_O 3) (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_i 3)) (pow.f32 v 4))) (fma.f32 1/4 (*.f32 (pow.f32 cosTheta_O 2) (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_i 2)) (pow.f32 v 3))) (*.f32 1/2 (+.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) (pow.f32 v 2)))))))
(fma.f32 1/12 (*.f32 (pow.f32 cosTheta_O 3) (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_i 3)) (pow.f32 v 4))) (fma.f32 1/4 (*.f32 (pow.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) 2) (/.f32 (exp.f32 (/.f32 -1 v)) v)) (*.f32 1/2 (+.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (*.f32 cosTheta_O (/.f32 (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_i) (pow.f32 v 2)))))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) v))
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1
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1
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1
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(cbrt.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 3))
(*.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_O cosTheta_i -1) (*.f32 sinTheta_O sinTheta_i)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))
(*.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_O cosTheta_i -1) (*.f32 sinTheta_O sinTheta_i)) v)) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))
(expm1.f32 (log1p.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(expm1.f32 (log1p.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_O cosTheta_i -1) (*.f32 sinTheta_O sinTheta_i)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(expm1.f32 (log1p.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_O cosTheta_i -1) (*.f32 sinTheta_O sinTheta_i)) v)) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))))
(log1p.f32 (expm1.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(*.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_O cosTheta_i -1) (*.f32 sinTheta_O sinTheta_i)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))
(*.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_O cosTheta_i -1) (*.f32 sinTheta_O sinTheta_i)) v)) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))

eval1.4s (7.7%)

Compiler

Compiled 64169 to 43420 computations (32.3% saved)

prune211.0ms (1.1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New7927799
Fresh11112
Picked415
Done000
Total79719816
Accuracy
99.9%
Counts
816 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.9%
(pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3) 1/3)
99.6%
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 (sqrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)))
99.5%
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 (cbrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)))
99.6%
(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))) 3)
99.6%
(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))
6.2%
(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
6.2%
(+.f32 1 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
97.9%
(*.f32 (pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v)) 3) 1/3) (exp.f32 6931/10000))
99.7%
(*.f32 (/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v) (exp.f32 6931/10000))
22.6%
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
99.7%
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
99.5%
(*.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (pow.f32 (cbrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 3))) (exp.f32 6931/10000))
99.6%
(*.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))) (exp.f32 6931/10000))
99.7%
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 1 v))))
43.0%
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
99.4%
(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3))
97.5%
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
99.6%
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
10.6%
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
Compiler

Compiled 759 to 594 computations (21.7% saved)

localize603.0ms (3.2%)

Localize:

Found 14 expressions with local error:

NewAccuracyProgram
99.9%
(*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v))
99.9%
(-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O))
99.7%
(exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))
97.9%
(pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v)) 3) 1/3)
99.9%
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 1 v))))
99.7%
(exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 1 v)))
99.2%
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
98.8%
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
99.9%
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
99.3%
(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
99.3%
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
100.0%
(*.f32 (/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v) (exp.f32 6931/10000))
99.9%
(/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v)
99.7%
(exp.f32 (/.f32 -1 v))
Compiler

Compiled 280 to 138 computations (50.7% saved)

series183.0ms (1%)

Counts
12 → 404
Calls

102 calls:

TimeVariablePointExpression
32.0ms
sinTheta_i
@inf
(pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v)) 3) 1/3)
7.0ms
cosTheta_i
@0
(pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v)) 3) 1/3)
7.0ms
cosTheta_O
@0
(pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v)) 3) 1/3)
7.0ms
sinTheta_i
@0
(pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v)) 3) 1/3)
7.0ms
sinTheta_O
@0
(pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v)) 3) 1/3)

rewrite115.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
351×log1p-expm1-u
351×expm1-log1p-u
347×add-exp-log
346×add-log-exp
345×add-cube-cbrt
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
050471
1805455
Stop Event
node limit
Counts
12 → 209
Calls
Call 1
Inputs
(exp.f32 (/.f32 -1 v))
(/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v)
(*.f32 (/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v) (exp.f32 6931/10000))
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 1 v)))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 1 v))))
(pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v)) 3) 1/3)
(exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))
(*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v))
Outputs
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 -1 v)))) 1)
(*.f32 1 (exp.f32 (/.f32 -1 v)))
(*.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 -1 v)) 2)) (cbrt.f32 (exp.f32 (/.f32 -1 v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 -1 v))) (sqrt.f32 (exp.f32 (/.f32 -1 v))))
(pow.f32 (exp.f32 (/.f32 -1 v)) 1)
(pow.f32 (cbrt.f32 (exp.f32 (/.f32 -1 v))) 3)
(pow.f32 (pow.f32 (exp.f32 (/.f32 -1 v)) 3) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (/.f32 -1 v))) 2)
(pow.f32 (exp.f32 1) (/.f32 -1 v))
(pow.f32 (exp.f32 -1) (/.f32 1 v))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (/.f32 -1 v)) 2)) (cbrt.f32 (/.f32 -1 v)))
(pow.f32 (exp.f32 (sqrt.f32 (/.f32 -1 v))) (sqrt.f32 (/.f32 -1 v)))
(log.f32 (exp.f32 (exp.f32 (/.f32 -1 v))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 -1 v)))))
(cbrt.f32 (pow.f32 (exp.f32 (/.f32 -1 v)) 3))
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 -1 v))))
(log1p.f32 (expm1.f32 (exp.f32 (/.f32 -1 v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v)))) 1)
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))
(*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (/.f32 1 v))
(*.f32 1 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v)))
(*.f32 (cbrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v)) 2)) (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))))
(*.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))) (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v)) 1)
(pow.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))) 3)
(pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))) 2)
(pow.f32 (/.f32 v (*.f32 (exp.f32 (/.f32 -1 v)) 1/2)) -1)
(log.f32 (pow.f32 (exp.f32 1/2) (/.f32 (exp.f32 (/.f32 -1 v)) v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v)))))
(cbrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v)) 3))
(cbrt.f32 (*.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) 3) (pow.f32 v -3)))
(cbrt.f32 (/.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) 3) (pow.f32 v 3)))
(expm1.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))))
(log1p.f32 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))))
(exp.f32 (-.f32 (+.f32 (/.f32 -1 v) (log.f32 1/2)) (log.f32 v)))
(exp.f32 (*.f32 (-.f32 (+.f32 (/.f32 -1 v) (log.f32 1/2)) (log.f32 v)) 1))
(-.f32 (exp.f32 (log1p.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v))) 1)
(/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v)
(pow.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v) 1)
(pow.f32 (cbrt.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v)) 3)
(pow.f32 (pow.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v) 3) 1/3)
(pow.f32 (sqrt.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v)) 2)
(log.f32 (pow.f32 (exp.f32 (exp.f32 6931/10000)) (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))))
(log.f32 (+.f32 1 (expm1.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v))))
(cbrt.f32 (pow.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v) 3))
(cbrt.f32 (*.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v)) 3) (pow.f32 (exp.f32 6931/10000) 3)))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 6931/10000) 3) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v)) 3)))
(expm1.f32 (log1p.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v)))
(log1p.f32 (expm1.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v)))
(exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (/.f32 -1 v) (log.f32 1/2)) (log.f32 v))))
(exp.f32 (*.f32 (+.f32 6931/10000 (-.f32 (+.f32 (/.f32 -1 v) (log.f32 1/2)) (log.f32 v))) 1))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))) 1)
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(pow.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)) 1)
(pow.f32 (cbrt.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) 3)
(pow.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) 2)
(neg.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(log.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_O)) (/.f32 sinTheta_i v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))))
(cbrt.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)) 3))
(cbrt.f32 (*.f32 (pow.f32 (/.f32 sinTheta_i v) 3) (pow.f32 (neg.f32 sinTheta_O) 3)))
(cbrt.f32 (*.f32 (pow.f32 (neg.f32 sinTheta_O) 3) (pow.f32 (/.f32 sinTheta_i v) 3)))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))))
(exp.f32 (log.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))))
(exp.f32 (*.f32 (log.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) 1))
(+.f32 0 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(+.f32 (log.f32 (cbrt.f32 (pow.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)) 2))) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)))))
(+.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))) 1)
(/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v)
(pow.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1)
(pow.f32 (cbrt.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))) 3)
(pow.f32 (pow.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))) 2)
(neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))
(log.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))))
(cbrt.f32 (pow.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)) 3))
(cbrt.f32 (*.f32 (pow.f32 (neg.f32 sinTheta_i) 3) (pow.f32 (/.f32 sinTheta_O v) 3)))
(cbrt.f32 (*.f32 (pow.f32 (/.f32 sinTheta_O v) 3) (pow.f32 (neg.f32 sinTheta_i) 3)))
(expm1.f32 (log1p.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))
(log1p.f32 (expm1.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))
(exp.f32 (log.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))
(exp.f32 (*.f32 (log.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))) 1))
(-.f32 (exp.f32 (log1p.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)))) 1)
(*.f32 1 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)))
(*.f32 (cbrt.f32 (pow.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)) 2)) (cbrt.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v))))
(*.f32 (sqrt.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v))) (sqrt.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v))))
(/.f32 1 (exp.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(pow.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)) 1)
(pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v))
(pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (*.f32 (/.f32 sinTheta_O v) 1))
(pow.f32 (exp.f32 (/.f32 sinTheta_O v)) (neg.f32 sinTheta_i))
(pow.f32 (cbrt.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v))) 3)
(pow.f32 (pow.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)) 3) 1/3)
(pow.f32 (sqrt.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v))) 2)
(pow.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) sinTheta_O) (/.f32 1 v))
(pow.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (cbrt.f32 (pow.f32 (/.f32 sinTheta_O v) 2))) (cbrt.f32 (/.f32 sinTheta_O v)))
(pow.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (sqrt.f32 (/.f32 sinTheta_O v))) (sqrt.f32 (/.f32 sinTheta_O v)))
(pow.f32 (exp.f32 1) (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)) 2))) (cbrt.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))
(pow.f32 (exp.f32 (sqrt.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))) (sqrt.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))))
(log.f32 (exp.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v))))
(log.f32 (+.f32 1 (expm1.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)))))
(cbrt.f32 (pow.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v)) 3))
(expm1.f32 (log1p.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v))))
(log1p.f32 (expm1.f32 (pow.f32 (exp.f32 (neg.f32 sinTheta_i)) (/.f32 sinTheta_O v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))) 1)
(/.f32 (*.f32 1/2 (exp.f32 6931/10000)) v)
(pow.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 1)
(pow.f32 (cbrt.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))) 3)
(pow.f32 (pow.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))) 2)
(log.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 6931/10000)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))))
(cbrt.f32 (pow.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 3))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 6931/10000) 3) (*.f32 1/8 (pow.f32 v -3))))
(cbrt.f32 (*.f32 (*.f32 1/8 (pow.f32 v -3)) (pow.f32 (exp.f32 6931/10000) 3)))
(expm1.f32 (log1p.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))))
(log1p.f32 (expm1.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))))
(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
(exp.f32 (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))) 1)
(*.f32 1 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
(*.f32 (pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O) (exp.f32 (neg.f32 (/.f32 1 v))))
(*.f32 (cbrt.f32 (pow.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 2)) (cbrt.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))
(*.f32 (sqrt.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) (sqrt.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))
(/.f32 (pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O) (exp.f32 (/.f32 1 v)))
(pow.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 1)
(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) 3)
(pow.f32 (pow.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 3) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) 2)
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 2)) (cbrt.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
(pow.f32 (exp.f32 (sqrt.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) (sqrt.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
(log.f32 (exp.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))))
(cbrt.f32 (pow.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 3))
(expm1.f32 (log1p.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))
(log1p.f32 (expm1.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))))) 1)
(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))) 1)
(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))) 3)
(pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))) 2)
(log.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))))))
(cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))) 3))
(cbrt.f32 (*.f32 (pow.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 3) (pow.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 3)))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 3) (pow.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 3)))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))))
(exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(exp.f32 (*.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) 1)
(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
(*.f32 1 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)) (/.f32 1/2 v))
(*.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) 2))
(*.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 2) 1/3))
(*.f32 (pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) 2) (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(*.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(*.f32 (pow.f32 1 1/3) (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 (pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 2) 1/3) (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(*.f32 (pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3/2) 1/3) (pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3/2) 1/3))
(*.f32 (cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3/2)) (cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3/2)))
(/.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)) 1/2) v)
(log.f32 (pow.f32 (exp.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (/.f32 1/2 v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
(cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) (log.f32 (/.f32 1/2 v))))
(exp.f32 (*.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) (log.f32 (/.f32 1/2 v))) 1))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) 1)
(*.f32 1 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 2) (cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (sqrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_i sinTheta_O)) v)) (exp.f32 (/.f32 1 v)))
(pow.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)) 1)
(pow.f32 (exp.f32 (*.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) 3)) 1/3)
(pow.f32 (exp.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1))) (/.f32 1 v))
(pow.f32 (cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3)
(pow.f32 (sqrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 2)
(pow.f32 (exp.f32 1) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))
(pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) 2))) (cbrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
(pow.f32 (exp.f32 (sqrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (sqrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
(log.f32 (exp.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(cbrt.f32 (exp.f32 (*.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) 3)))
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(log1p.f32 (expm1.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) 1)
(/.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)) 1/2) v)
(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 1)
(pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3) 1/3)
(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) 3)
(pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 6) 1/6)
(pow.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) 2)
(log.f32 (pow.f32 (exp.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (/.f32 1/2 v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
(cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) (log.f32 (/.f32 1/2 v))))
(exp.f32 (*.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) (log.f32 (/.f32 1/2 v))) 1))

simplify304.0ms (1.6%)

Algorithm
egg-herbie
Rules
795×associate-*l*
682×fma-define
632×times-frac
294×*-commutative
237×associate-+l+
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0106541427
1289340581
Stop Event
node limit
Counts
613 → 484
Calls
Call 1
Inputs
1
(-.f32 1 (/.f32 1 v))
(-.f32 (+.f32 1 (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (/.f32 1 v))
(-.f32 (+.f32 1 (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (/.f32 1 v)))
1
(-.f32 1 (/.f32 1 v))
(-.f32 (+.f32 1 (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (/.f32 1 v))
(-.f32 (+.f32 1 (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (/.f32 1 v)))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))
(/.f32 1/2 v)
(-.f32 (*.f32 1/2 (/.f32 1 v)) (*.f32 1/2 (/.f32 1 (pow.f32 v 2))))
(-.f32 (+.f32 (*.f32 1/4 (/.f32 1 (pow.f32 v 3))) (*.f32 1/2 (/.f32 1 v))) (*.f32 1/2 (/.f32 1 (pow.f32 v 2))))
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(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
(/.f32 1/2 v)
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(exp.f32 (*.f32 -1 (/.f32 (+.f32 1 (*.f32 sinTheta_O sinTheta_i)) v)))
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1
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(pow.f32 (sqrt.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) 2)
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 2)) (cbrt.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
(pow.f32 (exp.f32 (sqrt.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) (sqrt.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
(log.f32 (exp.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))))
(cbrt.f32 (pow.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 3))
(expm1.f32 (log1p.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))
(log1p.f32 (expm1.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))))) 1)
(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))) 1)
(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))) 3)
(pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))) 2)
(log.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))))))
(cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))) 3))
(cbrt.f32 (*.f32 (pow.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 3) (pow.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 3)))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) 3) (pow.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 3)))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))))
(exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(exp.f32 (*.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) 1)
(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
(*.f32 1 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)) (/.f32 1/2 v))
(*.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) 2))
(*.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 2) 1/3))
(*.f32 (pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) 2) (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(*.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(*.f32 (pow.f32 1 1/3) (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 (pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 2) 1/3) (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(*.f32 (pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3/2) 1/3) (pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3/2) 1/3))
(*.f32 (cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3/2)) (cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3/2)))
(/.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)) 1/2) v)
(log.f32 (pow.f32 (exp.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (/.f32 1/2 v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
(cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) (log.f32 (/.f32 1/2 v))))
(exp.f32 (*.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) (log.f32 (/.f32 1/2 v))) 1))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) 1)
(*.f32 1 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 2) (cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (sqrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_i sinTheta_O)) v)) (exp.f32 (/.f32 1 v)))
(pow.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)) 1)
(pow.f32 (exp.f32 (*.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) 3)) 1/3)
(pow.f32 (exp.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1))) (/.f32 1 v))
(pow.f32 (cbrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3)
(pow.f32 (sqrt.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 2)
(pow.f32 (exp.f32 1) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))
(pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) 2))) (cbrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
(pow.f32 (exp.f32 (sqrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (sqrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
(log.f32 (exp.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(cbrt.f32 (exp.f32 (*.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) 3)))
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(log1p.f32 (expm1.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) 1)
(/.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)) 1/2) v)
(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 1)
(pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3) 1/3)
(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) 3)
(pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 6) 1/6)
(pow.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) 2)
(log.f32 (pow.f32 (exp.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (/.f32 1/2 v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
(cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v))) 3))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
(exp.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) (log.f32 (/.f32 1/2 v))))
(exp.f32 (*.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) (log.f32 (/.f32 1/2 v))) 1))
Outputs
1
(-.f32 1 (/.f32 1 v))
(+.f32 1 (/.f32 -1 v))
(-.f32 (+.f32 1 (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (/.f32 1 v))
(+.f32 (+.f32 1 (/.f32 1/2 (pow.f32 v 2))) (/.f32 -1 v))
(+.f32 (/.f32 1/2 (pow.f32 v 2)) (+.f32 1 (/.f32 -1 v)))
(-.f32 (+.f32 1 (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (/.f32 1 v)))
(+.f32 1 (-.f32 (/.f32 1/2 (pow.f32 v 2)) (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))))
(-.f32 (+.f32 (/.f32 1/2 (pow.f32 v 2)) (+.f32 1 (/.f32 -1 v))) (/.f32 1/6 (pow.f32 v 3)))
1
(-.f32 1 (/.f32 1 v))
(+.f32 1 (/.f32 -1 v))
(-.f32 (+.f32 1 (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (/.f32 1 v))
(+.f32 (+.f32 1 (/.f32 1/2 (pow.f32 v 2))) (/.f32 -1 v))
(+.f32 (/.f32 1/2 (pow.f32 v 2)) (+.f32 1 (/.f32 -1 v)))
(-.f32 (+.f32 1 (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (/.f32 1 v)))
(+.f32 1 (-.f32 (/.f32 1/2 (pow.f32 v 2)) (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))))
(-.f32 (+.f32 (/.f32 1/2 (pow.f32 v 2)) (+.f32 1 (/.f32 -1 v))) (/.f32 1/6 (pow.f32 v 3)))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 -1 v)) v))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(/.f32 1/2 v)
(-.f32 (*.f32 1/2 (/.f32 1 v)) (*.f32 1/2 (/.f32 1 (pow.f32 v 2))))
(-.f32 (/.f32 1/2 v) (/.f32 1/2 (pow.f32 v 2)))
(+.f32 (/.f32 1/2 v) (/.f32 -1/2 (pow.f32 v 2)))
(-.f32 (+.f32 (*.f32 1/4 (/.f32 1 (pow.f32 v 3))) (*.f32 1/2 (/.f32 1 v))) (*.f32 1/2 (/.f32 1 (pow.f32 v 2))))
(+.f32 (/.f32 1/4 (pow.f32 v 3)) (-.f32 (/.f32 1/2 v) (/.f32 1/2 (pow.f32 v 2))))
(+.f32 (/.f32 1/4 (pow.f32 v 3)) (+.f32 (/.f32 1/2 v) (/.f32 -1/2 (pow.f32 v 2))))
(-.f32 (+.f32 (*.f32 1/4 (/.f32 1 (pow.f32 v 3))) (*.f32 1/2 (/.f32 1 v))) (+.f32 (*.f32 1/12 (/.f32 1 (pow.f32 v 4))) (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))))
(+.f32 (/.f32 1/4 (pow.f32 v 3)) (-.f32 (/.f32 1/2 v) (+.f32 (/.f32 1/2 (pow.f32 v 2)) (/.f32 1/12 (pow.f32 v 4)))))
(+.f32 (/.f32 1/2 v) (-.f32 (/.f32 1/4 (pow.f32 v 3)) (+.f32 (/.f32 1/2 (pow.f32 v 2)) (/.f32 1/12 (pow.f32 v 4)))))
(/.f32 1/2 v)
(-.f32 (*.f32 1/2 (/.f32 1 v)) (*.f32 1/2 (/.f32 1 (pow.f32 v 2))))
(-.f32 (/.f32 1/2 v) (/.f32 1/2 (pow.f32 v 2)))
(+.f32 (/.f32 1/2 v) (/.f32 -1/2 (pow.f32 v 2)))
(-.f32 (+.f32 (*.f32 1/4 (/.f32 1 (pow.f32 v 3))) (*.f32 1/2 (/.f32 1 v))) (*.f32 1/2 (/.f32 1 (pow.f32 v 2))))
(+.f32 (/.f32 1/4 (pow.f32 v 3)) (-.f32 (/.f32 1/2 v) (/.f32 1/2 (pow.f32 v 2))))
(+.f32 (/.f32 1/4 (pow.f32 v 3)) (+.f32 (/.f32 1/2 v) (/.f32 -1/2 (pow.f32 v 2))))
(-.f32 (+.f32 (*.f32 1/4 (/.f32 1 (pow.f32 v 3))) (*.f32 1/2 (/.f32 1 v))) (+.f32 (*.f32 1/12 (/.f32 1 (pow.f32 v 4))) (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))))
(+.f32 (/.f32 1/4 (pow.f32 v 3)) (-.f32 (/.f32 1/2 v) (+.f32 (/.f32 1/2 (pow.f32 v 2)) (/.f32 1/12 (pow.f32 v 4)))))
(+.f32 (/.f32 1/2 v) (-.f32 (/.f32 1/4 (pow.f32 v 3)) (+.f32 (/.f32 1/2 (pow.f32 v 2)) (/.f32 1/12 (pow.f32 v 4)))))
(*.f32 1/2 (/.f32 (*.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
(*.f32 1/2 (/.f32 (*.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
(*.f32 1/2 (/.f32 (*.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
(*.f32 1/2 (/.f32 (*.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
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1
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(-.f32 (+.f32 1 (fma.f32 1/6 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) 3) (pow.f32 v 3)) (fma.f32 1/2 (/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) 2) (pow.f32 v 2)) (*.f32 cosTheta_O (/.f32 cosTheta_i v))))) (+.f32 (/.f32 1 v) (*.f32 sinTheta_O (/.f32 sinTheta_i v))))
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1
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(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
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(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
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(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
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(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)) v))
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(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(exp.f32 (*.f32 (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v) (log.f32 (/.f32 1/2 v))) 1))
(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))

eval510.0ms (2.7%)

Compiler

Compiled 22551 to 15607 computations (30.8% saved)

prune183.0ms (1%)

Pruning

22 alts after pruning (18 fresh and 4 done)

PrunedKeptTotal
New54010550
Fresh5813
Picked235
Done011
Total54722569
Accuracy
99.9%
Counts
569 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.9%
(pow.f32 (pow.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v) 3) 1/3)
99.7%
(pow.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))) 2)
99.6%
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 (sqrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)))
99.5%
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 (cbrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)))
99.6%
(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))) 3)
99.6%
(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))
43.0%
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
99.6%
(/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (/.f32 -1 v) (log.f32 1/2)))) v)
6.2%
(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
77.0%
(+.f32 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))) -1)
99.6%
(*.f32 (/.f32 (*.f32 1/2 (pow.f32 (E.f32) (/.f32 -1 v))) v) (exp.f32 6931/10000))
99.7%
(*.f32 (/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v) (exp.f32 6931/10000))
22.6%
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
99.7%
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
99.5%
(*.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (pow.f32 (cbrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 3))) (exp.f32 6931/10000))
99.7%
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 -1 v)))
99.7%
(*.f32 (expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 1 v))))
22.6%
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
99.7%
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
97.5%
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
99.6%
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
10.6%
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
Compiler

Compiled 1146 to 764 computations (33.3% saved)

regimes151.0ms (0.8%)

Counts
48 → 1
Calls
Call 1
Inputs
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))) -1)
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 -1 v)))
(*.f32 (/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v) (exp.f32 6931/10000))
(/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (/.f32 -1 v) (log.f32 1/2)))) v)
(*.f32 (/.f32 (*.f32 1/2 (pow.f32 (E.f32) (/.f32 -1 v))) v) (exp.f32 6931/10000))
(*.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))) (exp.f32 6931/10000))
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 1 v))))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) (exp.f32 6931/10000))
(*.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v))) (exp.f32 6931/10000))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))) (exp.f32 6931/10000))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6931/10000)))
(*.f32 (/.f32 1/2 v) (*.f32 (exp.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) (exp.f32 6931/10000)))
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))
(pow.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))))) 2)
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) v)) 3) 1/3)
(pow.f32 (pow.f32 (/.f32 (*.f32 (*.f32 (exp.f32 (/.f32 -1 v)) 1/2) (exp.f32 6931/10000)) v) 3) 1/3)
(*.f32 (expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 1 v))))
(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3))
(*.f32 (pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 v)) 3) 1/3) (exp.f32 6931/10000))
(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3))
(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))) 3)
(*.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (pow.f32 (cbrt.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 3))) (exp.f32 6931/10000))
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 (cbrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)))
(pow.f32 (exp.f32 1) (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (pow.f32 (sqrt.f32 (-.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)))
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)) 2)) (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000))))
Outputs
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) (exp.f32 6931/10000))
Calls

9 calls:

24.0ms
cosTheta_O
21.0ms
cosTheta_i
21.0ms
sinTheta_O
21.0ms
sinTheta_i
15.0ms
(*.f32 cosTheta_i cosTheta_O)
Results
AccuracySegmentsBranch
99.7%1cosTheta_i
99.7%1cosTheta_O
99.7%1sinTheta_i
99.7%1sinTheta_O
99.7%1v
99.7%1(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
99.7%1(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
99.7%1(*.f32 cosTheta_i cosTheta_O)
99.7%1(*.f32 sinTheta_i sinTheta_O)
Compiler

Compiled 105 to 80 computations (23.8% saved)

regimes68.0ms (0.4%)

Counts
26 → 1
Calls
Call 1
Inputs
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))) -1)
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 -1 v)))
(*.f32 (/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v) (exp.f32 6931/10000))
(/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (/.f32 -1 v) (log.f32 1/2)))) v)
(*.f32 (/.f32 (*.f32 1/2 (pow.f32 (E.f32) (/.f32 -1 v))) v) (exp.f32 6931/10000))
(*.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))) (exp.f32 6931/10000))
(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 1 v))))
Outputs
(*.f32 (/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v) (exp.f32 6931/10000))
Calls

5 calls:

16.0ms
sinTheta_O
14.0ms
sinTheta_i
13.0ms
cosTheta_i
12.0ms
cosTheta_O
11.0ms
v
Results
AccuracySegmentsBranch
99.7%1cosTheta_i
99.7%1cosTheta_O
99.7%1sinTheta_i
99.7%1sinTheta_O
99.7%1v
Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes55.0ms (0.3%)

Counts
20 → 1
Calls
Call 1
Inputs
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))) -1)
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 -1 v)))
Outputs
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
Calls

5 calls:

14.0ms
sinTheta_O
11.0ms
cosTheta_O
10.0ms
sinTheta_i
9.0ms
cosTheta_i
8.0ms
v
Results
AccuracySegmentsBranch
99.7%1cosTheta_i
99.7%1cosTheta_O
99.7%1sinTheta_i
99.7%1sinTheta_O
99.7%1v
Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes46.0ms (0.2%)

Counts
17 → 1
Calls
Call 1
Inputs
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))) -1)
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v))
Outputs
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
Calls

5 calls:

10.0ms
sinTheta_O
9.0ms
sinTheta_i
9.0ms
cosTheta_i
8.0ms
cosTheta_O
8.0ms
v
Results
AccuracySegmentsBranch
99.7%1cosTheta_i
99.7%1cosTheta_O
99.7%1sinTheta_i
99.7%1sinTheta_O
99.7%1v
Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes42.0ms (0.2%)

Counts
15 → 1
Calls
Call 1
Inputs
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))) -1)
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
Outputs
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
Calls

5 calls:

9.0ms
sinTheta_i
9.0ms
cosTheta_O
8.0ms
v
8.0ms
sinTheta_O
8.0ms
cosTheta_i
Results
AccuracySegmentsBranch
97.5%1cosTheta_i
97.5%1cosTheta_O
97.5%1sinTheta_i
97.5%1sinTheta_O
97.5%1v
Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes41.0ms (0.2%)

Counts
14 → 1
Calls
Call 1
Inputs
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))) -1)
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(exp.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v))))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
Outputs
(+.f32 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))) -1)
Calls

5 calls:

8.0ms
cosTheta_O
8.0ms
v
8.0ms
sinTheta_O
8.0ms
cosTheta_i
7.0ms
sinTheta_i
Results
AccuracySegmentsBranch
77.0%1cosTheta_i
77.0%1cosTheta_O
77.0%1sinTheta_i
77.0%1sinTheta_O
77.0%1v
Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes28.0ms (0.2%)

Counts
8 → 1
Calls
Call 1
Inputs
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(+.f32 1 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(+.f32 1 (*.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
Outputs
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
Calls

5 calls:

6.0ms
cosTheta_O
6.0ms
sinTheta_O
5.0ms
v
5.0ms
sinTheta_i
5.0ms
cosTheta_i
Results
AccuracySegmentsBranch
43.0%1cosTheta_i
43.0%1sinTheta_O
43.0%1v
43.0%1cosTheta_O
43.0%1sinTheta_i
Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes20.0ms (0.1%)

Counts
2 → 1
Calls
Call 1
Inputs
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
Outputs
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
Calls

5 calls:

6.0ms
sinTheta_O
4.0ms
cosTheta_O
3.0ms
cosTheta_i
3.0ms
sinTheta_i
3.0ms
v
Results
AccuracySegmentsBranch
22.6%1cosTheta_O
22.6%1v
22.6%1cosTheta_i
22.6%1sinTheta_i
22.6%1sinTheta_O
Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes14.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
Outputs
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
Calls

5 calls:

3.0ms
cosTheta_i
3.0ms
cosTheta_O
3.0ms
sinTheta_O
3.0ms
sinTheta_i
3.0ms
v
Results
AccuracySegmentsBranch
22.6%1cosTheta_O
22.6%1cosTheta_i
22.6%1v
22.6%1sinTheta_i
22.6%1sinTheta_O
Compiler

Compiled 30 to 25 computations (16.7% saved)

simplify12.0ms (0.1%)

Algorithm
egg-herbie
Rules
24×*-commutative
18×+-commutative
15×sub-neg
12×neg-sub0
12×neg-mul-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053346
187346
2121346
3156346
4171346
5176346
Stop Event
fuel
saturated
Calls
Call 1
Inputs
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) (exp.f32 6931/10000))
(*.f32 (/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v) (exp.f32 6931/10000))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
(+.f32 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))) -1)
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
Outputs
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) (exp.f32 6931/10000))
(*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 -1 v)))) (exp.f32 6931/10000))
(*.f32 (/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v) (exp.f32 6931/10000))
(*.f32 (exp.f32 6931/10000) (/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) 6931/10000) (/.f32 1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) 6931/10000) (/.f32 -1 v))))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
(exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_O cosTheta_i) -1) v))
(+.f32 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))) -1)
(+.f32 -1 (-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v))))
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
(*.f32 sinTheta_i (/.f32 sinTheta_O (neg.f32 v)))
Compiler

Compiled 134 to 105 computations (21.6% saved)

soundness4.0s (21.4%)

Rules
795×exp-diff
795×associate-*l*
795×associate-*l*
795×associate-*l*
795×exp-diff
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01732130
14851898
214481854
357471854
035465
1518432
27461432
077755922
1204852595
2758552595
096955135
1234651169
01458231928275355
14441231928273962
0106541427
1289340581
050471
1805455
050471
1805455
0106541427
1289340581
077755922
1204852595
2758552595
01458231928275355
14441231928273962
0106541427
1289340581
01732130
14851898
214481854
357471854
Stop Event
node limit
node limit
node limit
node limit
node limit
node limit
node limit
node limit
node limit
node limit
node limit
node limit
node limit
Compiler

Compiled 1164 to 677 computations (41.8% saved)

end0.0ms (0%)

preprocess105.0ms (0.6%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 1128 to 846 computations (25% saved)

Profiling

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