Details

Time bar (total: 1.6min)

analyze2.0s (2.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%3%97%0
0%3%97%1
0%3%97%2
0%3%97%3
0%3%97%4
0%3%97%5
0%1.5%98.5%6
0%1.5%98.5%7
0%1.5%98.5%8
0%1.5%98.5%9
0%1.5%98.5%10
0.6%0.9%98.5%11
0.6%0.9%98.5%12
0.6%0.9%98.5%13
0.6%0.9%98.5%14
Compiler

Compiled 69 to 51 computations (26.1% saved)

sample2.7s (2.9%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results
2.6s8256×body128valid
39.0ms110×body128invalid
Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify24.0ms (0%)

Algorithm
egg-herbie
Rules
696×fma-def_binary32
512×exp-sum_binary32
492×fma-neg_binary32
429×exp-diff_binary32
212×times-frac_binary32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02235
15333
214731
358429
4286329
Stop Event
node limit
Counts
1 → 2

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.1b
(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)))))
0.1b
(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
Compiler

Compiled 160 to 112 computations (30% saved)

localize70.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
0.1b
(+.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))))
6.9b
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
7.1b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series300.0ms (0.3%)

Counts
4 → 84
Calls

4 calls:

221.0ms
(+.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))))
54.0ms
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
13.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
12.0ms
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

rewrite55.0ms (0.1%)

Algorithm
batch-egg-rewrite
Rules
245×add-sqr-sqrt_binary32
235×log1p-expm1-u_binary32
235×expm1-log1p-u_binary32
234×add-cbrt-cube_binary32
228×add-log-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02157
148957
Stop Event
node limit
Counts
4 → 96
Calls

4 calls:

51.0ms
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
51.0ms
(+.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))))
51.0ms
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
51.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

simplify59.0ms (0.1%)

Algorithm
egg-herbie
Rules
745×sub-neg_binary32
474×fma-def_binary32
441×+-commutative_binary32
389×fma-neg_binary32
263×associate--r+_binary32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0571955
11651949
24801575
316631573
438131569
Stop Event
node limit
Counts
180 → 118

prune147.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1162118
Fresh101
Picked101
Done000
Total1182120
Error
0.0b
Counts
120 → 2
Alt Table
StatusErrorProgram
0.0b
(exp.f32 (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))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
0.1b
(exp.f32 (fma.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))) (log.f32 (/.f32 1/2 v))))
Compiler

Compiled 3674 to 1921 computations (47.7% saved)

localize66.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))
0.3b
(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))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
0.6b
(pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) 2)
3.2b
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)

series47.3s (50.5%)

Counts
4 → 232
Calls

4 calls:

46.1s
(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))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
752.0ms
(pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) 2)
444.0ms
(cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))
27.0ms
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)

rewrite32.0ms (0%)

Algorithm
batch-egg-rewrite
Rules
242×add-sqr-sqrt_binary32
232×log1p-expm1-u_binary32
232×expm1-log1p-u_binary32
231×add-cbrt-cube_binary32
226×add-log-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02279
149879
Stop Event
node limit
Counts
4 → 72
Calls

4 calls:

31.0ms
(cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))
31.0ms
(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))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
31.0ms
(pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) 2)
31.0ms
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)

simplify194.0ms (0.2%)

Algorithm
egg-herbie
Rules
373×*-commutative_binary32
292×+-commutative_binary32
221×fma-def_binary32
200×associate-+r+_binary32
193×associate-/r*_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0111820366
1470820282
Stop Event
node limit
Counts
304 → 305

prune681.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New4391440
Fresh101
Picked011
Done000
Total4402442
Error
0.0b
Counts
442 → 2
Alt Table
StatusErrorProgram
0.0b
(exp.f32 (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))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
0.1b
(exp.f32 (fma.f32 (expm1.f32 (log1p.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)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
Compiler

Compiled 40055 to 22442 computations (44% saved)

localize80.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f32 (expm1.f32 (log1p.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)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
0.6b
(pow.f32 (cbrt.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) 2)
2.6b
(expm1.f32 (log1p.f32 (pow.f32 (cbrt.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) 2)))
3.2b
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v)

series38.2s (40.7%)

Counts
3 → 180
Calls

3 calls:

36.9s
(fma.f32 (expm1.f32 (log1p.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)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
627.0ms
(expm1.f32 (log1p.f32 (pow.f32 (cbrt.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) 2)))
622.0ms
(pow.f32 (cbrt.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) 2)

rewrite28.0ms (0%)

Algorithm
batch-egg-rewrite
Rules
262×expm1-log1p-u_binary32
261×log1p-expm1-u_binary32
258×add-cbrt-cube_binary32
252×add-log-exp_binary32
251×add-exp-log_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02769
159463
Stop Event
node limit
Counts
3 → 45
Calls

3 calls:

27.0ms
(fma.f32 (expm1.f32 (log1p.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)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
27.0ms
(pow.f32 (cbrt.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) 2)
27.0ms
(expm1.f32 (log1p.f32 (pow.f32 (cbrt.f32 (/.f32 (-.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) 2)))

simplify198.0ms (0.2%)

Algorithm
egg-herbie
Rules
768×fma-def_binary32
301×*-commutative_binary32
215×+-commutative_binary32
186×sub-neg_binary32
151×sqr-pow_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
088824008
1358922868
Stop Event
node limit
Counts
225 → 181

prune347.0ms (0.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New2070207
Fresh000
Picked011
Done011
Total2072209
Error
0.0b
Counts
209 → 2
Alt Table
StatusErrorProgram
0.0b
(exp.f32 (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))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
0.1b
(exp.f32 (fma.f32 (expm1.f32 (log1p.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)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
Compiler

Compiled 19606 to 11787 computations (39.9% saved)

regimes1.1s (1.1%)

Accuracy

Total 0.0b remaining (6.7%)

Threshold costs 0.0b (6.7%)

Counts
117 → 1
Compiler

Compiled 37146 to 27030 computations (27.2% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary32
sub-neg_binary32
*-commutative_binary32
neg-sub0_binary32
neg-mul-1_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02957
14357
26257
37257
47857
57957
Stop Event
saturated

end89.0ms (0.1%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 338 to 228 computations (32.5% saved)

Profiling

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