Details

Time bar (total: 11.1s)

analyze2.3s (20.4%)

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)

sample148.0ms (1.3%)

Algorithm
intervals
Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results
32.0ms256×body128valid
14.0ms259×pre128true
0.0msbody128nan
Compiler

Compiled 104 to 78 computations (25% saved)

simplify50.0ms (0.5%)

Algorithm
egg-herbie
Rules
788×fma-neg_binary32
718×fma-def_binary32
560×exp-diff_binary32
512×exp-sum_binary32
448×sub-neg_binary32
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02235
15333
214531
353229
4211929
5443129
6497529

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
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
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)))))
Compiler

Compiled 160 to 112 computations (30% saved)

localize53.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
0.0b
(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
0.0b
(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
0.1b
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

series237.0ms (2.1%)

Counts
4 → 180
Calls

4 calls:

133.0ms
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
51.0ms
(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
41.0ms
(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
11.0ms
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite51.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt_binary32
39×*-un-lft-identity_binary32
35×add-cube-cbrt_binary32
28×exp-sum_binary32
27×prod-diff_binary32
Counts
4 → 123
Calls

4 calls:

19.0ms
(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
12.0ms
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
3.0ms
(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
0.0ms
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

simplify184.0ms (1.7%)

Algorithm
egg-herbie
Rules
392×times-frac_binary32
288×associate-/l*_binary32
278×associate-*r*_binary32
275×associate-+r+_binary32
243×fma-def_binary32
Counts
303 → 237
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
044111185
1120310395
2515610395

prune387.0ms (3.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2325237
Fresh101
Picked101
Done000
Total2345239
Error
0.0b
Counts
239 → 5
Alt Table
StatusErrorProgram
0.1b
(*.f32 (sqrt.f32 (/.f32 1/2 v)) (*.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (/.f32 1 (sqrt.f32 v)) (*.f32 (/.f32 1/2 (sqrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (*.f32 (/.f32 1/2 (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (*.f32 (/.f32 1/2 v) (sqrt.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)))))) (sqrt.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))))))
0.1b
(*.f32 (/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (*.f32 (/.f32 (cbrt.f32 1/2) (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
Compiler

Compiled 11227 to 6484 computations (42.2% saved)

localize81.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(cbrt.f32 v)
0.2b
(/.f32 (cbrt.f32 1/2) (cbrt.f32 v))
0.3b
(/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
0.5b
(*.f32 (cbrt.f32 v) (cbrt.f32 v))

series210.0ms (1.9%)

Counts
4 → 48
Calls

4 calls:

82.0ms
(/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
55.0ms
(/.f32 (cbrt.f32 1/2) (cbrt.f32 v))
41.0ms
(*.f32 (cbrt.f32 v) (cbrt.f32 v))
32.0ms
(cbrt.f32 v)

rewrite26.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
61×cbrt-prod_binary32
49×add-sqr-sqrt_binary32
41×*-un-lft-identity_binary32
41×add-cube-cbrt_binary32
37×times-frac_binary32
Counts
4 → 140
Calls

4 calls:

7.0ms
(/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
6.0ms
(/.f32 (cbrt.f32 1/2) (cbrt.f32 v))
5.0ms
(*.f32 (cbrt.f32 v) (cbrt.f32 v))
1.0ms
(cbrt.f32 v)

simplify127.0ms (1.1%)

Algorithm
egg-herbie
Rules
665×unswap-sqr_binary32
517×associate-/l*_binary32
464×associate-*r*_binary32
325×log-prod_binary32
304×fma-def_binary32
Counts
188 → 202
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01692825
13082303
29582240
329632209
446242209
551442209

prune482.0ms (4.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2353238
Fresh134
Picked101
Done000
Total2376243
Error
0.0b
Counts
243 → 6
Alt Table
StatusErrorProgram
0.1b
(*.f32 (/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (*.f32 (*.f32 (cbrt.f32 (sqrt.f32 v)) (cbrt.f32 (sqrt.f32 v))) (*.f32 (cbrt.f32 (sqrt.f32 v)) (cbrt.f32 (sqrt.f32 v))))) (*.f32 (/.f32 (cbrt.f32 1/2) (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (sqrt.f32 (/.f32 1/2 v)) (*.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
24.5b
(*.f32 (/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (log.f32 (exp.f32 (pow.f32 v 2/3)))) (*.f32 (/.f32 (cbrt.f32 1/2) (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (*.f32 (/.f32 1/2 (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (*.f32 (/.f32 1/2 v) (sqrt.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)))))) (sqrt.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))))))
0.1b
(*.f32 (expm1.f32 (log1p.f32 (/.f32 (pow.f32 (cbrt.f32 1/2) 2) (pow.f32 v 2/3)))) (*.f32 (/.f32 (cbrt.f32 1/2) (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
Compiler

Compiled 9925 to 5609 computations (43.5% saved)

localize89.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f32 (cbrt.f32 1/2) (cbrt.f32 v))
0.3b
(/.f32 (pow.f32 (cbrt.f32 1/2) 2) (pow.f32 v 2/3))
2.7b
(expm1.f32 (log1p.f32 (/.f32 (pow.f32 (cbrt.f32 1/2) 2) (pow.f32 v 2/3))))
3.4b
(pow.f32 v 2/3)

series106.0ms (1%)

Counts
3 → 36
Calls

3 calls:

41.0ms
(/.f32 (pow.f32 (cbrt.f32 1/2) 2) (pow.f32 v 2/3))
40.0ms
(expm1.f32 (log1p.f32 (/.f32 (pow.f32 (cbrt.f32 1/2) 2) (pow.f32 v 2/3))))
25.0ms
(pow.f32 v 2/3)

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
87×unpow-prod-down_binary32
77×times-frac_binary32
53×*-un-lft-identity_binary32
53×add-sqr-sqrt_binary32
53×add-cube-cbrt_binary32
Counts
3 → 147
Calls

3 calls:

6.0ms
(/.f32 (pow.f32 (cbrt.f32 1/2) 2) (pow.f32 v 2/3))
5.0ms
(pow.f32 v 2/3)
0.0ms
(expm1.f32 (log1p.f32 (/.f32 (pow.f32 (cbrt.f32 1/2) 2) (pow.f32 v 2/3))))

simplify150.0ms (1.3%)

Algorithm
egg-herbie
Rules
526×times-frac_binary32
421×fma-def_binary32
396×associate-/l*_binary32
317×associate-/r*_binary32
280×fma-neg_binary32
Counts
183 → 190
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02093505
12803152
27332977
333152900
445122900
549362900

prune658.0ms (5.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2760276
Fresh055
Picked011
Done000
Total2766282
Error
0.0b
Counts
282 → 6
Alt Table
StatusErrorProgram
0.1b
(*.f32 (/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (*.f32 (*.f32 (cbrt.f32 (sqrt.f32 v)) (cbrt.f32 (sqrt.f32 v))) (*.f32 (cbrt.f32 (sqrt.f32 v)) (cbrt.f32 (sqrt.f32 v))))) (*.f32 (/.f32 (cbrt.f32 1/2) (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (sqrt.f32 (/.f32 1/2 v)) (*.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
24.5b
(*.f32 (/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (log.f32 (exp.f32 (pow.f32 v 2/3)))) (*.f32 (/.f32 (cbrt.f32 1/2) (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (*.f32 (/.f32 1/2 (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (*.f32 (/.f32 1/2 v) (sqrt.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)))))) (sqrt.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))))))
0.1b
(*.f32 (expm1.f32 (log1p.f32 (/.f32 (pow.f32 (cbrt.f32 1/2) 2) (pow.f32 v 2/3)))) (*.f32 (/.f32 (cbrt.f32 1/2) (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
Compiler

Compiled 12029 to 8132 computations (32.4% saved)

localize76.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(cbrt.f32 v)
0.3b
(/.f32 1/2 (cbrt.f32 v))
0.3b
(/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
0.5b
(*.f32 (cbrt.f32 v) (cbrt.f32 v))

series130.0ms (1.2%)

Counts
2 → 24
Calls

2 calls:

75.0ms
(/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
55.0ms
(/.f32 1/2 (cbrt.f32 v))

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
21×times-frac_binary32
19×*-un-lft-identity_binary32
19×add-sqr-sqrt_binary32
19×add-cube-cbrt_binary32
15×add-exp-log_binary32
Counts
2 → 78
Calls

2 calls:

5.0ms
(/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
3.0ms
(/.f32 1/2 (cbrt.f32 v))

simplify99.0ms (0.9%)

Algorithm
egg-herbie
Rules
769×fma-neg_binary32
490×times-frac_binary32
395×log-prod_binary32
287×unswap-sqr_binary32
235×associate-/l*_binary32
Counts
102 → 106
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01251298
12081144
23771072
37001072
42157996
52707996
64583996
75180996

prune417.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2172219
Fresh224
Picked101
Done011
Total2205225
Error
0.0b
Counts
225 → 5
Alt Table
StatusErrorProgram
24.5b
(*.f32 (/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (log.f32 (exp.f32 (pow.f32 v 2/3)))) (*.f32 (/.f32 (cbrt.f32 1/2) (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (expm1.f32 (log1p.f32 (pow.f32 (/.f32 1 v) 2/3))) (*.f32 (/.f32 1/2 (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (*.f32 (*.f32 (cbrt.f32 (sqrt.f32 v)) (cbrt.f32 (sqrt.f32 v))) (*.f32 (cbrt.f32 (sqrt.f32 v)) (cbrt.f32 (sqrt.f32 v))))) (*.f32 (/.f32 (cbrt.f32 1/2) (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (/.f32 1 (*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 v)) 5) (cbrt.f32 (cbrt.f32 v)))) (*.f32 (/.f32 1/2 (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
0.1b
(*.f32 (expm1.f32 (log1p.f32 (/.f32 (pow.f32 (cbrt.f32 1/2) 2) (pow.f32 v 2/3)))) (*.f32 (/.f32 (cbrt.f32 1/2) (cbrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
Compiler

Compiled 7517 to 3727 computations (50.4% saved)

regimes2.4s (21.4%)

Accuracy

Total 0.1b remaining (53.5%)

Threshold costs 0.1b (53.5%)

Counts
183 → 1
Compiler

Compiled 64053 to 45176 computations (29.5% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02444
13044
23444
33644
43744
53644

end25.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 170 to 125 computations (26.5% saved)

sample2.6s (23.8%)

Algorithm
intervals
Results
1.1s8000×body128valid
462.0ms8139×pre128true
17.0ms139×body128nan
Compiler

Compiled 306 to 220 computations (28.1% saved)

Profiling

Loading profile data...