Details

Time bar (total: 12.3s)

analyze108.0ms (0.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%0.6%99.4%0
0%0.6%99.4%1
0%0.6%99.4%2
0.3%0.3%99.4%3
0.3%0.3%99.4%4
0.5%0.2%99.4%5
0.5%0.2%99.4%6
0.6%0.1%99.4%7
0.6%0.1%99.4%8
0.6%0%99.4%9
0.6%0%99.4%10
0.6%0%99.4%11
0.6%0%99.4%12
0.6%0%99.4%13
0.6%0%99.4%14
Compiler

Compiled 41 to 27 computations (34.1% saved)

sample2.2s (17.6%)

Results
2.1s8256×body128valid
Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify71.0ms (0.6%)

Algorithm
egg-herbie
Rules
608×associate-/l*_binary32
462×associate-*l*_binary32
382×associate-*l/_binary32
363×associate-*r*_binary32
360×distribute-lft-in_binary32
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01433
14531
216031
366131
4279131
5486631
6497831

prune8.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.6b
(/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
0.5b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
Compiler

Compiled 145 to 87 computations (40% saved)

localize66.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(log.f32 (*.f32 alpha alpha))
0.2b
(*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta)
0.3b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.4b
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))

series238.0ms (1.9%)

Counts
4 → 72
Calls

4 calls:

141.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
43.0ms
(log.f32 (*.f32 alpha alpha))
29.0ms
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
24.0ms
(*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta)

rewrite55.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
24×pow1_binary32
20×add-exp-log_binary32
17×add-sqr-sqrt_binary32
17×add-cbrt-cube_binary32
13×*-un-lft-identity_binary32
Counts
4 → 107
Calls

4 calls:

22.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
11.0ms
(*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta)
9.0ms
(*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))
2.0ms
(log.f32 (*.f32 alpha alpha))

simplify107.0ms (0.9%)

Algorithm
egg-herbie
Rules
570×associate-*l*_binary32
566×times-frac_binary32
530×associate-/r*_binary32
299×associate-/l*_binary32
181×fma-def_binary32
Counts
179 → 215
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04055044
112374476
253534476

prune280.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2078215
Fresh101
Picked101
Done000
Total2098217
Error
0.0b
Counts
217 → 8
Alt Table
StatusErrorProgram
0.7b
(*.f32 (sqrt.f32 (/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))) (sqrt.f32 (/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))))
0.4b
(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
0.5b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.6b
(-.f32 (/.f32 (*.f32 alpha alpha) (*.f32 (*.f32 2 (*.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
0.6b
(*.f32 (/.f32 (+.f32 alpha 1) (*.f32 2 (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
0.6b
(/.f32 (+.f32 alpha 1) (/.f32 (*.f32 2 (*.f32 (PI.f32) (log.f32 alpha))) (/.f32 (+.f32 alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
0.7b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (*.f32 (*.f32 2 (log.f32 alpha)) (cbrt.f32 (PI.f32)))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.7b
(/.f32 (*.f32 (cbrt.f32 (-.f32 (*.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (*.f32 alpha alpha) 1))) (/.f32 (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))) (cbrt.f32 (-.f32 (*.f32 alpha alpha) 1))))
Compiler

Compiled 8537 to 4685 computations (45.1% saved)

localize108.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))
0.7b
(pow.f32 (fma.f32 alpha alpha -1) 3)
0.8b
(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
1.0b
(pow.f32 (PI.f32) 3)

series2.2s (17.9%)

Counts
4 → 48
Calls

4 calls:

2.2s
(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))
35.0ms
(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
5.0ms
(pow.f32 (fma.f32 alpha alpha -1) 3)
0.0ms
(pow.f32 (PI.f32) 3)

rewrite114.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
359×add-exp-log_binary32
253×prod-exp_binary32
173×pow-exp_binary32
145×pow-to-exp_binary32
120×div-exp_binary32
Counts
4 → 234
Calls

4 calls:

29.0ms
(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))
10.0ms
(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
3.0ms
(pow.f32 (fma.f32 alpha alpha -1) 3)
3.0ms
(pow.f32 (PI.f32) 3)

simplify756.0ms (6.2%)

Algorithm
egg-herbie
Rules
365×*-commutative_binary32
319×+-commutative_binary32
302×fma-def_binary32
271×associate-+r+_binary32
251×associate-/r*_binary32
Counts
282 → 231
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0122623961
1424823692
2499023692
3495523692

prune1.5s (12.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2292231
Fresh437
Picked011
Done000
Total2336239
Error
0b
Counts
239 → 6
Alt Table
StatusErrorProgram
0.6b
(*.f32 (/.f32 (+.f32 alpha 1) (*.f32 2 (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
0.7b
(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (*.f32 (pow.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) 3) (pow.f32 (cbrt.f32 (PI.f32)) 3)) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
0.4b
(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
0.5b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.4b
(cbrt.f32 (/.f32 (log1p.f32 (expm1.f32 (pow.f32 (fma.f32 alpha alpha -1) 3))) (*.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
0.7b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (*.f32 (*.f32 2 (log.f32 alpha)) (cbrt.f32 (PI.f32)))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
Compiler

Compiled 25938 to 20187 computations (22.2% saved)

localize166.0ms (1.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(log1p.f32 (expm1.f32 (pow.f32 (fma.f32 alpha alpha -1) 3)))
0.7b
(pow.f32 (fma.f32 alpha alpha -1) 3)
0.8b
(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
1.0b
(pow.f32 (PI.f32) 3)

series9.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

9.0ms
(log1p.f32 (expm1.f32 (pow.f32 (fma.f32 alpha alpha -1) 3)))

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary32
add-sqr-sqrt_binary32
add-cube-cbrt_binary32
add-cbrt-cube_binary32
add-exp-log_binary32
Counts
1 → 11
Calls

1 calls:

1.0ms
(log1p.f32 (expm1.f32 (pow.f32 (fma.f32 alpha alpha -1) 3)))

simplify101.0ms (0.8%)

Algorithm
egg-herbie
Rules
601×unswap-sqr_binary32
538×fma-neg_binary32
500×distribute-rgt-in_binary32
488×distribute-lft-in_binary32
343×exp-prod_binary32
Counts
23 → 30
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
034302
180264
2210250
3725244
42796234
54845234
65160234

prune355.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1310131
Fresh044
Picked011
Done011
Total1316137
Error
0b
Counts
137 → 6
Alt Table
StatusErrorProgram
0.6b
(*.f32 (/.f32 (+.f32 alpha 1) (*.f32 2 (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
0.7b
(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (*.f32 (pow.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) 3) (pow.f32 (cbrt.f32 (PI.f32)) 3)) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
0.4b
(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
0.5b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.4b
(cbrt.f32 (/.f32 (log1p.f32 (expm1.f32 (pow.f32 (fma.f32 alpha alpha -1) 3))) (*.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
0.7b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (*.f32 (*.f32 2 (log.f32 alpha)) (cbrt.f32 (PI.f32)))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
Compiler

Compiled 5065 to 3680 computations (27.3% saved)

localize110.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
0.2b
(*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta)
0.3b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
3.1b
(pow.f32 (*.f32 alpha alpha) (PI.f32))

series454.0ms (3.7%)

Counts
3 → 60
Calls

3 calls:

278.0ms
(pow.f32 (*.f32 alpha alpha) (PI.f32))
155.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
21.0ms
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)

rewrite35.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
16×add-exp-log_binary32
16×pow1_binary32
13×add-cbrt-cube_binary32
*-un-lft-identity_binary32
add-sqr-sqrt_binary32
Counts
3 → 79
Calls

3 calls:

11.0ms
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
10.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
4.0ms
(pow.f32 (*.f32 alpha alpha) (PI.f32))

simplify237.0ms (1.9%)

Algorithm
egg-herbie
Rules
529×associate-*l*_binary32
455×associate-/r*_binary32
438×times-frac_binary32
280×associate-/l*_binary32
184×fma-def_binary32
Counts
139 → 162
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03964747
112104233
249504233
350264233

prune488.0ms (4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New2100210
Fresh033
Picked011
Done022
Total2106216
Error
0b
Counts
216 → 6
Alt Table
StatusErrorProgram
0.6b
(*.f32 (/.f32 (+.f32 alpha 1) (*.f32 2 (*.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
0.7b
(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (*.f32 (pow.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) 3) (pow.f32 (cbrt.f32 (PI.f32)) 3)) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
0.4b
(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
0.5b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.4b
(cbrt.f32 (/.f32 (log1p.f32 (expm1.f32 (pow.f32 (fma.f32 alpha alpha -1) 3))) (*.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
0.7b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (*.f32 (*.f32 2 (log.f32 alpha)) (cbrt.f32 (PI.f32)))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
Compiler

Compiled 8017 to 4349 computations (45.8% saved)

regimes2.2s (18.1%)

Accuracy

Total 0.4b remaining (94.6%)

Threshold costs 0.4b (94.6%)

Counts
192 → 1
Compiler

Compiled 26678 to 17943 computations (32.7% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary32
1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02556
13156
23056

end303.0ms (2.5%)

Compiler

Compiled 268 to 200 computations (25.4% saved)

Profiling

Loading profile data...