Details

Time bar (total: 10.1s)

analyze1.2s (12.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
23.4%51.5%25.1%7
24.2%50.7%25.1%8
24.6%50.3%25.1%9
36.9%25.5%37.6%10
37.2%25.3%37.6%11
37.3%25.1%37.6%12
43.5%12.7%43.8%13
43.6%12.6%43.8%14
Compiler

Compiled 32 to 21 computations (34.4% saved)

sample93.0ms (0.9%)

Algorithm
intervals
Results
58.0ms256×body128valid
10.0ms36×body128nan
Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify138.0ms (1.4%)

Algorithm
egg-herbie
Rules
1042×fma-def_binary64
693×fma-neg_binary64
662×cube-prod_binary64
522×pow-sqr_binary64
453×associate-/l*_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01920
13519
25712
3809
4899
52169
64869
79789
812969
919969
1022879
1133119
1243679
1346449
1447219
1549869
1648269

prune9.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.3b
(/.f64 (atan2.f64 im re) (log.f64 base))
30.9b
(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))
Compiler

Compiled 117 to 73 computations (37.6% saved)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (atan2.f64 im re) (log.f64 base))

series788.0ms (7.8%)

Counts
1 → 8
Calls

1 calls:

788.0ms
(/.f64 (atan2.f64 im re) (log.f64 base))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
pow1_binary64
Counts
1 → 33
Calls

1 calls:

7.0ms
(/.f64 (atan2.f64 im re) (log.f64 base))

simplify135.0ms (1.3%)

Algorithm
egg-herbie
Rules
763×fma-neg_binary64
574×neg-mul-1_binary64
543×neg-sub0_binary64
429×sub-neg_binary64
336×div-sub_binary64
Counts
41 → 35
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
065663
1108615
2213585
3384585
41312585
52948585
63524585
74593585
84969585

prune67.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New26935
Fresh011
Picked011
Done000
Total261137
Error
0.0b
Counts
37 → 11
Alt Table
StatusErrorProgram
0.3b
(/.f64 (atan2.f64 im re) (log.f64 base))
1.8b
(/.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))
8.5b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (atan2.f64 im re) (log.f64 base))) (/.f64 (atan2.f64 im re) (log.f64 base))))
32.6b
(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
1.2b
(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
0.3b
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
0.8b
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
32.6b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
1.2b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
30.9b
(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))
31.2b
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
Compiler

Compiled 836 to 320 computations (61.7% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (log.f64 base))
0.3b
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))

series798.0ms (7.9%)

Counts
2 → 44
Calls

2 calls:

730.0ms
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
68.0ms
(/.f64 1 (log.f64 base))

rewrite29.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt_binary64
26×times-frac_binary64
21×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
16×associate-*r*_binary64
Counts
2 → 78
Calls

2 calls:

12.0ms
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
5.0ms
(/.f64 1 (log.f64 base))

simplify147.0ms (1.5%)

Algorithm
egg-herbie
Rules
460×unsub-neg_binary64
434×div-sub_binary64
409×sub-neg_binary64
351×associate-*r/_binary64
251×times-frac_binary64
Counts
122 → 97
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0801290
11451159
23201159
37491159
418281159
538501159
649461159

prune145.0ms (1.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New93497
Fresh189
Picked011
Done011
Total9414108
Error
0.0b
Counts
108 → 14
Alt Table
StatusErrorProgram
0.3b
(/.f64 (atan2.f64 im re) (log.f64 base))
1.8b
(/.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))
0.3b
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
1.2b
(*.f64 (atan2.f64 im re) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 1 (cbrt.f64 (log.f64 base)))))
32.6b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
0.7b
(*.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
30.9b
(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))
0.7b
(*.f64 (atan2.f64 im re) (cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))
32.6b
(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
1.2b
(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
0.8b
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
1.2b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
32.7b
(*.f64 (*.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
31.2b
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
Compiler

Compiled 1837 to 873 computations (52.5% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))
0.3b
(*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))
0.5b
(*.f64 (log.f64 base) (log.f64 base))
0.7b
(cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))

series346.0ms (3.4%)

Counts
4 → 48
Calls

4 calls:

143.0ms
(/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))
103.0ms
(cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
58.0ms
(*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))
42.0ms
(*.f64 (log.f64 base) (log.f64 base))

rewrite82.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
125×add-exp-log_binary64
91×prod-exp_binary64
50×add-cbrt-cube_binary64
39×1-exp_binary64
37×pow1_binary64
Counts
4 → 149
Calls

4 calls:

21.0ms
(/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))
17.0ms
(cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
10.0ms
(*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))
8.0ms
(*.f64 (log.f64 base) (log.f64 base))

simplify241.0ms (2.4%)

Algorithm
egg-herbie
Rules
734×times-frac_binary64
514×div-sub_binary64
409×fma-neg_binary64
336×distribute-rgt-in_binary64
309×log-prod_binary64
Counts
197 → 186
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01262108
12131793
26401721
323851646
436061522
546651522
649851522
748831522

prune308.0ms (3.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1824186
Fresh3811
Picked101
Done112
Total18713200
Error
0b
Counts
200 → 13
Alt Table
StatusErrorProgram
0.3b
(/.f64 (atan2.f64 im re) (log.f64 base))
1.8b
(/.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))
1.0b
(*.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (expm1.f64 (log1p.f64 (pow.f64 (log.f64 base) 2))) (log.f64 base)))))
0.8b
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
0.8b
(*.f64 (atan2.f64 im re) (cbrt.f64 (cbrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))) (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))) (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))))
1.2b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
32.6b
(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
1.2b
(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
1.2b
(*.f64 (atan2.f64 im re) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 1 (cbrt.f64 (log.f64 base)))))
32.6b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
30.9b
(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))
1.2b
(*.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))) (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))) (cbrt.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))))
0.6b
(*.f64 (atan2.f64 im re) (/.f64 (cbrt.f64 (*.f64 (*.f64 1 1) 1)) (cbrt.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
Compiler

Compiled 4928 to 2487 computations (49.5% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (atan2.f64 im re) (/.f64 (cbrt.f64 (*.f64 (*.f64 1 1) 1)) (cbrt.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
0.3b
(*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))
0.5b
(*.f64 (log.f64 base) (log.f64 base))
0.5b
(cbrt.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))

series799.0ms (7.9%)

Counts
2 → 48
Calls

2 calls:

760.0ms
(*.f64 (atan2.f64 im re) (/.f64 (cbrt.f64 (*.f64 (*.f64 1 1) 1)) (cbrt.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
38.0ms
(cbrt.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))

rewrite32.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
20×associate-*r*_binary64
17×times-frac_binary64
17×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
Counts
2 → 53
Calls

2 calls:

16.0ms
(*.f64 (atan2.f64 im re) (/.f64 (cbrt.f64 (*.f64 (*.f64 1 1) 1)) (cbrt.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
7.0ms
(cbrt.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))

simplify144.0ms (1.4%)

Algorithm
egg-herbie
Rules
696×div-sub_binary64
531×sub-neg_binary64
322×associate-/l*_binary64
313×fma-def_binary64
301×fma-neg_binary64
Counts
101 → 96
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0801619
11521156
2374931
3591927
42266927
53974927
65184927

prune317.0ms (3.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1823185
Fresh5611
Picked011
Done011
Total18711198
Error
0b
Counts
198 → 11
Alt Table
StatusErrorProgram
1.0b
(*.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (expm1.f64 (log1p.f64 (pow.f64 (log.f64 base) 2))) (log.f64 base)))))
0.8b
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
0.9b
(*.f64 (atan2.f64 im re) (/.f64 (cbrt.f64 (*.f64 (*.f64 1 1) 1)) (cbrt.f64 (*.f64 (expm1.f64 (log1p.f64 (pow.f64 (log.f64 base) 2))) (log.f64 base)))))
1.2b
(*.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))) (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))) (cbrt.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))))
32.6b
(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
1.2b
(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
0.8b
(*.f64 (/.f64 (atan2.f64 im re) (cbrt.f64 (*.f64 (log.f64 base) (log.f64 base)))) (/.f64 (cbrt.f64 1) (cbrt.f64 (log.f64 base))))
0.3b
(/.f64 (atan2.f64 im re) (log.f64 base))
0.8b
(*.f64 (atan2.f64 im re) (cbrt.f64 (cbrt.f64 (*.f64 (*.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))) (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))) (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))))
0.6b
(*.f64 (atan2.f64 im re) (/.f64 (cbrt.f64 (*.f64 (*.f64 1 1) 1)) (cbrt.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
0.9b
(*.f64 (atan2.f64 im re) (/.f64 (cbrt.f64 (*.f64 (*.f64 1 1) 1)) (cbrt.f64 (*.f64 (exp.f64 (log.f64 (*.f64 (log.f64 base) (log.f64 base)))) (log.f64 base)))))
Compiler

Compiled 4928 to 2330 computations (52.7% saved)

regimes1.1s (11.1%)

Accuracy

Total 0.3b remaining (83.9%)

Threshold costs 0.3b (83.9%)

Counts
110 → 1
Compiler

Compiled 11041 to 7771 computations (29.6% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
179

end1.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample3.0s (30%)

Algorithm
intervals
Results
1.9s8000×body128valid
224.0ms1027×body128nan
Compiler

Compiled 320 to 208 computations (35% saved)

Profiling

Loading profile data...