Details

Time bar (total: 11.9s)

analyze1.7s (14.3%)

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
0%74.9%25.1%7
0%74.9%25.1%8
0%74.9%25.1%9
0%62.4%37.6%10
0%62.4%37.6%11
0%62.4%37.6%12
0%56.2%43.8%13
0%56.2%43.8%14
Compiler

Compiled 32 to 21 computations (34.4% saved)

sample2.0s (16.9%)

Symmetry

(sort re im)

Results
1.7s8256×body128valid
196.0ms1062×body128invalid
Compiler

Compiled 63 to 41 computations (34.9% saved)

simplify94.0ms (0.8%)

Algorithm
egg-herbie
Rules
666×fma-def_binary64
620×associate-/l/_binary64
557×cube-prod_binary64
533×sqr-pow_binary64
502×pow-sqr_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01922
12821
23421
34514
46211
56511
617611
747911
876911
983911
10123311
11152311
12234111
13345511
14439911
15487411
16487211

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
31.8b
(/.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 base)) (*.f64 (atan2.f64 im re) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))
0.3b
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
Compiler

Compiled 120 to 77 computations (35.8% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series838.0ms (7.1%)

Counts
1 → 36
Calls

1 calls:

838.0ms
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

rewrite5.0ms (0%)

Algorithm
rewrite-expression-head
Rules
16×times-frac_binary64
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
11×pow1_binary64
Counts
1 → 38
Calls

1 calls:

3.0ms
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

simplify89.0ms (0.8%)

Algorithm
egg-herbie
Rules
890×fma-neg_binary64
369×div-sub_binary64
319×times-frac_binary64
242×associate-/l*_binary64
231×associate-/r*_binary64
Counts
74 → 93
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01461913
13451739
28551699
328821699
447101699
555081699

prune75.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New791493
Fresh101
Picked101
Done000
Total811495
Error
0.0b
Counts
95 → 14
Alt Table
StatusErrorProgram
0.4b
(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
17.7b
(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
41.7b
(exp.f64 (-.f64 (log.f64 (log.f64 (hypot.f64 re im))) (log.f64 (log.f64 base))))
1.6b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
30.5b
(*.f64 -1 (/.f64 (log.f64 (/.f64 1 im)) (log.f64 base)))
1.3b
(*.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
30.7b
(neg.f64 (/.f64 (log.f64 (/.f64 -1 re)) (log.f64 base)))
1.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
0.9b
(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
1.8b
(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
32.6b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 base))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 base))))
32.3b
(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
1.3b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
Compiler

Compiled 2370 to 1038 computations (56.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series783.0ms (6.6%)

Counts
2 → 44
Calls

2 calls:

749.0ms
(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
34.0ms
(/.f64 1 (log.f64 base))

rewrite17.0ms (0.1%)

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 → 79
Calls

2 calls:

10.0ms
(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
3.0ms
(/.f64 1 (log.f64 base))

simplify104.0ms (0.9%)

Algorithm
egg-herbie
Rules
453×div-sub_binary64
341×times-frac_binary64
295×associate-/l*_binary64
248×fma-def_binary64
229×sub-neg_binary64
Counts
123 → 141
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01602246
13821983
29841943
334581943
447571943
557511943

prune103.0ms (0.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1392141
Fresh31013
Picked011
Done000
Total14213155
Error
0.0b
Counts
155 → 13
Alt Table
StatusErrorProgram
0.4b
(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
1.3b
(*.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
30.7b
(neg.f64 (/.f64 (log.f64 (/.f64 -1 re)) (log.f64 base)))
1.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
0.8b
(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
0.9b
(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
17.7b
(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
1.8b
(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
1.6b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
32.3b
(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
1.3b
(*.f64 (*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))))) (/.f64 1 (cbrt.f64 (log.f64 base))))
1.3b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
Compiler

Compiled 3065 to 1470 computations (52% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
0.3b
(*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
0.5b
(*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
0.6b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

series2.3s (19.8%)

Counts
3 → 108
Calls

3 calls:

849.0ms
(*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
787.0ms
(*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
709.0ms
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

rewrite63.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
125×times-frac_binary64
101×pow1_binary64
80×*-un-lft-identity_binary64
72×log-pow_binary64
71×add-sqr-sqrt_binary64
Counts
3 → 202
Calls

3 calls:

12.0ms
(*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
12.0ms
(*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
8.0ms
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))

simplify242.0ms (2%)

Algorithm
egg-herbie
Rules
726×times-frac_binary64
554×associate-/r*_binary64
522×associate-/l*_binary64
265×fma-def_binary64
158×*-commutative_binary64
Counts
310 → 374
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
056213385
1182310078
2497810078
3498310078

prune499.0ms (4.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New6494653
Fresh5611
Picked011
Done101
Total65511666
Error
0b
Counts
666 → 11
Alt Table
StatusErrorProgram
0.8b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))))
17.7b
(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
32.3b
(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
0.8b
(/.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3) (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) 2)))
1.3b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
0.6b
(/.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3)) (log.f64 base))
0.8b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) (cbrt.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))) (cbrt.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
0.8b
(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
1.8b
(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
1.3b
(*.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
Compiler

Compiled 25220 to 8375 computations (66.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3)) (log.f64 base))
0.5b
(cbrt.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3))
0.7b
(pow.f64 (log.f64 (hypot.f64 im re)) 3)

series785.0ms (6.6%)

Counts
3 → 84
Calls

3 calls:

685.0ms
(/.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3)) (log.f64 base))
76.0ms
(pow.f64 (log.f64 (hypot.f64 im re)) 3)
23.0ms
(cbrt.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3))

rewrite28.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
84×cbrt-prod_binary64
68×times-frac_binary64
47×*-un-lft-identity_binary64
47×add-sqr-sqrt_binary64
47×add-cube-cbrt_binary64
Counts
3 → 155
Calls

3 calls:

13.0ms
(/.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3)) (log.f64 base))
2.0ms
(pow.f64 (log.f64 (hypot.f64 im re)) 3)
2.0ms
(cbrt.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3))

simplify179.0ms (1.5%)

Algorithm
egg-herbie
Rules
467×fma-neg_binary64
366×unswap-sqr_binary64
323×sub-neg_binary64
237×fma-def_binary64
186×associate-/l*_binary64
Counts
239 → 287
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
04306375
111155812
235645771
348895738
449835738

prune243.0ms (2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2852287
Fresh279
Picked011
Done011
Total28711298
Error
0b
Counts
298 → 11
Alt Table
StatusErrorProgram
0.6b
(/.f64 (cbrt.f64 (cbrt.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3) (pow.f64 (log.f64 (hypot.f64 im re)) 3)) (pow.f64 (log.f64 (hypot.f64 im re)) 3)))) (log.f64 base))
0.8b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) (cbrt.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))) (cbrt.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
0.4b
(/.f64 (cbrt.f64 1) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
32.3b
(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
0.8b
(/.f64 (cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3) (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) 2)))
1.3b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
0.6b
(/.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 im re)) 3)) (log.f64 base))
0.8b
(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
17.7b
(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
1.3b
(*.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
Compiler

Compiled 7221 to 3889 computations (46.1% saved)

regimes1.5s (12.5%)

Accuracy

Total 0.3b remaining (89.4%)

Threshold costs 0.3b (89.4%)

Counts
239 → 1
Compiler

Compiled 27681 to 16496 computations (40.4% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
*-lft-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01011
11311
21211

end153.0ms (1.3%)

Remove

(sort re im)

Compiler

Compiled 293 to 154 computations (47.4% saved)

Profiling

Loading profile data...