Details

Time bar (total: 23.4s)

analyze630.0ms (2.7%)

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)

sample49.0ms (0.2%)

Algorithm
intervals
Results
30.0ms256×body128valid
4.0ms37×body128nan
Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify135.0ms (0.6%)

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

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
0.3b
(/.f64 (atan2.f64 im re) (log.f64 base))
31.6b
(/.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)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite4.0ms (0%)

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:

3.0ms
(/.f64 (atan2.f64 im re) (log.f64 base))

series1.5s (6.2%)

Counts
1 → 8
Calls

1 calls:

1.5s
(/.f64 (atan2.f64 im re) (log.f64 base))

simplify165.0ms (0.7%)

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 → 60
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
065663
1108615
2213585
3384585
41312585
52948585
63524585
74593585
84969585

prune73.0ms (0.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New481260
Fresh011
Picked101
Done000
Total491362
Error
0.0b
Counts
62 → 13
Alt Table
StatusErrorProgram
33.4b
(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
6.7b
(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
0.3b
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
0.9b
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
0.3b
(expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (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))))
37.7b
(*.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
31.6b
(/.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)))
1.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
1.7b
(*.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
31.4b
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
1.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
1.7b
(/.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))
Compiler

Compiled 955 to 374 computations (60.8% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))
0.2b
(expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
0.3b
(/.f64 (atan2.f64 im re) (log.f64 base))

rewrite3.0ms (0%)

Algorithm
rewrite-expression-head
Rules
expm1-log1p-u_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 22
Calls

2 calls:

1.0ms
(log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))
1.0ms
(expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))

series9.1s (39%)

Counts
2 → 72
Calls

2 calls:

4.6s
(expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
4.5s
(log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))

simplify235.0ms (1%)

Algorithm
egg-herbie
Rules
920×fma-def_binary64
384×unsub-neg_binary64
366×times-frac_binary64
320×distribute-rgt-in_binary64
270×distribute-lft-in_binary64
Counts
94 → 177
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0481027
166985
2141985
3393985
41323985
53716985
64462985
74919985
84918985

prune128.0ms (0.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2334237
Fresh11112
Picked101
Done000
Total23515250
Error
0.0b
Counts
250 → 15
Alt Table
StatusErrorProgram
31.4b
(expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
0.3b
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
0.9b
(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))
1.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
33.4b
(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
6.7b
(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
6.8b
(expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))
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))))
37.7b
(*.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
31.6b
(/.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)))
14.9b
(expm1.f64 (log.f64 (+.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))))
1.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
1.7b
(*.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
31.4b
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
1.7b
(/.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))
Compiler

Compiled 1536 to 601 computations (60.9% 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)))

rewrite30.0ms (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 → 78
Calls

2 calls:

16.0ms
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
5.0ms
(/.f64 1 (log.f64 base))

series2.3s (10%)

Counts
2 → 44
Calls

2 calls:

1.9s
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
473.0ms
(/.f64 1 (log.f64 base))

simplify178.0ms (0.8%)

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 → 196
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0801290
11451159
23201159
37491159
418281159
538501159
649461159

prune168.0ms (0.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1915196
Fresh5914
Picked011
Done000
Total19615211
Error
0.0b
Counts
211 → 15
Alt Table
StatusErrorProgram
31.4b
(expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
0.3b
(*.f64 (atan2.f64 im re) (/.f64 1 (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))))
1.2b
(*.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 1 (cbrt.f64 (log.f64 base))))
0.9b
(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))
1.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
6.7b
(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
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)))))
33.6b
(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
6.8b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))
6.8b
(expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))
14.9b
(expm1.f64 (log.f64 (+.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))))
1.7b
(*.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
31.4b
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
0.8b
(*.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
Compiler

Compiled 1873 to 890 computations (52.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (atan2.f64 im re) (cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))
0.4b
(*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))
0.5b
(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base)))
0.6b
(cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base))))

rewrite146.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
295×add-exp-log_binary64
149×prod-exp_binary64
114×div-exp_binary64
86×times-frac_binary64
82×pow1_binary64
Counts
4 → 310
Calls

4 calls:

36.0ms
(*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))
25.0ms
(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base)))
20.0ms
(cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base))))
9.0ms
(*.f64 (atan2.f64 im re) (cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))

series3.0s (12.9%)

Counts
4 → 72
Calls

4 calls:

1.6s
(*.f64 (atan2.f64 im re) (cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))
491.0ms
(*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))
471.0ms
(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base)))
461.0ms
(cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base))))

simplify480.0ms (2.1%)

Algorithm
egg-herbie
Rules
620×unswap-sqr_binary64
496×fma-def_binary64
492×times-frac_binary64
321×log-prod_binary64
288×associate-/l*_binary64
Counts
382 → 705
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02115682
13304021
28133580
322043449
439293353
549633353
649493353

prune592.0ms (2.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New7005705
Fresh5813
Picked101
Done011
Total70614720
Error
0.0b
Counts
720 → 14
Alt Table
StatusErrorProgram
31.4b
(expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
0.3b
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
33.8b
(*.f64 (atan2.f64 im re) (cbrt.f64 (exp.f64 (*.f64 (log.f64 (log.f64 base)) -3))))
0.8b
(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)) -1)))
1.0b
(/.f64 (*.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 1 (log.f64 base)))) (cbrt.f64 (*.f64 (log.f64 base) (log.f64 base))))
1.7b
(*.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
0.9b
(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))
1.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
33.6b
(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
6.8b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (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))))
0.8b
(/.f64 (*.f64 (atan2.f64 im re) (cbrt.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))))) (cbrt.f64 (log.f64 base)))
0.6b
(/.f64 (atan2.f64 im re) (cbrt.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
31.4b
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
Compiler

Compiled 8590 to 4567 computations (46.8% saved)

regimes1.5s (6.5%)

Accuracy

Total 0.3b remaining (86.5%)

Threshold costs 0.3b (86.5%)

Compiler

Compiled 13436 to 9246 computations (31.2% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
179

end1.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample2.8s (12.1%)

Algorithm
intervals
Results
1.8s8000×body128valid
216.0ms1081×body128nan
Compiler

Compiled 303 to 178 computations (41.3% saved)

Profiling

Loading profile data...