Details

Time bar (total: 8.5s)

analyze571.0ms (6.7%)

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)

sample2.4s (28%)

Symmetry

(sort re im)

Results
1.9s8256×body128valid
356.0ms1044×body128invalid
Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify92.0ms (1.1%)

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 (0.1%)

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
31.3b
(/.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)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 re im)
0.3b
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

series626.0ms (7.4%)

Counts
2 → 60
Calls

2 calls:

614.0ms
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
12.0ms
(hypot.f64 re im)

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×times-frac_binary64
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
12×pow1_binary64
Counts
2 → 48
Calls

2 calls:

3.0ms
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
0.0ms
(hypot.f64 re im)

simplify91.0ms (1.1%)

Algorithm
egg-herbie
Rules
787×times-frac_binary64
599×fma-neg_binary64
441×associate-/r*_binary64
410×associate-/l*_binary64
341×fma-def_binary64
Counts
108 → 142
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01942481
14842312
212912236
345832236
449842236

prune112.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1339142
Fresh011
Picked101
Done000
Total13410144
Error
0.0b
Counts
144 → 10
Alt Table
StatusErrorProgram
1.2b
(*.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))))
1.6b
(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
14.7b
(*.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)))
32.8b
(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
14.7b
(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
31.3b
(/.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)))
0.4b
(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
0.4b
(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
0.6b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
Compiler

Compiled 2998 to 1397 computations (53.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 re im)
0.3b
(/.f64 1 (log.f64 base))
0.3b
(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

series593.0ms (7%)

Counts
2 → 44
Calls

2 calls:

559.0ms
(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
34.0ms
(/.f64 1 (log.f64 base))

rewrite15.0ms (0.2%)

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:

9.0ms
(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
2.0ms
(/.f64 1 (log.f64 base))

simplify106.0ms (1.2%)

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

prune135.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1845189
Fresh459
Picked101
Done000
Total18910199
Error
0b
Counts
199 → 10
Alt Table
StatusErrorProgram
1.2b
(*.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
14.7b
(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
0.7b
(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
0.7b
(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
5.4b
(*.f64 (log.f64 (hypot.f64 re im)) (log.f64 (exp.f64 (/.f64 1 (log.f64 base)))))
32.8b
(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
0.4b
(*.f64 (log.f64 (hypot.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 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
0.4b
(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
0.6b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
Compiler

Compiled 3788 to 1937 computations (48.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 im re)
0.3b
(/.f64 1 (log.f64 base))
0.3b
(*.f64 (log.f64 (hypot.f64 im re)) (/.f64 1 (log.f64 base)))

series569.0ms (6.7%)

Counts
2 → 60
Calls

2 calls:

559.0ms
(*.f64 (log.f64 (hypot.f64 im re)) (/.f64 1 (log.f64 base)))
9.0ms
(hypot.f64 im re)

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
16×associate-*r*_binary64
14×times-frac_binary64
12×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
Counts
2 → 52
Calls

2 calls:

6.0ms
(*.f64 (log.f64 (hypot.f64 im re)) (/.f64 1 (log.f64 base)))
0.0ms
(hypot.f64 im re)

simplify92.0ms (1.1%)

Algorithm
egg-herbie
Rules
784×times-frac_binary64
599×fma-neg_binary64
425×associate-/r*_binary64
424×associate-/l*_binary64
344×fma-def_binary64
Counts
112 → 151
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01992403
15132191
213852110
346982110
450992110

prune129.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1891190
Fresh189
Picked011
Done000
Total19010200
Error
0b
Counts
200 → 10
Alt Table
StatusErrorProgram
1.2b
(*.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
14.7b
(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
15.9b
(expm1.f64 (log1p.f64 (*.f64 (log.f64 (hypot.f64 im re)) (/.f64 1 (log.f64 base)))))
0.6b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
0.7b
(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
0.7b
(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
5.4b
(*.f64 (log.f64 (hypot.f64 re im)) (log.f64 (exp.f64 (/.f64 1 (log.f64 base)))))
0.4b
(*.f64 (log.f64 (hypot.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 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
0.4b
(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
Compiler

Compiled 3782 to 1936 computations (48.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 re im)
0.3b
(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
0.4b
(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

series1.1s (13.4%)

Counts
2 → 72
Calls

2 calls:

599.0ms
(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
535.0ms
(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
140×times-frac_binary64
69×*-un-lft-identity_binary64
69×add-sqr-sqrt_binary64
69×add-cube-cbrt_binary64
45×pow1_binary64
Counts
2 → 144
Calls

2 calls:

5.0ms
(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
3.0ms
(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

simplify145.0ms (1.7%)

Algorithm
egg-herbie
Rules
432×fma-neg_binary64
429×times-frac_binary64
347×associate-/r*_binary64
294×associate-/l*_binary64
190×fma-def_binary64
Counts
216 → 240
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03946731
112315978
247495978
350955978

prune212.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2853288
Fresh358
Picked101
Done011
Total2899298
Error
0b
Counts
298 → 9
Alt Table
StatusErrorProgram
0.7b
(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
0.7b
(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
1.2b
(*.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
14.7b
(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
0.6b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
0.4b
(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im)))))
0.7b
(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
18.6b
(/.f64 1 (expm1.f64 (log1p.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
0.4b
(*.f64 (log.f64 (hypot.f64 im re)) (/.f64 1 (log.f64 base)))
Compiler

Compiled 7656 to 3797 computations (50.4% saved)

regimes1.1s (13.4%)

Accuracy

Total 0.3b remaining (85.9%)

Threshold costs 0.3b (85.9%)

Counts
222 → 1
Compiler

Compiled 19006 to 13061 computations (31.3% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01011
11311
21211

end282.0ms (3.3%)

Remove

(sort re im)

Compiler

Compiled 193 to 127 computations (34.2% saved)

Profiling

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