Details

Time bar (total: 6.4s)

analyze671.0ms (10.4%)

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)

sample2.0s (30.7%)

Results
1.7s8256×body128valid
192.0ms1012×body128invalid
Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify133.0ms (2.1%)

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 (0.1%)

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
0.3b
(/.f64 (atan2.f64 im re) (log.f64 base))
30.5b
(/.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 (0.1%)

Local error

Found 1 expressions with local error:

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

series366.0ms (5.7%)

Counts
1 → 8
Calls

1 calls:

366.0ms
(/.f64 (atan2.f64 im re) (log.f64 base))

rewrite4.0ms (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:

2.0ms
(/.f64 (atan2.f64 im re) (log.f64 base))

simplify88.0ms (1.4%)

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

prune41.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New221335
Fresh011
Picked101
Done000
Total231437
Error
0.1b
Counts
37 → 14
Alt Table
StatusErrorProgram
1.2b
(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
8.7b
(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))))
0.4b
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
16.3b
(log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
0.7b
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
31.6b
(exp.f64 (log.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))))
0.3b
(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
1.8b
(*.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)))
31.0b
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
8.7b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
1.5b
(*.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))))
30.5b
(/.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 991 to 390 computations (60.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series741.0ms (11.5%)

Counts
2 → 72
Calls

2 calls:

377.0ms
(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
364.0ms
(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))

rewrite2.0ms (0%)

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

2 calls:

0.0ms
(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))
0.0ms
(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))

simplify70.0ms (1.1%)

Algorithm
egg-herbie
Rules
792×div-sub_binary64
412×distribute-rgt-in_binary64
350×distribute-lft-in_binary64
288×fma-def_binary64
269×associate-+l+_binary64
Counts
94 → 35
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0441035
165993
2125984
3251984
4622984
53635984
65403984

prune64.0ms (1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New65570
Fresh21113
Picked011
Done000
Total671784
Error
0.1b
Counts
84 → 17
Alt Table
StatusErrorProgram
8.7b
(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))
31.0b
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
8.7b
(log1p.f64 (cbrt.f64 (*.f64 (*.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
8.7b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
31.6b
(log1p.f64 (exp.f64 (log.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
1.5b
(*.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))))
0.4b
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
16.3b
(log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
0.7b
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
31.6b
(exp.f64 (log.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))))
0.3b
(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
1.8b
(*.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))))
8.7b
(log1p.f64 (expm1.f64 (cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))))
16.4b
(log1p.f64 (log.f64 (exp.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (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)))
30.5b
(/.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 1577 to 616 computations (60.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series399.0ms (6.2%)

Counts
2 → 44
Calls

2 calls:

366.0ms
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
32.0ms
(/.f64 1 (log.f64 base))

rewrite12.0ms (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 → 78
Calls

2 calls:

6.0ms
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
2.0ms
(/.f64 1 (log.f64 base))

simplify86.0ms (1.3%)

Algorithm
egg-herbie
Rules
460×unsub-neg_binary64
434×div-sub_binary64
409×sub-neg_binary64
377×associate-*r/_binary64
274×associate-/l*_binary64
Counts
122 → 98
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0801290
11451159
23201159
37491159
418261159
538501159
649461159

prune148.0ms (2.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New91798
Fresh51015
Picked101
Done011
Total9718115
Error
0.0b
Counts
115 → 18
Alt Table
StatusErrorProgram
8.7b
(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))
31.0b
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
8.7b
(log1p.f64 (cbrt.f64 (*.f64 (*.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
8.7b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
0.7b
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
31.6b
(exp.f64 (log.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))))
0.3b
(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
1.2b
(*.f64 (atan2.f64 im re) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (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)))))
1.5b
(*.f64 (atan2.f64 im re) (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))) (cbrt.f64 (/.f64 1 (log.f64 base)))))
0.8b
(*.f64 (atan2.f64 im re) (cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))
32.0b
(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
1.5b
(*.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))))
16.4b
(log1p.f64 (log.f64 (exp.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (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)))))
30.5b
(/.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)))
31.8b
(*.f64 (atan2.f64 im re) (*.f64 (sqrt.f64 (/.f64 1 (log.f64 base))) (sqrt.f64 (/.f64 1 (log.f64 base)))))
Compiler

Compiled 2057 to 998 computations (51.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (log.f64 base) (atan2.f64 im re))
0.6b
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

series695.0ms (10.8%)

Counts
2 → 44
Calls

2 calls:

349.0ms
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
345.0ms
(/.f64 (log.f64 base) (atan2.f64 im re))

rewrite18.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
108×times-frac_binary64
60×*-un-lft-identity_binary64
60×add-sqr-sqrt_binary64
60×add-cube-cbrt_binary64
19×associate-/r*_binary64
Counts
2 → 123
Calls

2 calls:

5.0ms
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
2.0ms
(/.f64 (log.f64 base) (atan2.f64 im re))

simplify126.0ms (2%)

Algorithm
egg-herbie
Rules
991×div-sub_binary64
742×fma-neg_binary64
273×times-frac_binary64
234×neg-mul-1_binary64
167×*-commutative_binary64
Counts
167 → 145
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01122859
11932535
24622498
312522498
427212498
549772498
655282498

prune105.0ms (1.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1396145
Fresh8816
Picked011
Done011
Total14716163
Error
0.0b
Counts
163 → 16
Alt Table
StatusErrorProgram
0.8b
(*.f64 (atan2.f64 im re) (cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))
0.8b
(/.f64 1 (*.f64 (log.f64 base) (/.f64 1 (atan2.f64 im re))))
8.7b
(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))
31.0b
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
8.7b
(log1p.f64 (cbrt.f64 (*.f64 (*.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
8.7b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
8.6b
(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3)))
0.7b
(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (/.f64 1 (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))))
0.3b
(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
8.6b
(/.f64 1 (cbrt.f64 (/.f64 (*.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)) (*.f64 (*.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)))))
32.9b
(/.f64 (/.f64 1 (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
1.2b
(*.f64 (atan2.f64 im re) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base))))
13.7b
(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))))
0.7b
(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
31.8b
(*.f64 (atan2.f64 im re) (*.f64 (sqrt.f64 (/.f64 1 (log.f64 base))) (sqrt.f64 (/.f64 1 (log.f64 base)))))
Compiler

Compiled 2750 to 946 computations (65.6% saved)

regimes465.0ms (7.2%)

Accuracy

Total 0.3b remaining (86.7%)

Threshold costs 0.3b (86.7%)

Counts
95 → 1
Compiler

Compiled 8241 to 5336 computations (35.3% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
1913

end185.0ms (2.9%)

Compiler

Compiled 309 to 189 computations (38.8% saved)

Profiling

Loading profile data...