Details

Time bar (total: 5.9s)

analyze5.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
74.9%25%0.1%3
87.4%12.5%0.1%4
93.7%6.2%0.1%5
96.8%3.1%0.1%6
98.3%1.6%0.1%7
99.1%0.8%0.1%8
99.5%0.4%0.1%9
99.7%0.2%0.1%10
99.8%0.1%0.1%11
99.9%0%0.1%12
99.9%0%0.1%13
99.9%0%0.1%14
Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.2s (21.1%)

Symmetry

(sort re im)

Results
1.2s8256×body128valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
hypot-def_binary64
fma-def_binary64
+-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01111
11411
21611
31611

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.6b
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
Compiler

Compiled 39 to 29 computations (25.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.6b
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

series33.0ms (0.6%)

Counts
1 → 24
Calls

1 calls:

33.0ms
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

rewrite5.0ms (0.1%)

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 10))

simplify89.0ms (1.5%)

Algorithm
egg-herbie
Rules
556×associate-/l/_binary64
403×associate-/r/_binary64
315×times-frac_binary64
236×associate-/l*_binary64
233×sub-neg_binary64
Counts
62 → 71
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01341669
13311611
28521567
328131547
448951547
550331547

prune62.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New581371
Fresh000
Picked101
Done000
Total591372
Error
0.0b
Counts
72 → 13
Alt Table
StatusErrorProgram
0.7b
(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
32.4b
(*.f64 -1 (/.f64 (log.f64 (/.f64 1 im)) (log.f64 10)))
17.1b
(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 10) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
17.4b
(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
1.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 10))))
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))) (log.f64 10)))
0.6b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
17.0b
(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
0.7b
(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 10) (log.f64 10)) (log.f64 10))))
1.2b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
1.2b
(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 10) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
16.8b
(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
Compiler

Compiled 1988 to 1321 computations (33.6% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
0.4b
(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

series72.0ms (1.2%)

Counts
2 → 48
Calls

2 calls:

38.0ms
(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))
34.0ms
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))

rewrite38.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
99×times-frac_binary64
96×add-sqr-sqrt_binary64
59×sqrt-prod_binary64
56×*-un-lft-identity_binary64
50×add-cube-cbrt_binary64
Counts
2 → 151
Calls

2 calls:

19.0ms
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
4.0ms
(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

simplify225.0ms (3.8%)

Algorithm
egg-herbie
Rules
605×fma-def_binary64
563×associate-/r*_binary64
405×fma-neg_binary64
308×associate-/l/_binary64
218×cancel-sign-sub-inv_binary64
Counts
199 → 236
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02655977
17315300
221855063
345895035
449925035
549865035
649605035

prune331.0ms (5.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2315236
Fresh6612
Picked101
Done000
Total23811249
Error
0.0b
Counts
249 → 11
Alt Table
StatusErrorProgram
0.7b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
1.3b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
0.7b
(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
0.6b
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10)))
17.1b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
1.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 10))))
17.0b
(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
17.1b
(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 10) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
1.2b
(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 10) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
Compiler

Compiled 6766 to 5058 computations (25.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
1.0b
(/.f64 1 (log.f64 10))
3.9b
(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))

series384.0ms (6.5%)

Counts
4 → 72
Calls

4 calls:

147.0ms
(log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))))
135.0ms
(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
100.0ms
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
0.0ms
(/.f64 1 (log.f64 10))

rewrite62.0ms (1%)

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt_binary64
49×times-frac_binary64
46×*-un-lft-identity_binary64
44×add-cube-cbrt_binary64
30×sqrt-prod_binary64
Counts
4 → 159
Calls

4 calls:

9.0ms
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
4.0ms
(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
4.0ms
(/.f64 1 (log.f64 10))
2.0ms
(log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))))

simplify286.0ms (4.8%)

Algorithm
egg-herbie
Rules
376×associate-*r*_binary64
343×fma-def_binary64
323×associate-*l*_binary64
316×fma-neg_binary64
249×associate-/l*_binary64
Counts
231 → 330
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
04618758
113888271
247918090
347007998
449227994
550337994

prune440.0ms (7.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3282330
Fresh5510
Picked011
Done000
Total3338341
Error
0b
Counts
341 → 8
Alt Table
StatusErrorProgram
0.7b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
1.3b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
1.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 10))))
17.1b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (log.f64 (hypot.f64 re im))))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (log.f64 (hypot.f64 re im))))))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
0.2b
(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
1.2b
(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 10) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
Compiler

Compiled 12151 to 10154 computations (16.4% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))
1.0b
(/.f64 1 (log.f64 10))
4.4b
(pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))))

series137.0ms (2.3%)

Counts
2 → 48
Calls

2 calls:

76.0ms
(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))
60.0ms
(pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))))

rewrite42.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
217×times-frac_binary64
188×sqrt-prod_binary64
137×pow-unpow_binary64
107×*-un-lft-identity_binary64
107×add-sqr-sqrt_binary64
Counts
2 → 174
Calls

2 calls:

11.0ms
(pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))))
2.0ms
(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))

simplify176.0ms (3%)

Algorithm
egg-herbie
Rules
336×times-frac_binary64
293×associate-/r*_binary64
283×associate-/l*_binary64
241×fma-neg_binary64
189×sub-neg_binary64
Counts
222 → 249
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03677123
112047011
245817009
350487009

prune331.0ms (5.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2832285
Fresh336
Picked011
Done011
Total2867293
Error
0b
Counts
293 → 7
Alt Table
StatusErrorProgram
16.9b
(*.f64 (sqrt.f64 (log.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))) (sqrt.f64 (log.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))))
17.1b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (log.f64 (hypot.f64 re im))))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (log.f64 (hypot.f64 re im))))))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
0.4b
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))))))) (log.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))))
0.2b
(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
1.2b
(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 10) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
Compiler

Compiled 9583 to 7991 computations (16.6% saved)

regimes1.7s (28.9%)

Accuracy

Total 0.1b remaining (88.3%)

Threshold costs 0.1b (88.3%)

Counts
169 → 1
Compiler

Compiled 29690 to 24411 computations (17.8% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
11626
21526

end174.0ms (2.9%)

Remove

(sort re im)

Compiler

Compiled 261 to 211 computations (19.2% saved)

Profiling

Loading profile data...