Details

Time bar (total: 8.3s)

analyze222.0ms (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%74.9%25.1%4
0%74.9%25.1%5
0%62.4%37.6%6
12.5%43.7%43.8%7
12.5%43.7%43.8%8
25%28.1%47%9
28.1%20.3%51.6%10
28.1%20.3%51.6%11
34.3%13.3%52.4%12
35.9%9.8%54.4%13
35.9%9.8%54.4%14
Compiler

Compiled 16 to 12 computations (25% saved)

sample263.0ms (3.2%)

Algorithm
intervals
Results
15.0ms256×body128valid
0.0msbody128invalid
0.0msbody128nan
Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify288.0ms (3.5%)

Algorithm
egg-herbie
Rules
990×fma-def_binary64
806×fma-neg_binary64
746×unsub-neg_binary64
520×distribute-rgt-in_binary64
485×distribute-neg-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01216
12916
25916
311516
427014
551414
679214
7119114
8143514
9171614
10234314
11263914
12270414
13325114
14376614
15397714
16412414
17423414
18426014
19408514
20411114
21414914
22418914
23418914
24418914
25487114
26499914
27490714

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.1b
(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
Compiler

Compiled 51 to 31 computations (39.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
0.0b
(-.f64 (log.f64 z) z)
0.2b
(fma.f64 y (-.f64 (log.f64 z) z) y)

series302.0ms (3.7%)

Counts
3 → 69
Calls

3 calls:

213.0ms
(fma.f64 y (-.f64 (log.f64 z) z) y)
85.0ms
(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
5.0ms
(-.f64 (log.f64 z) z)

rewrite7.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
12×prod-diff_binary64
pow1_binary64
Counts
3 → 58
Calls

3 calls:

4.0ms
(-.f64 (log.f64 z) z)
0.0ms
(fma.f64 y (-.f64 (log.f64 z) z) y)
0.0ms
(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))

simplify126.0ms (1.5%)

Algorithm
egg-herbie
Rules
710×fma-neg_binary64
513×fma-def_binary64
353×associate-*l*_binary64
311×exp-prod_binary64
278×associate-*r*_binary64
Counts
127 → 93
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01331706
12741350
28031312
332261312
446611312
549851312
649891312
749051312

prune169.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New87693
Fresh000
Picked011
Done000
Total87794
Error
0.0b
Counts
94 → 7
Alt Table
StatusErrorProgram
0.1b
(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
31.0b
(fma.f64 x 1/2 (*.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))))
32.6b
(*.f64 (sqrt.f64 (fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))) (sqrt.f64 (fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))))
0.8b
(fma.f64 x 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))))
17.8b
(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (*.f64 (*.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)) (-.f64 (log.f64 z) z))) y))
0.1b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z))))
0.1b
(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
Compiler

Compiled 1827 to 690 computations (62.2% saved)

localize239.0ms (2.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z))
0.0b
(log.f64 (/.f64 1 z))
0.1b
(-.f64 y (+.f64 (*.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z)))
0.3b
(*.f64 (log.f64 (/.f64 1 z)) y)

series857.0ms (10.4%)

Counts
4 → 58
Calls

4 calls:

313.0ms
(+.f64 (*.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z))
268.0ms
(*.f64 (log.f64 (/.f64 1 z)) y)
255.0ms
(-.f64 y (+.f64 (*.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z)))
20.0ms
(log.f64 (/.f64 1 z))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
23×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
13×log-prod_binary64
11×add-log-exp_binary64
Counts
4 → 101
Calls

4 calls:

5.0ms
(-.f64 y (+.f64 (*.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z)))
3.0ms
(*.f64 (log.f64 (/.f64 1 z)) y)
3.0ms
(+.f64 (*.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z))
2.0ms
(log.f64 (/.f64 1 z))

simplify92.0ms (1.1%)

Algorithm
egg-herbie
Rules
740×unsub-neg_binary64
301×*-commutative_binary64
295×distribute-rgt-in_binary64
262×cancel-sign-sub-inv_binary64
255×distribute-lft-in_binary64
Counts
159 → 164
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01592406
13691963
213281765
338751758
450461758

prune216.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1595164
Fresh235
Picked011
Done101
Total1629171
Error
0.0b
Counts
171 → 9
Alt Table
StatusErrorProgram
33.3b
(fma.f64 x 1/2 (*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (*.f64 y (-.f64 z (log.f64 z))))) (-.f64 (sqrt.f64 y) (sqrt.f64 (*.f64 y (-.f64 z (log.f64 z)))))))
33.2b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (*.f64 (neg.f64 (log.f64 z)) (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 y z))))
29.3b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (sqrt.f64 (log.f64 (/.f64 1 z))) (*.f64 y (sqrt.f64 (neg.f64 (log.f64 z))))) (*.f64 y z))))
33.2b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (sqrt.f64 (neg.f64 (*.f64 (log.f64 z) y))) (sqrt.f64 (neg.f64 (*.f64 (log.f64 z) y)))) (*.f64 y z))))
0.1b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z))))
0.2b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (cbrt.f64 (pow.f64 (neg.f64 (log.f64 z)) 3)) y) (*.f64 y z))))
31.0b
(fma.f64 x 1/2 (*.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))))
32.6b
(*.f64 (sqrt.f64 (fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))) (sqrt.f64 (fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))))
0.1b
(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
Compiler

Compiled 4227 to 2244 computations (46.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
0.2b
(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
0.5b
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
0.6b
(cbrt.f64 z)

series2.0s (23.9%)

Counts
4 → 60
Calls

4 calls:

1.6s
(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
249.0ms
(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
46.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
30.0ms
(cbrt.f64 z)

rewrite27.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity_binary64
34×pow1_binary64
33×add-sqr-sqrt_binary64
25×associate-+r+_binary64
25×add-cube-cbrt_binary64
Counts
4 → 127
Calls

4 calls:

11.0ms
(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
4.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms
(cbrt.f64 z)
0.0ms
(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)

simplify94.0ms (1.1%)

Algorithm
egg-herbie
Rules
669×distribute-rgt-in_binary64
601×distribute-lft-in_binary64
521×fma-neg_binary64
322×cancel-sign-sub-inv_binary64
273×log-prod_binary64
Counts
187 → 188
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01872646
13901654
213651572
341361562
450981562

prune225.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2222224
Fresh257
Picked101
Done011
Total2258233
Error
0.0b
Counts
233 → 8
Alt Table
StatusErrorProgram
33.3b
(fma.f64 x 1/2 (*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (*.f64 y (-.f64 z (log.f64 z))))) (-.f64 (sqrt.f64 y) (sqrt.f64 (*.f64 y (-.f64 z (log.f64 z)))))))
33.2b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (*.f64 (neg.f64 (log.f64 z)) (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 y z))))
33.2b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (sqrt.f64 (neg.f64 (*.f64 (log.f64 z) y))) (sqrt.f64 (neg.f64 (*.f64 (log.f64 z) y)))) (*.f64 y z))))
0.1b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z))))
0.1b
(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (expm1.f64 (log1p.f64 (pow.f64 z 2/3)))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
31.0b
(fma.f64 x 1/2 (*.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))))
32.6b
(*.f64 (sqrt.f64 (fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))) (sqrt.f64 (fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))))
18.8b
(fma.f64 x 1/2 (+.f64 y (+.f64 (*.f64 y (log.f64 (pow.f64 z 2/3))) (*.f64 y (log.f64 (pow.f64 z 1/3))))))
Compiler

Compiled 5416 to 1900 computations (64.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 y (+.f64 (log.f64 (expm1.f64 (log1p.f64 (pow.f64 z 2/3)))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
0.6b
(cbrt.f64 z)
2.2b
(expm1.f64 (log1p.f64 (pow.f64 z 2/3)))
5.9b
(pow.f64 z 2/3)

series1.3s (15.5%)

Counts
3 → 48
Calls

3 calls:

1.2s
(fma.f64 y (+.f64 (log.f64 (expm1.f64 (log1p.f64 (pow.f64 z 2/3)))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
23.0ms
(pow.f64 z 2/3)
23.0ms
(expm1.f64 (log1p.f64 (pow.f64 z 2/3)))

rewrite3.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-exp-log_binary64
pow1_binary64
Counts
3 → 40
Calls

3 calls:

1.0ms
(pow.f64 z 2/3)
0.0ms
(fma.f64 y (+.f64 (log.f64 (expm1.f64 (log1p.f64 (pow.f64 z 2/3)))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
0.0ms
(expm1.f64 (log1p.f64 (pow.f64 z 2/3)))

simplify98.0ms (1.2%)

Algorithm
egg-herbie
Rules
399×exp-sum_binary64
388×cancel-sign-sub-inv_binary64
338×exp-prod_binary64
330×fma-neg_binary64
275×fma-def_binary64
Counts
88 → 66
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01101190
1239886
2633781
32088698
43944674
54963674
64899674

prune93.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New84084
Fresh066
Picked011
Done011
Total84892
Error
0.0b
Counts
92 → 8
Alt Table
StatusErrorProgram
33.3b
(fma.f64 x 1/2 (*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (*.f64 y (-.f64 z (log.f64 z))))) (-.f64 (sqrt.f64 y) (sqrt.f64 (*.f64 y (-.f64 z (log.f64 z)))))))
33.2b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (*.f64 (neg.f64 (log.f64 z)) (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 y z))))
33.2b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (sqrt.f64 (neg.f64 (*.f64 (log.f64 z) y))) (sqrt.f64 (neg.f64 (*.f64 (log.f64 z) y)))) (*.f64 y z))))
0.1b
(fma.f64 x 1/2 (-.f64 y (+.f64 (*.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z))))
0.1b
(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (expm1.f64 (log1p.f64 (pow.f64 z 2/3)))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
31.0b
(fma.f64 x 1/2 (*.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))))
32.6b
(*.f64 (sqrt.f64 (fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))) (sqrt.f64 (fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))))
18.8b
(fma.f64 x 1/2 (+.f64 y (+.f64 (*.f64 y (log.f64 (pow.f64 z 2/3))) (*.f64 y (log.f64 (pow.f64 z 1/3))))))
Compiler

Compiled 2003 to 1127 computations (43.7% saved)

regimes715.0ms (8.6%)

Accuracy

Total 0.1b remaining (80.1%)

Threshold costs 0.1b (80.1%)

Counts
97 → 1
Compiler

Compiled 12693 to 7941 computations (37.4% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01221
12221
23221
33821
44221
54321
64321

end1.0ms (0%)

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample913.0ms (11%)

Algorithm
intervals
Results
489.0ms8000×body128valid
17.0ms300×body128invalid
3.0ms73×body128nan
Compiler

Compiled 218 to 130 computations (40.4% saved)

Profiling

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