Details

Time bar (total: 8.5s)

analyze246.0ms (2.9%)

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)

sample1.4s (15.8%)

Results
1.1s8256×body128valid
43.0ms360×body128invalid
Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify287.0ms (3.4%)

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)

localize9.0ms (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)

series260.0ms (3%)

Counts
3 → 69
Calls

3 calls:

179.0ms
(fma.f64 y (-.f64 (log.f64 z) z) y)
77.0ms
(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
4.0ms
(-.f64 (log.f64 z) z)

rewrite6.0ms (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:

3.0ms
(-.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))

simplify128.0ms (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

prune79.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New86793
Fresh000
Picked101
Done000
Total87794
Error
0.0b
Counts
94 → 7
Alt Table
StatusErrorProgram
16.2b
(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 (+.f64 (*.f64 (log.f64 z) y) 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))
33.4b
(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))))
0.3b
(fma.f64 x 1/2 (fma.f64 y (fma.f64 (*.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 (log.f64 z))) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y))
10.9b
(fma.f64 x 1/2 (fma.f64 y (/.f64 (-.f64 (*.f64 (log.f64 z) (log.f64 z)) (*.f64 z z)) (+.f64 (log.f64 z) z)) y))
16.2b
(fma.f64 x 1/2 (fma.f64 y (/.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) (fma.f64 z z (*.f64 (log.f64 z) (+.f64 z (log.f64 z))))) y))
Compiler

Compiled 1840 to 708 computations (61.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series768.0ms (9%)

Counts
4 → 85
Calls

4 calls:

253.0ms
(+.f64 (*.f64 (log.f64 z) y) y)
209.0ms
(*.f64 (log.f64 z) y)
185.0ms
(-.f64 (+.f64 (*.f64 (log.f64 z) y) y) (*.f64 y z))
121.0ms
(fma.f64 x 1/2 (-.f64 (+.f64 (*.f64 (log.f64 z) y) y) (*.f64 y z)))

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
11×add-log-exp_binary64
10×add-sqr-sqrt_binary64
add-cube-cbrt_binary64
pow1_binary64
Counts
4 → 74
Calls

4 calls:

6.0ms
(-.f64 (+.f64 (*.f64 (log.f64 z) y) y) (*.f64 y z))
3.0ms
(+.f64 (*.f64 (log.f64 z) y) y)
3.0ms
(*.f64 (log.f64 z) y)
0.0ms
(fma.f64 x 1/2 (-.f64 (+.f64 (*.f64 (log.f64 z) y) y) (*.f64 y z)))

simplify81.0ms (1%)

Algorithm
egg-herbie
Rules
708×fma-def_binary64
554×fma-neg_binary64
487×unsub-neg_binary64
334×distribute-rgt-in_binary64
312×distribute-lft-in_binary64
Counts
159 → 141
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01472276
13591880
210461687
335641685
450401685

prune137.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1401141
Fresh156
Picked011
Done000
Total1417148
Error
0.0b
Counts
148 → 7
Alt Table
StatusErrorProgram
16.2b
(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 (+.f64 (*.f64 (log.f64 z) y) 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))
33.4b
(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))))
10.9b
(fma.f64 x 1/2 (fma.f64 y (/.f64 (-.f64 (*.f64 (log.f64 z) (log.f64 z)) (*.f64 z z)) (+.f64 (log.f64 z) z)) y))
14.3b
(fma.f64 x 1/2 (-.f64 (/.f64 (*.f64 y (*.f64 y (fma.f64 (log.f64 z) (log.f64 z) -1))) (-.f64 (*.f64 y (log.f64 z)) y)) (*.f64 y z)))
16.2b
(fma.f64 x 1/2 (fma.f64 y (/.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) (fma.f64 z z (*.f64 (log.f64 z) (+.f64 z (log.f64 z))))) y))
Compiler

Compiled 2864 to 964 computations (66.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series1.8s (21.5%)

Counts
4 → 60
Calls

4 calls:

1.5s
(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
259.0ms
(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
36.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
30.0ms
(cbrt.f64 z)

rewrite28.0ms (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:

12.0ms
(+.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)

simplify87.0ms (1%)

Algorithm
egg-herbie
Rules
664×distribute-rgt-in_binary64
592×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
213591572
341361562
450981562

prune241.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2222224
Fresh325
Picked011
Done011
Total2256231
Error
0b
Counts
231 → 6
Alt Table
StatusErrorProgram
10.9b
(fma.f64 x 1/2 (fma.f64 y (/.f64 (-.f64 (*.f64 (log.f64 z) (log.f64 z)) (*.f64 z z)) (+.f64 (log.f64 z) z)) y))
17.4b
(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))))))
0.1b
(fma.f64 x 1/2 (-.f64 (+.f64 (*.f64 (log.f64 z) y) y) (*.f64 y z)))
0.1b
(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (pow.f64 (pow.f64 z 1/6) 5)) (-.f64 (log.f64 (sqrt.f64 (cbrt.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))
14.3b
(fma.f64 x 1/2 (-.f64 (/.f64 (*.f64 y (*.f64 y (fma.f64 (log.f64 z) (log.f64 z) -1))) (-.f64 (*.f64 y (log.f64 z)) y)) (*.f64 y z)))
Compiler

Compiled 5293 to 1843 computations (65.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 y (+.f64 (log.f64 (pow.f64 (pow.f64 z 1/6) 5)) (-.f64 (log.f64 (sqrt.f64 (cbrt.f64 z))) z)) y)
0.6b
(cbrt.f64 z)
1.1b
(pow.f64 (pow.f64 z 1/6) 5)
4.1b
(pow.f64 z 1/6)

series1.7s (19.5%)

Counts
3 → 40
Calls

3 calls:

1.6s
(fma.f64 y (+.f64 (log.f64 (pow.f64 (pow.f64 z 1/6) 5)) (-.f64 (log.f64 (sqrt.f64 (cbrt.f64 z))) z)) y)
41.0ms
(pow.f64 (pow.f64 z 1/6) 5)
23.0ms
(pow.f64 z 1/6)

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
13×unpow-prod-down_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-exp-log_binary64
Counts
3 → 54
Calls

3 calls:

2.0ms
(pow.f64 (pow.f64 z 1/6) 5)
1.0ms
(pow.f64 z 1/6)
0.0ms
(fma.f64 y (+.f64 (log.f64 (pow.f64 (pow.f64 z 1/6) 5)) (-.f64 (log.f64 (sqrt.f64 (cbrt.f64 z))) z)) y)

simplify75.0ms (0.9%)

Algorithm
egg-herbie
Rules
707×fma-neg_binary64
379×exp-prod_binary64
338×fma-def_binary64
317×cancel-sign-sub-inv_binary64
317×unswap-sqr_binary64
Counts
94 → 90
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01281566
12901376
27391114
32426908
43960837
54870837

prune129.0ms (1.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1080108
Fresh033
Picked011
Done022
Total1086114
Error
0b
Counts
114 → 6
Alt Table
StatusErrorProgram
10.9b
(fma.f64 x 1/2 (fma.f64 y (/.f64 (-.f64 (*.f64 (log.f64 z) (log.f64 z)) (*.f64 z z)) (+.f64 (log.f64 z) z)) y))
17.4b
(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))))))
0.1b
(fma.f64 x 1/2 (-.f64 (+.f64 (*.f64 (log.f64 z) y) y) (*.f64 y z)))
0.1b
(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (pow.f64 (pow.f64 z 1/6) 5)) (-.f64 (log.f64 (sqrt.f64 (cbrt.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))
14.3b
(fma.f64 x 1/2 (-.f64 (/.f64 (*.f64 y (*.f64 y (fma.f64 (log.f64 z) (log.f64 z) -1))) (-.f64 (*.f64 y (log.f64 z)) y)) (*.f64 y z)))
Compiler

Compiled 2598 to 1447 computations (44.3% saved)

regimes950.0ms (11.1%)

Accuracy

Total 0.1b remaining (71.7%)

Threshold costs 0.1b (71.7%)

Counts
124 → 1
Compiler

Compiled 16086 to 10299 computations (36% saved)

simplify2.0ms (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
01219
12319
23119
33619
43819
53719

end106.0ms (1.2%)

Compiler

Compiled 162 to 102 computations (37% saved)

Profiling

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