Details

Time bar (total: 4.2s)

analyze583.0ms (14%)

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
21.8%78%0.1%6
26.5%73.3%0.1%7
32%67.9%0.1%8
46.4%52.7%0.9%9
50.9%47.2%1.9%10
54.3%43.3%2.4%11
62.1%32.5%5.4%12
64.3%28.1%7.6%13
66.3%24.6%9.2%14
Compiler

Compiled 16 to 11 computations (31.3% saved)

sample54.0ms (1.3%)

Algorithm
intervals
Results
12.0ms256×body128valid
2.0ms38×body128invalid
Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify71.0ms (1.7%)

Algorithm
egg-herbie
Rules
1167×fma-def_binary64
1073×fma-neg_binary64
225×cancel-sign-sub-inv_binary64
222×distribute-rgt-in_binary64
163×distribute-lft-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 8 (0.0ms)

IterNodesCost
01118
12218
24318
37518
412316
521316
630216
747216
8100913
9132813
10154213
11155913
12155613
13155613
14145313

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 2
Alt Table
StatusErrorProgram
4.1b
(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
1.3b
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
Compiler

Compiled 66 to 44 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 (+.f64 x 4) y)
0.0b
(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
3.5b
(*.f64 (/.f64 x y) z)

rewrite165.0ms (4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
31×add-cube-cbrt_binary64
19×pow1_binary64
18×add-sqr-sqrt_binary64
16×add-exp-log_binary64
15×add-cbrt-cube_binary64
Counts
3 → 137
Calls

3 calls:

18.0ms
(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
15.0ms
(*.f64 (/.f64 x y) z)
13.0ms
(/.f64 (+.f64 x 4) y)
Compiler

Compiled 2445 to 1173 computations (52% saved)

series79.0ms (1.9%)

Error
0.0b
Counts
3 → 33
Calls

3 calls:

35.0ms
(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
19.0ms
(*.f64 (/.f64 x y) z)
15.0ms
(/.f64 (+.f64 x 4) y)
Compiler

Compiled 1070 to 689 computations (35.6% saved)

simplify98.0ms (2.3%)

Algorithm
egg-herbie
Rules
548×fma-def_binary64
523×fma-neg_binary64
290×cancel-sign-sub-inv_binary64
283×distribute-rgt-in_binary64
257×distribute-lft-in_binary64
Counts
170 → 89
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01861848
14561811
217921677
342401668
449641668

prune46.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New83689
Fresh011
Picked101
Done000
Total84791
Error
0b
Counts
91 → 7
Alt Table
StatusErrorProgram
4.1b
(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
1.6b
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))))
20.4b
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (sqrt.f64 (*.f64 z (*.f64 z (pow.f64 (/.f64 x y) 2))))))
31.6b
(fabs.f64 (neg.f64 (*.f64 x (-.f64 (/.f64 z y) (/.f64 1 y)))))
30.7b
(fabs.f64 (*.f64 (+.f64 (neg.f64 z) 1) (/.f64 x y)))
32.6b
(fabs.f64 (/.f64 (*.f64 y (-.f64 (+.f64 x 4) (*.f64 z x))) (*.f64 y y)))
16.3b
(fabs.f64 (-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 4 3)) (*.f64 y (fma.f64 x x (fma.f64 x -4 16)))) (*.f64 (/.f64 x y) z)))
Compiler

Compiled 1253 to 680 computations (45.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y)))
9.0b
(cbrt.f64 (/.f64 x y))
9.0b
(cbrt.f64 (/.f64 x y))
9.0b
(cbrt.f64 (/.f64 x y))

rewrite150.0ms (3.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
31×cbrt-div_binary64
28×add-cube-cbrt_binary64
27×pow1/3_binary64
17×add-sqr-sqrt_binary64
12×add-exp-log_binary64
Counts
4 → 156
Calls

4 calls:

16.0ms
(*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y)))
12.0ms
(cbrt.f64 (/.f64 x y))
11.0ms
(cbrt.f64 (/.f64 x y))
10.0ms
(cbrt.f64 (/.f64 x y))
Compiler

Compiled 3077 to 951 computations (69.1% saved)

series160.0ms (3.8%)

Error
0b
Counts
4 → 24
Calls

4 calls:

46.0ms
(*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y)))
34.0ms
(cbrt.f64 (/.f64 x y))
33.0ms
(cbrt.f64 (/.f64 x y))
31.0ms
(cbrt.f64 (/.f64 x y))
Compiler

Compiled 2238 to 1478 computations (34% saved)

simplify108.0ms (2.6%)

Algorithm
egg-herbie
Rules
644×times-frac_binary64
604×fma-def_binary64
509×log-prod_binary64
306×associate-*l*_binary64
246×exp-prod_binary64
Counts
180 → 80
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01291707
12781385
25541287
320291226
445251226
554181226

prune50.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New80080
Fresh066
Picked011
Done000
Total80787
Error
0b
Counts
87 → 7
Alt Table
StatusErrorProgram
4.1b
(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
1.6b
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))))
20.4b
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (sqrt.f64 (*.f64 z (*.f64 z (pow.f64 (/.f64 x y) 2))))))
31.6b
(fabs.f64 (neg.f64 (*.f64 x (-.f64 (/.f64 z y) (/.f64 1 y)))))
30.7b
(fabs.f64 (*.f64 (+.f64 (neg.f64 z) 1) (/.f64 x y)))
32.6b
(fabs.f64 (/.f64 (*.f64 y (-.f64 (+.f64 x 4) (*.f64 z x))) (*.f64 y y)))
16.3b
(fabs.f64 (-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 4 3)) (*.f64 y (fma.f64 x x (fma.f64 x -4 16)))) (*.f64 (/.f64 x y) z)))
Compiler

Compiled 1405 to 670 computations (52.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(-.f64 x (fma.f64 x z -4))
3.9b
(/.f64 (-.f64 x (fma.f64 x z -4)) y)

rewrite111.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
31×add-cube-cbrt_binary64
10×add-sqr-sqrt_binary64
10×add-cbrt-cube_binary64
add-log-exp_binary64
add-exp-log_binary64
Counts
2 → 100
Calls

2 calls:

16.0ms
(-.f64 x (fma.f64 x z -4))
15.0ms
(/.f64 (-.f64 x (fma.f64 x z -4)) y)
Compiler

Compiled 2071 to 1231 computations (40.6% saved)

series52.0ms (1.2%)

Error
0b
Counts
2 → 27
Calls

2 calls:

28.0ms
(/.f64 (-.f64 x (fma.f64 x z -4)) y)
14.0ms
(-.f64 x (fma.f64 x z -4))
Compiler

Compiled 697 to 477 computations (31.6% saved)

simplify113.0ms (2.7%)

Algorithm
egg-herbie
Rules
510×fma-def_binary64
463×distribute-rgt-in_binary64
452×fma-neg_binary64
423×distribute-lft-in_binary64
241×cancel-sign-sub-inv_binary64
Counts
127 → 86
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01591637
13971548
215961422
345831416
450001416
548861416

prune57.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New84286
Fresh235
Picked011
Done011
Total86793
Error
0b
Counts
93 → 7
Alt Table
StatusErrorProgram
4.1b
(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
30.7b
(fabs.f64 (*.f64 (/.f64 x y) (-.f64 1 z)))
1.6b
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))))
32.6b
(fabs.f64 (/.f64 (*.f64 y (fma.f64 x (-.f64 1 z) 4)) (*.f64 y y)))
20.4b
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (sqrt.f64 (*.f64 z (*.f64 z (pow.f64 (/.f64 x y) 2))))))
31.6b
(fabs.f64 (neg.f64 (*.f64 x (-.f64 (/.f64 z y) (/.f64 1 y)))))
16.3b
(fabs.f64 (-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 4 3)) (*.f64 y (fma.f64 x x (fma.f64 x -4 16)))) (*.f64 (/.f64 x y) z)))
Compiler

Compiled 1169 to 765 computations (34.6% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 4 3)) (*.f64 y (fma.f64 x x (fma.f64 x -4 16)))) (*.f64 (/.f64 x y) z))
0.0b
(*.f64 y (fma.f64 x x (fma.f64 x -4 16)))
3.5b
(*.f64 (/.f64 x y) z)
15.8b
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 4 3)) (*.f64 y (fma.f64 x x (fma.f64 x -4 16))))

rewrite238.0ms (5.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
31×add-cube-cbrt_binary64
30×pow1_binary64
26×add-sqr-sqrt_binary64
24×add-exp-log_binary64
20×add-cbrt-cube_binary64
Counts
4 → 180
Calls

4 calls:

20.0ms
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 4 3)) (*.f64 y (fma.f64 x x (fma.f64 x -4 16))))
20.0ms
(-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 4 3)) (*.f64 y (fma.f64 x x (fma.f64 x -4 16)))) (*.f64 (/.f64 x y) z))
17.0ms
(*.f64 y (fma.f64 x x (fma.f64 x -4 16)))
13.0ms
(*.f64 (/.f64 x y) z)
Compiler

Compiled 5710 to 3486 computations (38.9% saved)

series200.0ms (4.8%)

Error
0b
Counts
4 → 45
Calls

4 calls:

98.0ms
(-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 4 3)) (*.f64 y (fma.f64 x x (fma.f64 x -4 16)))) (*.f64 (/.f64 x y) z))
36.0ms
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 4 3)) (*.f64 y (fma.f64 x x (fma.f64 x -4 16))))
26.0ms
(*.f64 y (fma.f64 x x (fma.f64 x -4 16)))
22.0ms
(*.f64 (/.f64 x y) z)
Compiler

Compiled 2456 to 1737 computations (29.3% saved)

simplify124.0ms (3%)

Algorithm
egg-herbie
Rules
481×cancel-sign-sub-inv_binary64
307×fma-neg_binary64
258×unswap-sqr_binary64
210×associate-*l*_binary64
193×associate-*r*_binary64
Counts
225 → 130
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02644321
16973964
227853830
349893830

prune93.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1300130
Fresh044
Picked011
Done022
Total1307137
Error
0b
Counts
137 → 7
Alt Table
StatusErrorProgram
4.1b
(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
30.7b
(fabs.f64 (*.f64 (/.f64 x y) (-.f64 1 z)))
1.6b
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))))
32.6b
(fabs.f64 (/.f64 (*.f64 y (fma.f64 x (-.f64 1 z) 4)) (*.f64 y y)))
20.4b
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (sqrt.f64 (*.f64 z (*.f64 z (pow.f64 (/.f64 x y) 2))))))
31.6b
(fabs.f64 (neg.f64 (*.f64 x (-.f64 (/.f64 z y) (/.f64 1 y)))))
16.3b
(fabs.f64 (-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 4 3)) (*.f64 y (fma.f64 x x (fma.f64 x -4 16)))) (*.f64 (/.f64 x y) z)))
Compiler

Compiled 2690 to 1605 computations (40.3% saved)

regimes691.0ms (16.6%)

Accuracy

Total 0.1b remaining (90.6%)

Threshold costs 0.1b (90.6%)

Compiler

Compiled 8101 to 5460 computations (32.6% saved)

bsearch3.0ms (0.1%)

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify16.0ms (0.4%)

Algorithm
egg-herbie
Rules
76×cancel-sign-sub-inv_binary64
47×distribute-rgt-neg-in_binary64
36×distribute-neg-in_binary64
36×sub-neg_binary64
32×neg-sub0_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03198
16098
29496
312796
416496
519696
622296
725196
828496
931096
1033096
1135496
1236396
1336196
1435396

end1.0ms (0%)

Compiler

Compiled 67 to 35 computations (47.8% saved)

sample859.0ms (20.6%)

Algorithm
intervals
Results
385.0ms8000×body128valid
60.0ms1254×body128invalid
Compiler

Compiled 212 to 132 computations (37.7% saved)

Profiling

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