Details

Time bar (total: 8.2s)

analyze1.1s (13.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
5.8%94%0.2%9
7.6%92.2%0.2%10
11.6%88.2%0.2%11
18.5%81.3%0.2%12
32.3%66.9%0.8%13
37%62.2%0.8%14
Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (14.6%)

Symmetry

(sort x y)

Results
933.0ms8256×body128valid
168.0ms1582×body128invalid
Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify170.0ms (2.1%)

Algorithm
egg-herbie
Rules
1483×associate-/l/_binary64
1068×associate-/l*_binary64
1015×associate-/r/_binary64
675×*-commutative_binary64
404×sqr-pow_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0913
11710
2417
3917
43667
512287
612127
712257
812387
912457
1012527
1112597
1212667
1312737
1412807
1512877
1612947
1713017
1813087
1913157
2013227
2130327
2227537
2327817
2428337
2529777
2630747
2734947
2837437
2940337
3044737
3150287

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
5.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
5.6b
(*.f64 x (/.f64 y z))
15.4b
(*.f64 x (/.f64 (*.f64 (/.f64 y z) t) t))
Compiler

Compiled 62 to 37 computations (40.3% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

NewErrorProgram
5.3b
(*.f64 x (/.f64 y z))

series11.0ms (0.1%)

Counts
1 → 36
Calls

1 calls:

11.0ms
(*.f64 x (/.f64 y z))

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
1 → 34
Calls

1 calls:

8.0ms
(*.f64 x (/.f64 y z))

simplify111.0ms (1.4%)

Algorithm
egg-herbie
Rules
736×fabs-mul_binary64
732×sqr-pow_binary64
503×pow-sqr_binary64
384×associate-/l/_binary64
307×unswap-sqr_binary64
Counts
70 → 50
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
072642
1162597
2526597
31312597
42135597
52239597
62445597
72751597
83643597
94500597
104489597
115931597

prune36.0ms (0.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New42850
Fresh011
Picked011
Done000
Total421052
Error
0.0b
Counts
52 → 10
Alt Table
StatusErrorProgram
15.4b
(*.f64 x (/.f64 (*.f64 (/.f64 y z) t) t))
2.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
5.8b
(*.f64 (*.f64 x y) (/.f64 1 z))
6.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 y x) z)) (cbrt.f64 (/.f64 (*.f64 y x) z))) (cbrt.f64 (/.f64 (*.f64 y x) z)))
19.5b
(*.f64 (*.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
5.7b
(/.f64 (*.f64 y x) z)
5.8b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
5.6b
(*.f64 x (/.f64 y z))
6.4b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
5.6b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
Compiler

Compiled 831 to 320 computations (61.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(cbrt.f64 z)
0.6b
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
0.6b
(cbrt.f64 y)
1.8b
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.3s (15.8%)

Counts
4 → 72
Calls

4 calls:

1.2s
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
40.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
34.0ms
(cbrt.f64 y)
31.0ms
(cbrt.f64 z)

rewrite24.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt_binary64
24×add-exp-log_binary64
22×cbrt-prod_binary64
16×*-un-lft-identity_binary64
16×add-cube-cbrt_binary64
Counts
4 → 100
Calls

4 calls:

9.0ms
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
9.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms
(cbrt.f64 z)
1.0ms
(cbrt.f64 y)

simplify107.0ms (1.3%)

Algorithm
egg-herbie
Rules
796×associate-*l/_binary64
584×fma-def_binary64
303×fma-neg_binary64
256×log-prod_binary64
236×unswap-sqr_binary64
Counts
172 → 154
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01812641
13851963
214361783
339491777
449531777
549481777

prune127.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2242226
Fresh178
Picked101
Done011
Total22610236
Error
0.0b
Counts
236 → 10
Alt Table
StatusErrorProgram
5.8b
(*.f64 (*.f64 x y) (/.f64 1 z))
6.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 y x) z)) (cbrt.f64 (/.f64 (*.f64 y x) z))) (cbrt.f64 (/.f64 (*.f64 y x) z)))
17.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y))) (cbrt.f64 z)))
19.5b
(*.f64 (*.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
5.7b
(/.f64 (*.f64 y x) z)
5.8b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
5.6b
(*.f64 x (/.f64 y z))
6.4b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
5.6b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
4.9b
(*.f64 (*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
Compiler

Compiled 5688 to 1522 computations (73.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(cbrt.f64 z)
0.6b
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
0.6b
(cbrt.f64 y)
4.1b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.2s (14.5%)

Counts
1 → 36
Calls

1 calls:

1.2s
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

rewrite22.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
79×add-exp-log_binary64
51×prod-exp_binary64
25×add-cbrt-cube_binary64
21×cbrt-unprod_binary64
12×div-exp_binary64
Counts
1 → 53
Calls

1 calls:

16.0ms
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

simplify119.0ms (1.5%)

Algorithm
egg-herbie
Rules
744×times-frac_binary64
378×fma-def_binary64
318×associate-/l*_binary64
317×*-commutative_binary64
261×fma-neg_binary64
Counts
89 → 72
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01452278
13561709
29521625
335091547
447981547
549861547
650261547

prune147.0ms (1.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2381239
Fresh088
Picked011
Done011
Total23811249
Error
0.0b
Counts
249 → 11
Alt Table
StatusErrorProgram
4.9b
(*.f64 (*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
5.6b
(*.f64 x (/.f64 y z))
5.8b
(*.f64 (*.f64 x y) (/.f64 1 z))
6.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 y x) z)) (cbrt.f64 (/.f64 (*.f64 y x) z))) (cbrt.f64 (/.f64 (*.f64 y x) z)))
17.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y))) (cbrt.f64 z)))
19.5b
(*.f64 (*.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
5.7b
(/.f64 (*.f64 y x) z)
5.8b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
6.4b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
5.6b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
4.9b
(*.f64 (*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
Compiler

Compiled 6594 to 1964 computations (70.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
0.6b
(cbrt.f64 y)
0.7b
(cbrt.f64 (cbrt.f64 y))
4.1b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.8s (21.5%)

Counts
3 → 60
Calls

3 calls:

1.2s
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
310.0ms
(cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
259.0ms
(cbrt.f64 (cbrt.f64 y))

rewrite33.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
121×add-exp-log_binary64
82×prod-exp_binary64
37×add-cbrt-cube_binary64
34×cbrt-unprod_binary64
17×pow1_binary64
Counts
3 → 91
Calls

3 calls:

18.0ms
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
2.0ms
(cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
1.0ms
(cbrt.f64 (cbrt.f64 y))

simplify133.0ms (1.6%)

Algorithm
egg-herbie
Rules
608×*-commutative_binary64
517×associate-/l*_binary64
440×fma-def_binary64
357×log-prod_binary64
315×associate-*l*_binary64
Counts
151 → 122
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01994503
14623231
213812385
341072385
449022385
549862385

prune130.0ms (1.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New2120212
Fresh088
Picked011
Done022
Total21211223
Error
0.0b
Counts
223 → 11
Alt Table
StatusErrorProgram
4.9b
(*.f64 (*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
5.6b
(*.f64 x (/.f64 y z))
5.8b
(*.f64 (*.f64 x y) (/.f64 1 z))
6.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 y x) z)) (cbrt.f64 (/.f64 (*.f64 y x) z))) (cbrt.f64 (/.f64 (*.f64 y x) z)))
17.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y))) (cbrt.f64 z)))
19.5b
(*.f64 (*.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
5.7b
(/.f64 (*.f64 y x) z)
5.8b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
6.4b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
5.6b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
4.9b
(*.f64 (*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
Compiler

Compiled 7454 to 1919 computations (74.3% saved)

regimes253.0ms (3.1%)

Accuracy

Total 1.9b remaining (98.2%)

Threshold costs 0b (0%)

Counts
37 → 1
Compiler

Compiled 5371 to 2977 computations (44.6% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01231
11431
21431

end129.0ms (1.6%)

Remove

(sort x y)

Compiler

Compiled 292 to 159 computations (45.5% saved)

Profiling

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