Details

Time bar (total: 5.8s)

analyze1.1s (19.4%)

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)

sample1.3s (21.9%)

Symmetry

(sort x y)

Results
1.0s8256×body128valid
182.0ms1578×body128invalid
Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify301.0ms (5.2%)

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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
3.7b
Counts
3 → 2
Alt Table
StatusErrorProgram
13.6b
(*.f64 x (/.f64 (*.f64 (/.f64 y z) t) t))
3.7b
(*.f64 x (/.f64 y z))
Compiler

Compiled 62 to 37 computations (40.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
3.6b
(*.f64 x (/.f64 y z))

series12.0ms (0.2%)

Counts
1 → 36
Calls

1 calls:

12.0ms
(*.f64 x (/.f64 y z))

rewrite12.0ms (0.2%)

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:

10.0ms
(*.f64 x (/.f64 y z))

simplify119.0ms (2%)

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

prune78.0ms (1.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New391150
Fresh101
Picked011
Done000
Total401252
Error
0.0b
Counts
52 → 12
Alt Table
StatusErrorProgram
4.5b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z)))
3.7b
(*.f64 x (/.f64 y z))
34.9b
(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 y (sqrt.f64 z)))
28.7b
(*.f64 (sqrt.f64 (*.f64 x (/.f64 y z))) (sqrt.f64 (*.f64 x (/.f64 y z))))
5.3b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
5.3b
(*.f64 (*.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
17.5b
(*.f64 (*.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
5.3b
(/.f64 (*.f64 y x) z)
4.9b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
1.4b
(*.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)))
49.6b
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 y z)))
4.4b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
Compiler

Compiled 897 to 358 computations (60.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series145.0ms (2.5%)

Counts
4 → 48
Calls

4 calls:

41.0ms
(*.f64 (cbrt.f64 y) (cbrt.f64 y))
38.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
35.0ms
(cbrt.f64 y)
30.0ms
(cbrt.f64 z)

rewrite15.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64
38×cbrt-prod_binary64
22×*-un-lft-identity_binary64
22×add-cube-cbrt_binary64
18×pow1_binary64
Counts
4 → 110
Calls

4 calls:

4.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
4.0ms
(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 z)

simplify103.0ms (1.8%)

Algorithm
egg-herbie
Rules
742×fma-def_binary64
708×log-prod_binary64
594×unswap-sqr_binary64
324×exp-prod_binary64
238×*-commutative_binary64
Counts
158 → 148
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01021220
11741108
25581032
38951004
42346820
54061820
64265820
74815820

prune164.0ms (2.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2191220
Fresh1910
Picked011
Done011
Total22012232
Error
0.0b
Counts
232 → 12
Alt Table
StatusErrorProgram
4.5b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z)))
3.7b
(*.f64 x (/.f64 y z))
1.5b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 z)))
4.4b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
34.9b
(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 y (sqrt.f64 z)))
28.7b
(*.f64 (sqrt.f64 (*.f64 x (/.f64 y z))) (sqrt.f64 (*.f64 x (/.f64 y z))))
5.3b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
5.3b
(*.f64 (*.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
17.5b
(*.f64 (*.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
5.3b
(/.f64 (*.f64 y x) z)
4.9b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
1.4b
(*.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)))
Compiler

Compiled 5444 to 1410 computations (74.1% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series604.0ms (10.4%)

Counts
2 → 24
Calls

2 calls:

331.0ms
(cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
273.0ms
(cbrt.f64 (cbrt.f64 y))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 27
Calls

2 calls:

3.0ms
(cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
1.0ms
(cbrt.f64 (cbrt.f64 y))

simplify107.0ms (1.8%)

Algorithm
egg-herbie
Rules
693×sqr-pow_binary64
622×fma-def_binary64
548×unswap-sqr_binary64
376×distribute-rgt-in_binary64
318×*-commutative_binary64
Counts
51 → 42
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
047474
178474
2138474
3283468
4779450
51271450
61449450
71730450
82156450
92689450
103638450
114799450
124840450

prune126.0ms (2.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1860186
Fresh099
Picked011
Done022
Total18612198
Error
0.0b
Counts
198 → 12
Alt Table
StatusErrorProgram
4.5b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z)))
3.7b
(*.f64 x (/.f64 y z))
1.5b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 z)))
4.4b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
34.9b
(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 y (sqrt.f64 z)))
28.7b
(*.f64 (sqrt.f64 (*.f64 x (/.f64 y z))) (sqrt.f64 (*.f64 x (/.f64 y z))))
5.3b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
5.3b
(*.f64 (*.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
17.5b
(*.f64 (*.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
5.3b
(/.f64 (*.f64 y x) z)
4.9b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
1.4b
(*.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)))
Compiler

Compiled 6112 to 1237 computations (79.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.5b
(cbrt.f64 x)
1.7b
(*.f64 (cbrt.f64 x) (/.f64 y z))
2.2b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))

series560.0ms (9.6%)

Counts
4 → 96
Calls

4 calls:

465.0ms
(*.f64 (cbrt.f64 x) (/.f64 y z))
36.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
31.0ms
(cbrt.f64 x)
28.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))

rewrite31.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64
32×add-exp-log_binary64
25×pow1_binary64
24×cbrt-prod_binary64
22×*-un-lft-identity_binary64
Counts
4 → 123
Calls

4 calls:

11.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
6.0ms
(*.f64 (cbrt.f64 x) (/.f64 y z))
4.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms
(cbrt.f64 x)

simplify117.0ms (2%)

Algorithm
egg-herbie
Rules
750×fma-def_binary64
444×associate-*r/_binary64
392×associate-*l/_binary64
383×*-commutative_binary64
360×associate-/l*_binary64
Counts
219 → 176
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01522212
13221944
212141889
332861874
446051874
552441874

prune138.0ms (2.4%)

Pruning

13 alts after pruning (9 fresh and 4 done)

PrunedKeptTotal
New2111212
Fresh088
Picked011
Done033
Total21113224
Error
0.0b
Counts
224 → 13
Alt Table
StatusErrorProgram
34.9b
(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 y (sqrt.f64 z)))
4.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x)) (/.f64 y z))
4.5b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z)))
3.7b
(*.f64 x (/.f64 y z))
1.5b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 z)))
4.4b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
28.7b
(*.f64 (sqrt.f64 (*.f64 x (/.f64 y z))) (sqrt.f64 (*.f64 x (/.f64 y z))))
5.3b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))
5.3b
(*.f64 (*.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
17.5b
(*.f64 (*.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
5.3b
(/.f64 (*.f64 y x) z)
4.9b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
1.4b
(*.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)))
Compiler

Compiled 3801 to 911 computations (76% saved)

regimes445.0ms (7.6%)

Accuracy

Total 2.0b remaining (98.7%)

Threshold costs 0b (0%)

Counts
62 → 1
Compiler

Compiled 9463 to 5172 computations (45.3% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01329
11529
21529

end296.0ms (5.1%)

Compiler

Compiled 305 to 171 computations (43.9% saved)

Profiling

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