Details

Time bar (total: 4.4s)

analyze287.0ms (6.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
0%50%50%4
6.2%43.7%50%5
9.4%28.1%62.5%6
12.5%25%62.5%7
15.6%15.6%68.8%8
16.8%14.4%68.8%9
18.5%8.8%72.7%10
19.2%7.7%73.1%11
20.1%4.6%75.2%12
20.5%4%75.5%13
21%2.4%76.6%14
Compiler

Compiled 23 to 20 computations (13% saved)

sample33.0ms (0.7%)

Algorithm
intervals
Results
21.0ms256×body128valid
1.0msbody128nan
0.0msbody128invalid
Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify66.0ms (1.5%)

Algorithm
egg-herbie
Rules
189×distribute-rgt-in_binary64
173×cancel-sign-sub-inv_binary64
159×sub-neg_binary64
156×distribute-lft-in_binary64
149×unsub-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01524
13221
27121
315021
426621
546021
661821
798721
8118521
9114821
10119121
11119021
12118721
13104921

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.2b
Counts
2 → 2
Alt Table
StatusErrorProgram
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
0.2b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
Compiler

Compiled 92 to 77 computations (16.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (-.f64 a 1/3) 9)
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
0.2b
(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b
(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite159.0ms (3.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
25×add-sqr-sqrt_binary64
23×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
12×times-frac_binary64
11×pow1_binary64
Counts
4 → 99
Calls

4 calls:

12.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
6.0ms
(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
5.0ms
(*.f64 (-.f64 a 1/3) 9)
4.0ms
(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
Compiler

Compiled 2230 to 1765 computations (20.9% saved)

series62.0ms (1.4%)

Error
0.0b
Counts
4 → 24
Calls

4 calls:

24.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
18.0ms
(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms
(*.f64 (-.f64 a 1/3) 9)
5.0ms
(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
Compiler

Compiled 783 to 624 computations (20.3% saved)

simplify97.0ms (2.2%)

Algorithm
egg-herbie
Rules
686×distribute-rgt-in_binary64
671×distribute-lft-in_binary64
299×associate-*l/_binary64
277×associate-*r/_binary64
200×times-frac_binary64
Counts
123 → 104
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01922238
14472076
213602067
347702067
449682067

prune106.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New977104
Fresh101
Picked101
Done000
Total997106
Error
0b
Counts
106 → 7
Alt Table
StatusErrorProgram
0.6b
(*.f64 (sqrt.f64 (-.f64 a 1/3)) (*.f64 (sqrt.f64 (+.f64 -1/3 a)) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
0.3b
(+.f64 -1/3 (+.f64 a (*.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))
35.5b
(/.f64 (*.f64 (-.f64 (*.f64 a a) 1/9) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))) (+.f64 a 1/3))
39.7b
(/.f64 (*.f64 (-.f64 (*.f64 a a) 1/9) (-.f64 1 (*.f64 rand (/.f64 rand (+.f64 -3 (*.f64 a 9)))))) (*.f64 (+.f64 1/3 a) (-.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 1/3 rand))))
31.7b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 (sqrt.f64 rand) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 (sqrt.f64 rand) 3))))
Compiler

Compiled 2131 to 1668 computations (21.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (+.f64 -1/3 a))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
0.2b
(/.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
0.3b
(/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))

rewrite361.0ms (8.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
330×times-frac_binary64
233×*-un-lft-identity_binary64
188×sqrt-prod_binary64
182×add-sqr-sqrt_binary64
177×add-cube-cbrt_binary64
Counts
4 → 302
Calls

4 calls:

38.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
13.0ms
(/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))
5.0ms
(/.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
4.0ms
(sqrt.f64 (+.f64 -1/3 a))
Compiler

Compiled 6333 to 5015 computations (20.8% saved)

series75.0ms (1.7%)

Error
0b
Counts
4 → 24
Calls

4 calls:

26.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
20.0ms
(/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))
18.0ms
(/.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
5.0ms
(sqrt.f64 (+.f64 -1/3 a))
Compiler

Compiled 905 to 730 computations (19.3% saved)

simplify254.0ms (5.8%)

Algorithm
egg-herbie
Rules
591×associate-*l/_binary64
559×associate-*r/_binary64
469×associate-/r*_binary64
416×times-frac_binary64
358×associate-/l*_binary64
Counts
326 → 298
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03587875
18217703
222577703
349907703
449587703

prune193.0ms (4.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2971298
Fresh156
Picked011
Done000
Total2987305
Error
0b
Counts
305 → 7
Alt Table
StatusErrorProgram
0.6b
(*.f64 (sqrt.f64 (-.f64 a 1/3)) (*.f64 (sqrt.f64 (+.f64 -1/3 a)) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
0.3b
(+.f64 -1/3 (+.f64 a (*.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))
35.5b
(/.f64 (*.f64 (-.f64 (*.f64 a a) 1/9) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))) (+.f64 a 1/3))
39.7b
(/.f64 (*.f64 (-.f64 (*.f64 a a) 1/9) (-.f64 1 (*.f64 rand (/.f64 rand (+.f64 -3 (*.f64 a 9)))))) (*.f64 (+.f64 1/3 a) (-.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 1/3 rand))))
Compiler

Compiled 4472 to 3477 computations (22.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (-.f64 a 1/3))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
0.2b
(*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))
0.4b
(/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))

rewrite186.0ms (4.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
69×add-sqr-sqrt_binary64
58×*-un-lft-identity_binary64
50×times-frac_binary64
41×sqrt-prod_binary64
40×add-cube-cbrt_binary64
Counts
4 → 146
Calls

4 calls:

12.0ms
(*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))
6.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
5.0ms
(/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))
3.0ms
(sqrt.f64 (-.f64 a 1/3))
Compiler

Compiled 3069 to 2481 computations (19.2% saved)

series55.0ms (1.3%)

Error
0b
Counts
4 → 21
Calls

4 calls:

24.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
18.0ms
(*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))
6.0ms
(/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))
5.0ms
(sqrt.f64 (-.f64 a 1/3))
Compiler

Compiled 758 to 610 computations (19.5% saved)

simplify119.0ms (2.7%)

Algorithm
egg-herbie
Rules
653×distribute-rgt-in_binary64
636×distribute-lft-in_binary64
254×times-frac_binary64
244×associate-/l*_binary64
201×associate-*l*_binary64
Counts
167 → 82
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02192986
15202847
218002798
348842798
449632798

prune122.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New82082
Fresh055
Picked011
Done011
Total82789
Error
0b
Counts
89 → 7
Alt Table
StatusErrorProgram
0.6b
(*.f64 (sqrt.f64 (-.f64 a 1/3)) (*.f64 (sqrt.f64 (+.f64 -1/3 a)) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
0.3b
(+.f64 -1/3 (+.f64 a (*.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))
35.5b
(/.f64 (*.f64 (-.f64 (*.f64 a a) 1/9) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))) (+.f64 a 1/3))
39.7b
(/.f64 (*.f64 (-.f64 (*.f64 a a) 1/9) (-.f64 1 (*.f64 rand (/.f64 rand (+.f64 -3 (*.f64 a 9)))))) (*.f64 (+.f64 1/3 a) (-.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 1/3 rand))))
Compiler

Compiled 1400 to 1107 computations (20.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 1/3 rand))))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 1/3 rand))
0.3b
(/.f64 1 (sqrt.f64 (+.f64 -1/3 a)))
0.3b
(*.f64 1/3 rand)

rewrite220.0ms (5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
54×*-un-lft-identity_binary64
44×add-sqr-sqrt_binary64
42×times-frac_binary64
38×add-cube-cbrt_binary64
35×associate-*l*_binary64
Counts
4 → 150
Calls

4 calls:

10.0ms
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 1/3 rand))
8.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 1/3 rand))))
7.0ms
(/.f64 1 (sqrt.f64 (+.f64 -1/3 a)))
3.0ms
(*.f64 1/3 rand)
Compiler

Compiled 3340 to 2769 computations (17.1% saved)

series111.0ms (2.5%)

Error
0b
Counts
4 → 21
Calls

4 calls:

77.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 1/3 rand))))
20.0ms
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 1/3 rand))
6.0ms
(*.f64 1/3 rand)
5.0ms
(/.f64 1 (sqrt.f64 (+.f64 -1/3 a)))
Compiler

Compiled 757 to 611 computations (19.3% saved)

simplify144.0ms (3.3%)

Algorithm
egg-herbie
Rules
514×times-frac_binary64
450×associate-*l/_binary64
308×associate-*r/_binary64
223×associate-*l*_binary64
218×associate-/l*_binary64
Counts
171 → 139
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02092716
15102541
217762468
343162419
449682419
549482419

prune140.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1381139
Fresh314
Picked101
Done022
Total1424146
Error
0b
Counts
146 → 4
Alt Table
StatusErrorProgram
0.5b
(*.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 (*.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
0.3b
(+.f64 -1/3 (+.f64 a (*.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
Compiler

Compiled 1887 to 1534 computations (18.7% saved)

regimes546.0ms (12.5%)

Accuracy

Total 0.1b remaining (82.8%)

Threshold costs 0.1b (82.8%)

Compiler

Compiled 10414 to 8454 computations (18.8% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01524
12324
22424
32124

end1.0ms (0%)

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample996.0ms (22.8%)

Algorithm
intervals
Results
653.0ms8000×body128valid
20.0ms238×body128invalid
19.0ms277×body128nan
Compiler

Compiled 105 to 87 computations (17.1% saved)

Profiling

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