Details

Time bar (total: 5.8s)

analyze422.0ms (7.2%)

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)

sample51.0ms (0.9%)

Algorithm
intervals
Results
35.0ms256×body128valid
1.0msbody128invalid
1.0msbody128nan
Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify111.0ms (1.9%)

Algorithm
egg-herbie
Rules
1035×fma-def_binary64
742×fma-neg_binary64
189×distribute-rgt-in_binary64
173×cancel-sign-sub-inv_binary64
156×distribute-lft-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01524
13221
27519
316819
435819
567819
690119
7144619
8191419
9187319
10191619
11191519
12191219
13246519
14246519
15232119

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.1b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
Compiler

Compiled 109 to 91 computations (16.5% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)
0.3b
(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
0.6b
(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

rewrite101.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64
29×*-un-lft-identity_binary64
28×times-frac_binary64
26×associate-*l*_binary64
24×add-cube-cbrt_binary64
Counts
4 → 134
Calls

4 calls:

32.0ms
(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
21.0ms
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)
18.0ms
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
16.0ms
(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))

series215.0ms (3.7%)

Counts
4 → 41
Calls

4 calls:

92.0ms
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)
87.0ms
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
21.0ms
(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
14.0ms
(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

simplify185.0ms (3.2%)

Algorithm
egg-herbie
Rules
682×distribute-rgt-in_binary64
675×times-frac_binary64
199×associate-*r*_binary64
193×cancel-sign-sub-inv_binary64
178×associate-*l*_binary64
Counts
175 → 335
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02813587
17713326
227673268
354413268

prune600.0ms (10.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3296335
Fresh011
Picked101
Done000
Total3307337
Error
0b
Counts
337 → 7
Alt Table
StatusErrorProgram
0.1b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))) rand)))
39.5b
(/.f64 (*.f64 (fma.f64 a a -1/9) (-.f64 1 (*.f64 rand (*.f64 rand (/.f64 1/9 (+.f64 -1/3 a)))))) (*.f64 (+.f64 a 1/3) (-.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9))))))
4.2b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 (*.f64 a a) (*.f64 (/.f64 1 3) (/.f64 1 3)))))) (*.f64 rand (sqrt.f64 (+.f64 a 1/3))))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.2b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9))))) rand)))
0.1b
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
9.9b
(*.f64 (sqrt.f64 (*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))) (sqrt.f64 (*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))))
Compiler

Compiled 7842 to 6610 computations (15.7% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite15.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
associate-*r*_binary64
*-un-lft-identity_binary64
sqrt-prod_binary64
add-cube-cbrt_binary64
Counts
2 → 37
Calls

2 calls:

12.0ms
(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
1.0ms
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a)

series90.0ms (1.5%)

Counts
2 → 34
Calls

2 calls:

49.0ms
(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
41.0ms
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a)

simplify117.0ms (2%)

Algorithm
egg-herbie
Rules
424×associate-/l/_binary64
379×fma-neg_binary64
253×associate-*r*_binary64
252×associate-*l*_binary64
244×times-frac_binary64
Counts
71 → 120
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01091028
1249971
2756963
32655960
44947956
54929956

prune156.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1182120
Fresh246
Picked011
Done000
Total1207127
Error
0b
Counts
127 → 7
Alt Table
StatusErrorProgram
0.1b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))) rand)))
4.2b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 (*.f64 a a) (*.f64 (/.f64 1 3) (/.f64 1 3)))))) (*.f64 rand (sqrt.f64 (+.f64 a 1/3))))))
9.9b
(+.f64 -1/3 (*.f64 (sqrt.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a)) (sqrt.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.2b
(+.f64 -1/3 (fma.f64 1/3 (*.f64 (*.f64 rand (fabs.f64 (cbrt.f64 (-.f64 a 1/3)))) (sqrt.f64 (cbrt.f64 (+.f64 -1/3 a)))) a))
0.2b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9))))) rand)))
0.1b
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
Compiler

Compiled 1747 to 1334 computations (23.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 a 9 -3)
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.2b
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
0.6b
(sqrt.f64 (fma.f64 a 9 -3))

rewrite36.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt_binary64
26×*-un-lft-identity_binary64
22×add-cube-cbrt_binary64
18×times-frac_binary64
15×sqrt-prod_binary64
Counts
4 → 99
Calls

4 calls:

20.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
6.0ms
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
2.0ms
(sqrt.f64 (fma.f64 a 9 -3))
1.0ms
(fma.f64 a 9 -3)

series201.0ms (3.5%)

Counts
4 → 50
Calls

4 calls:

103.0ms
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
75.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
13.0ms
(sqrt.f64 (fma.f64 a 9 -3))
10.0ms
(fma.f64 a 9 -3)

simplify177.0ms (3%)

Algorithm
egg-herbie
Rules
754×fma-def_binary64
652×distribute-rgt-in_binary64
401×times-frac_binary64
187×cancel-sign-sub-inv_binary64
151×fma-neg_binary64
Counts
149 → 245
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02422971
16482791
221982639
349752621
449642621

prune355.0ms (6.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2441245
Fresh145
Picked011
Done011
Total2457252
Error
0b
Counts
252 → 7
Alt Table
StatusErrorProgram
0.1b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))) rand)))
9.9b
(+.f64 -1/3 (*.f64 (sqrt.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a)) (sqrt.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.2b
(+.f64 -1/3 (fma.f64 1/3 (*.f64 (*.f64 rand (fabs.f64 (cbrt.f64 (-.f64 a 1/3)))) (sqrt.f64 (cbrt.f64 (+.f64 -1/3 a)))) a))
0.2b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9))))) rand)))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
0.1b
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
Compiler

Compiled 3973 to 3083 computations (22.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
0.1b
(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
0.6b
(/.f64 1 (fma.f64 a 9 -3))

rewrite35.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64
32×*-un-lft-identity_binary64
31×times-frac_binary64
29×sqrt-prod_binary64
28×add-cube-cbrt_binary64
Counts
4 → 117
Calls

4 calls:

16.0ms
(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
4.0ms
(/.f64 1 (fma.f64 a 9 -3))
4.0ms
(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
1.0ms
(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)

series133.0ms (2.3%)

Counts
4 → 36
Calls

4 calls:

87.0ms
(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
25.0ms
(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
16.0ms
(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
4.0ms
(/.f64 1 (fma.f64 a 9 -3))

simplify181.0ms (3.1%)

Algorithm
egg-herbie
Rules
826×fma-def_binary64
571×times-frac_binary64
332×distribute-rgt-in_binary64
293×distribute-lft-in_binary64
237×fma-neg_binary64
Counts
153 → 265
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02433027
16562737
219752681
349162673
449302673

prune526.0ms (9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New2632265
Fresh314
Picked011
Done022
Total2666272
Error
0b
Counts
272 → 6
Alt Table
StatusErrorProgram
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.2b
(+.f64 -1/3 (fma.f64 1/3 (*.f64 (*.f64 rand (fabs.f64 (cbrt.f64 (-.f64 a 1/3)))) (sqrt.f64 (cbrt.f64 (+.f64 -1/3 a)))) a))
0.1b
(+.f64 a (fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
0.1b
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
0.2b
(+.f64 a (fma.f64 rand (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) (sqrt.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))) (+.f64 a -1/3)) -1/3))
Compiler

Compiled 5003 to 3955 computations (20.9% saved)

regimes929.0ms (15.9%)

Accuracy

Total 0.1b remaining (88.9%)

Threshold costs 0.1b (88.9%)

Compiler

Compiled 14304 to 11818 computations (17.4% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01321
11621
21621

end1.0ms (0%)

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.1s (18.9%)

Algorithm
intervals
Results
652.0ms8000×body128valid
18.0ms251×body128invalid
14.0ms212×body128nan
Compiler

Compiled 152 to 122 computations (19.7% saved)

Profiling

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