Details

Time bar (total: 4.3s)

analyze120.0ms (2.8%)

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
0%50%50%5
6.2%31.2%62.5%6
9.4%28.1%62.5%7
14%17.2%68.8%8
14.8%16.4%68.8%9
17.6%9.8%72.7%10
18.1%8.8%73.1%11
19.6%5.2%75.2%12
20%4.5%75.5%13
20.7%2.7%76.6%14
Compiler

Compiled 23 to 20 computations (13% saved)

sample1.5s (34.6%)

Results
1.2s8256×body128valid
68.0ms543×body128invalid
Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify97.0ms (2.3%)

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

prune4.0ms (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 (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
Compiler

Compiled 109 to 91 computations (16.5% saved)

localize9.0ms (0.2%)

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)))))
0.1b
(sqrt.f64 (fma.f64 a 9 -3))
0.2b
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

series70.0ms (1.6%)

Counts
4 → 50
Calls

4 calls:

34.0ms
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
24.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
10.0ms
(sqrt.f64 (fma.f64 a 9 -3))
2.0ms
(fma.f64 a 9 -3)

rewrite22.0ms (0.5%)

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:

11.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
4.0ms
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
1.0ms
(sqrt.f64 (fma.f64 a 9 -3))
0.0ms
(fma.f64 a 9 -3)

simplify101.0ms (2.4%)

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 → 195
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02422971
16482791
221982639
349752621
449642621

prune246.0ms (5.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1887195
Fresh101
Picked101
Done000
Total1907197
Error
0b
Counts
197 → 7
Alt Table
StatusErrorProgram
39.3b
(/.f64 (*.f64 (-.f64 (*.f64 a a) (*.f64 1/3 1/3)) (-.f64 (*.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (*.f64 (+.f64 a 1/3) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
0.3b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
10.4b
(*.f64 (*.f64 (-.f64 a 1/3) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
30.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 (*.f64 a 9) -3)))))
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
Compiler

Compiled 4774 to 3696 computations (22.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series60.0ms (1.4%)

Counts
4 → 36
Calls

4 calls:

33.0ms
(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
13.0ms
(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
10.0ms
(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
4.0ms
(/.f64 1 (fma.f64 9 a -3))

rewrite19.0ms (0.4%)

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:

8.0ms
(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
2.0ms
(/.f64 1 (fma.f64 9 a -3))
2.0ms
(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
0.0ms
(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)

simplify97.0ms (2.3%)

Algorithm
egg-herbie
Rules
826×fma-def_binary64
571×times-frac_binary64
332×distribute-rgt-in_binary64
293×distribute-lft-in_binary64
238×fma-neg_binary64
Counts
153 → 220
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02433027
16552737
219752681
349162673
449302673

prune304.0ms (7.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2182220
Fresh246
Picked101
Done000
Total2216227
Error
0b
Counts
227 → 6
Alt Table
StatusErrorProgram
39.3b
(/.f64 (*.f64 (-.f64 (*.f64 a a) (*.f64 1/3 1/3)) (-.f64 (*.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (*.f64 (+.f64 a 1/3) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
0.3b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (pow.f64 (fma.f64 9 a -3) -1/2) (+.f64 a -1/3)) -1/3))
16.9b
(+.f64 a (fma.f64 rand (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 -1/3 a)) 3)) -1/3))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 (*.f64 a 9) -3)))))
10.4b
(*.f64 (*.f64 (-.f64 a 1/3) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
Compiler

Compiled 5729 to 4527 computations (21% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 9 a -3)
0.1b
(fma.f64 rand (*.f64 (pow.f64 (fma.f64 9 a -3) -1/2) (+.f64 a -1/3)) -1/3)
0.1b
(pow.f64 (fma.f64 9 a -3) -1/2)
0.3b
(*.f64 (pow.f64 (fma.f64 9 a -3) -1/2) (+.f64 a -1/3))

series54.0ms (1.3%)

Counts
4 → 44
Calls

4 calls:

32.0ms
(fma.f64 rand (*.f64 (pow.f64 (fma.f64 9 a -3) -1/2) (+.f64 a -1/3)) -1/3)
16.0ms
(*.f64 (pow.f64 (fma.f64 9 a -3) -1/2) (+.f64 a -1/3))
5.0ms
(pow.f64 (fma.f64 9 a -3) -1/2)
2.0ms
(fma.f64 9 a -3)

rewrite10.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
10×add-exp-log_binary64
add-cube-cbrt_binary64
associate-*l*_binary64
Counts
4 → 71
Calls

4 calls:

6.0ms
(*.f64 (pow.f64 (fma.f64 9 a -3) -1/2) (+.f64 a -1/3))
1.0ms
(pow.f64 (fma.f64 9 a -3) -1/2)
0.0ms
(fma.f64 9 a -3)
0.0ms
(fma.f64 rand (*.f64 (pow.f64 (fma.f64 9 a -3) -1/2) (+.f64 a -1/3)) -1/3)

simplify66.0ms (1.5%)

Algorithm
egg-herbie
Rules
728×fma-def_binary64
449×times-frac_binary64
314×distribute-rgt-in_binary64
308×associate-/l*_binary64
305×distribute-lft-in_binary64
Counts
115 → 168
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02212421
15972157
218612025
349322025

prune217.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1680168
Fresh055
Picked011
Done000
Total1686174
Error
0b
Counts
174 → 6
Alt Table
StatusErrorProgram
39.3b
(/.f64 (*.f64 (-.f64 (*.f64 a a) (*.f64 1/3 1/3)) (-.f64 (*.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (*.f64 (+.f64 a 1/3) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
0.3b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (pow.f64 (fma.f64 9 a -3) -1/2) (+.f64 a -1/3)) -1/3))
16.9b
(+.f64 a (fma.f64 rand (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 -1/3 a)) 3)) -1/3))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 (*.f64 a 9) -3)))))
10.4b
(*.f64 (*.f64 (-.f64 a 1/3) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
Compiler

Compiled 4362 to 3411 computations (21.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series65.0ms (1.5%)

Counts
4 → 49
Calls

4 calls:

27.0ms
(/.f64 rand (sqrt.f64 (+.f64 (*.f64 a 9) -3)))
25.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 (*.f64 a 9) -3)))))
11.0ms
(sqrt.f64 (+.f64 (*.f64 a 9) -3))
1.0ms
(+.f64 (*.f64 a 9) -3)

rewrite29.0ms (0.7%)

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 → 107
Calls

4 calls:

12.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 (*.f64 a 9) -3)))))
7.0ms
(/.f64 rand (sqrt.f64 (+.f64 (*.f64 a 9) -3)))
3.0ms
(+.f64 (*.f64 a 9) -3)
3.0ms
(sqrt.f64 (+.f64 (*.f64 a 9) -3))

simplify82.0ms (1.9%)

Algorithm
egg-herbie
Rules
851×fma-def_binary64
680×distribute-rgt-in_binary64
405×times-frac_binary64
210×cancel-sign-sub-inv_binary64
128×distribute-lft-in_binary64
Counts
156 → 208
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02623093
17182897
223882741
352562741

prune227.0ms (5.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2080208
Fresh044
Picked011
Done011
Total2086214
Error
0b
Counts
214 → 6
Alt Table
StatusErrorProgram
39.3b
(/.f64 (*.f64 (-.f64 (*.f64 a a) (*.f64 1/3 1/3)) (-.f64 (*.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (*.f64 (+.f64 a 1/3) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
0.3b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (pow.f64 (fma.f64 9 a -3) -1/2) (+.f64 a -1/3)) -1/3))
16.9b
(+.f64 a (fma.f64 rand (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 -1/3 a)) 3)) -1/3))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 (*.f64 a 9) -3)))))
10.4b
(*.f64 (*.f64 (-.f64 a 1/3) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
Compiler

Compiled 5079 to 3975 computations (21.7% saved)

regimes737.0ms (17.2%)

Accuracy

Total 0.1b remaining (72.7%)

Threshold costs 0.1b (72.7%)

Counts
157 → 1
Compiler

Compiled 13890 to 11002 computations (20.8% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01431
11831
21831

end132.0ms (3.1%)

Compiler

Compiled 202 to 159 computations (21.3% saved)

Profiling

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