Details

Time bar (total: 4.7s)

analyze123.0ms (2.6%)

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)

sample1.4s (30.5%)

Results
1.1s8256×body128valid
75.0ms575×body128invalid
Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify95.0ms (2%)

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)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(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)))

series62.0ms (1.3%)

Counts
4 → 50
Calls

4 calls:

29.0ms
(/.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)))))
8.0ms
(sqrt.f64 (fma.f64 a 9 -3))
1.0ms
(fma.f64 a 9 -3)

rewrite20.0ms (0.4%)

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:

10.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
3.0ms
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
1.0ms
(fma.f64 a 9 -3)
1.0ms
(sqrt.f64 (fma.f64 a 9 -3))

simplify99.0ms (2.1%)

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

prune339.0ms (7.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1905195
Fresh101
Picked101
Done000
Total1925197
Error
0.0b
Counts
197 → 5
Alt Table
StatusErrorProgram
11.6b
(/.f64 (*.f64 (+.f64 a -1/3) (-.f64 1 (/.f64 (*.f64 rand rand) (fma.f64 9 a -3)))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.3b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (fabs.f64 (cbrt.f64 (fma.f64 9 a -3)))) (sqrt.f64 (cbrt.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))
0.4b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))) (/.f64 (cbrt.f64 rand) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
0.1b
(*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
Compiler

Compiled 4644 to 3590 computations (22.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(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)))

series25.0ms (0.5%)

Counts
1 → 18
Calls

1 calls:

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

rewrite15.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
flip-+_binary64
flip3-+_binary64
add-sqr-sqrt_binary64
associate-*r*_binary64
Counts
1 → 32
Calls

1 calls:

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

simplify67.0ms (1.4%)

Algorithm
egg-herbie
Rules
681×fma-def_binary64
660×distribute-rgt-in_binary64
628×distribute-lft-in_binary64
240×associate-/l*_binary64
224×times-frac_binary64
Counts
50 → 67
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01321497
14311384
215151240
349631222
449591222

prune274.0ms (5.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1930193
Fresh044
Picked011
Done000
Total1935198
Error
0.0b
Counts
198 → 5
Alt Table
StatusErrorProgram
11.6b
(/.f64 (*.f64 (+.f64 a -1/3) (-.f64 1 (/.f64 (*.f64 rand rand) (fma.f64 9 a -3)))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.3b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (fabs.f64 (cbrt.f64 (fma.f64 9 a -3)))) (sqrt.f64 (cbrt.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))
0.4b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))) (/.f64 (cbrt.f64 rand) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
0.1b
(*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
Compiler

Compiled 4587 to 3546 computations (22.7% saved)

localize10.0ms (0.2%)

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

series60.0ms (1.3%)

Counts
4 → 36
Calls

4 calls:

34.0ms
(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
12.0ms
(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
11.0ms
(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)

simplify101.0ms (2.1%)

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

prune306.0ms (6.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2191220
Fresh123
Picked011
Done011
Total2205225
Error
0b
Counts
225 → 5
Alt Table
StatusErrorProgram
0.1b
(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
0.3b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (fabs.f64 (cbrt.f64 (fma.f64 9 a -3)))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))
0.4b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))) (/.f64 (cbrt.f64 rand) (cbrt.f64 (sqrt.f64 (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
(+.f64 a (fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3))) -1/3))
Compiler

Compiled 5606 to 4430 computations (21% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series61.0ms (1.3%)

Counts
4 → 36
Calls

4 calls:

36.0ms
(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3))) -1/3)
16.0ms
(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3)))
8.0ms
(sqrt.f64 (fma.f64 9 a -3))
2.0ms
(fma.f64 9 a -3)

rewrite11.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity_binary64
24×times-frac_binary64
23×add-sqr-sqrt_binary64
22×add-cube-cbrt_binary64
18×sqrt-prod_binary64
Counts
4 → 85
Calls

4 calls:

5.0ms
(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3)))
1.0ms
(sqrt.f64 (fma.f64 9 a -3))
0.0ms
(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3))) -1/3)
0.0ms
(fma.f64 9 a -3)

simplify85.0ms (1.8%)

Algorithm
egg-herbie
Rules
519×fma-neg_binary64
501×fma-def_binary64
467×times-frac_binary64
366×associate-/l*_binary64
246×associate-*l*_binary64
Counts
121 → 161
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01932461
14822204
213922155
347322149
450982149

prune193.0ms (4.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1601161
Fresh112
Picked101
Done022
Total1624166
Error
0b
Counts
166 → 4
Alt Table
StatusErrorProgram
0.1b
(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
0.3b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (fabs.f64 (cbrt.f64 (fma.f64 9 a -3)))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))
0.1b
(*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.3b
(+.f64 a (fma.f64 rand (*.f64 (/.f64 (sqrt.f64 (+.f64 -1/3 a)) (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (/.f64 (sqrt.f64 (+.f64 -1/3 a)) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))) -1/3))
Compiler

Compiled 3712 to 2858 computations (23% saved)

regimes1.2s (25.4%)

Accuracy

Total 0.1b remaining (69%)

Threshold costs 0.1b (69%)

Counts
213 → 1
Compiler

Compiled 20266 to 16210 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
*-lft-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01520
12020
21820

end88.0ms (1.8%)

Compiler

Compiled 118 to 93 computations (21.2% saved)

Profiling

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