Details

Time bar (total: 4.1s)

analyze100.0ms (2.5%)

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)

sample270.0ms (6.6%)

Algorithm
intervals
Results
19.0ms256×body128valid
1.0ms13×body128invalid
0.0msbody128nan
Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify96.0ms (2.4%)

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)

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))
0.3b
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

series79.0ms (1.9%)

Counts
4 → 50
Calls

4 calls:

44.0ms
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
25.0ms
(*.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))
2.0ms
(fma.f64 a 9 -3)

rewrite20.0ms (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:

12.0ms
(*.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
(sqrt.f64 (fma.f64 a 9 -3))
0.0ms
(fma.f64 a 9 -3)

simplify102.0ms (2.5%)

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

prune256.0ms (6.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1878195
Fresh011
Picked101
Done000
Total1889197
Error
0b
Counts
197 → 9
Alt Table
StatusErrorProgram
1.3b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (cbrt.f64 (*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))) (cbrt.f64 (*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.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)))))))
31.0b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 (sqrt.f64 rand) (/.f64 (sqrt.f64 rand) (sqrt.f64 (fma.f64 9 a -3))))))
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))))
0.1b
(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
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 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
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))))))
0.6b
(*.f64 (sqrt.f64 (-.f64 a 1/3)) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
Compiler

Compiled 4830 to 3746 computations (22.4% saved)

localize8.0ms (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))
0.3b
(/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))
7.8b
(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))

series160.0ms (3.9%)

Counts
4 → 48
Calls

4 calls:

68.0ms
(sqrt.f64 (fma.f64 9 a -3))
58.0ms
(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))
32.0ms
(/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))
2.0ms
(fma.f64 9 a -3)

rewrite22.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt_binary64
38×times-frac_binary64
36×*-un-lft-identity_binary64
34×add-cube-cbrt_binary64
25×sqrt-prod_binary64
Counts
4 → 115
Calls

4 calls:

9.0ms
(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))
3.0ms
(/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))
1.0ms
(sqrt.f64 (fma.f64 9 a -3))
0.0ms
(fma.f64 9 a -3)

simplify77.0ms (1.9%)

Algorithm
egg-herbie
Rules
545×associate-/l*_binary64
489×fma-def_binary64
422×times-frac_binary64
321×distribute-rgt-in_binary64
308×distribute-lft-in_binary64
Counts
163 → 211
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02222948
15542766
219072703
351582703

prune339.0ms (8.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2083211
Fresh538
Picked011
Done000
Total2137220
Error
0b
Counts
220 → 7
Alt Table
StatusErrorProgram
0.1b
(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
0.2b
(+.f64 (+.f64 a -1/3) (*.f64 (sqrt.f64 (+.f64 a -1/3)) (*.f64 (sqrt.f64 (+.f64 a -1/3)) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
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))))))
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)))))))
30.9b
(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (*.f64 (sqrt.f64 rand) (/.f64 (sqrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))
0.1b
(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))))
Compiler

Compiled 5368 to 4005 computations (25.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))
0.2b
(*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))
0.2b
(/.f64 1 (-.f64 (*.f64 9 a) 3))
7.8b
(*.f64 (+.f64 a -1/3) (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))))

series84.0ms (2.1%)

Counts
4 → 36
Calls

4 calls:

37.0ms
(*.f64 (+.f64 a -1/3) (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))))
32.0ms
(*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))
12.0ms
(sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))
3.0ms
(/.f64 1 (-.f64 (*.f64 9 a) 3))

rewrite53.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64
33×sqrt-prod_binary64
33×*-un-lft-identity_binary64
31×times-frac_binary64
29×add-cube-cbrt_binary64
Counts
4 → 132
Calls

4 calls:

20.0ms
(/.f64 1 (-.f64 (*.f64 9 a) 3))
10.0ms
(*.f64 (+.f64 a -1/3) (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))))
9.0ms
(*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))
5.0ms
(sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))

simplify109.0ms (2.7%)

Algorithm
egg-herbie
Rules
745×fma-def_binary64
494×times-frac_binary64
341×distribute-rgt-in_binary64
236×fma-neg_binary64
193×associate-*r*_binary64
Counts
168 → 236
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02593058
16702870
222002775
346032773
449662773

prune325.0ms (8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2360236
Fresh055
Picked011
Done011
Total2367243
Error
0b
Counts
243 → 7
Alt Table
StatusErrorProgram
0.1b
(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
0.2b
(+.f64 (+.f64 a -1/3) (*.f64 (sqrt.f64 (+.f64 a -1/3)) (*.f64 (sqrt.f64 (+.f64 a -1/3)) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
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))))))
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)))))))
30.9b
(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (*.f64 (sqrt.f64 rand) (/.f64 (sqrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))
0.1b
(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))))
Compiler

Compiled 6594 to 5243 computations (20.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series64.0ms (1.6%)

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)
15.0ms
(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
12.0ms
(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
3.0ms
(/.f64 1 (fma.f64 9 a -3))

rewrite21.0ms (0.5%)

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:

11.0ms
(*.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 (2.5%)

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

prune296.0ms (7.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New2200220
Fresh044
Picked011
Done022
Total2207227
Error
0b
Counts
227 → 7
Alt Table
StatusErrorProgram
0.1b
(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
0.2b
(+.f64 (+.f64 a -1/3) (*.f64 (sqrt.f64 (+.f64 a -1/3)) (*.f64 (sqrt.f64 (+.f64 a -1/3)) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
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))))))
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)))))))
30.9b
(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (*.f64 (sqrt.f64 rand) (/.f64 (sqrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))
0.1b
(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))))
Compiler

Compiled 5572 to 4404 computations (21% saved)

regimes464.0ms (11.4%)

Accuracy

Total 0.1b remaining (85%)

Threshold costs 0.1b (85%)

Counts
105 → 1
Compiler

Compiled 8894 to 6994 computations (21.4% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11522
21522

end1.0ms (0%)

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample990.0ms (24.3%)

Algorithm
intervals
Results
616.0ms8000×body128valid
22.0ms278×body128nan
19.0ms272×body128invalid
Compiler

Compiled 193 to 154 computations (20.2% saved)

Profiling

Loading profile data...