Details

Time bar (total: 9.2s)

analyze1.7s (18.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
1.6%98.1%0.3%13
2.3%97.4%0.3%14
Compiler

Compiled 24 to 18 computations (25% saved)

sample243.0ms (2.7%)

Algorithm
intervals
Symmetry

(sort y z t)

(sort a b)

Results
14.0ms256×body128valid
5.0ms97×body128invalid
Compiler

Compiled 53 to 41 computations (22.6% saved)

simplify71.0ms (0.8%)

Algorithm
egg-herbie
Rules
712×fma-neg_binary64
641×fma-def_binary64
213×cancel-sign-sub-inv_binary64
172×distribute-rgt-neg-in_binary64
157×unsub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01825
13923
211521
330821
455221
590221
6120121
7143321
8167221
9178721
10179121
11179121
12179121
13167421

prune4.0ms (0%)

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
2.7b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b)))
4.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
Compiler

Compiled 126 to 90 computations (28.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x 2 (*.f64 (*.f64 a 27) b))
0.2b
(*.f64 (*.f64 a 27) b)
0.2b
(*.f64 (*.f64 z t) -9)
2.4b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b)))

series52.0ms (0.6%)

Counts
4 → 156
Calls

4 calls:

34.0ms
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b)))
7.0ms
(*.f64 (*.f64 z t) -9)
7.0ms
(fma.f64 x 2 (*.f64 (*.f64 a 27) b))
4.0ms
(*.f64 (*.f64 a 27) b)

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube_binary64
14×add-exp-log_binary64
14×pow1_binary64
associate-*r*_binary64
cbrt-unprod_binary64
Counts
4 → 60
Calls

4 calls:

4.0ms
(*.f64 (*.f64 z t) -9)
3.0ms
(*.f64 (*.f64 a 27) b)
0.0ms
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b)))
0.0ms
(fma.f64 x 2 (*.f64 (*.f64 a 27) b))

simplify99.0ms (1.1%)

Algorithm
egg-herbie
Rules
868×unswap-sqr_binary64
419×*-commutative_binary64
321×distribute-lft-in_binary64
321×distribute-rgt-in_binary64
310×fma-def_binary64
Counts
216 → 107
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01222976
12502724
28732724
314852724
429222724
552892724

prune104.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1025107
Fresh011
Picked101
Done000
Total1036109
Error
0.0b
Counts
109 → 6
Alt Table
StatusErrorProgram
2.7b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 y (*.f64 t z))))
4.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
3.0b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 (*.f64 a 27) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))
2.9b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 a (*.f64 27 b))))
28.2b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (sqrt.f64 (*.f64 (*.f64 a 27) b)) (sqrt.f64 (*.f64 (*.f64 a 27) b)))))
3.7b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b)))) (cbrt.f64 (fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b))))) (cbrt.f64 (fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b)))))
Compiler

Compiled 2462 to 1426 computations (42.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 y (*.f64 t z))))
0.2b
(*.f64 9 (*.f64 y (*.f64 t z)))
0.3b
(*.f64 27 (*.f64 a b))
6.9b
(*.f64 y (*.f64 t z))

series54.0ms (0.6%)

Counts
4 → 18
Calls

4 calls:

33.0ms
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 y (*.f64 t z))))
9.0ms
(*.f64 9 (*.f64 y (*.f64 t z)))
8.0ms
(*.f64 y (*.f64 t z))
4.0ms
(*.f64 27 (*.f64 a b))

rewrite25.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
23×pow1_binary64
12×cbrt-unprod_binary64
12×prod-exp_binary64
Counts
4 → 85
Calls

4 calls:

8.0ms
(*.f64 9 (*.f64 y (*.f64 t z)))
6.0ms
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 y (*.f64 t z))))
3.0ms
(*.f64 y (*.f64 t z))
3.0ms
(*.f64 27 (*.f64 a b))

simplify84.0ms (0.9%)

Algorithm
egg-herbie
Rules
535×*-commutative_binary64
493×cancel-sign-sub-inv_binary64
462×fma-def_binary64
344×fma-neg_binary64
215×associate-*r*_binary64
Counts
103 → 110
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01491662
13451372
212381339
333341327
449461327
548101327

prune123.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1064110
Fresh145
Picked011
Done000
Total1079116
Error
0.0b
Counts
116 → 9
Alt Table
StatusErrorProgram
2.9b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 a (*.f64 27 b))))
34.8b
(/.f64 (-.f64 (*.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x))) (*.f64 (*.f64 9 (*.f64 y (*.f64 t z))) (*.f64 9 (*.f64 y (*.f64 t z))))) (+.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 y (*.f64 t z)))))
2.7b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 y (*.f64 t z))))
4.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
2.9b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 (*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))))
3.0b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 (*.f64 a 27) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))
2.7b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3)))
28.2b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (sqrt.f64 (*.f64 (*.f64 a 27) b)) (sqrt.f64 (*.f64 (*.f64 a 27) b)))))
4.9b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 (*.f64 y t) z)))
Compiler

Compiled 3151 to 1682 computations (46.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3))
0.2b
(*.f64 (*.f64 y (*.f64 t z)) 3)
0.3b
(*.f64 27 (*.f64 a b))
6.9b
(*.f64 y (*.f64 t z))

series22.0ms (0.2%)

Counts
2 → 72
Calls

2 calls:

12.0ms
(*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3))
9.0ms
(*.f64 (*.f64 y (*.f64 t z)) 3)

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
25×add-cbrt-cube_binary64
25×add-exp-log_binary64
25×pow1_binary64
16×cbrt-unprod_binary64
16×prod-exp_binary64
Counts
2 → 52
Calls

2 calls:

7.0ms
(*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3))
5.0ms
(*.f64 (*.f64 y (*.f64 t z)) 3)

simplify98.0ms (1.1%)

Algorithm
egg-herbie
Rules
486×sqr-pow_binary64
440×*-commutative_binary64
302×fma-def_binary64
299×cube-prod_binary64
257×pow-sqr_binary64
Counts
124 → 69
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0831577
11881346
27641346
313851346
422061346
533061346
646591346
749711346

prune168.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1090109
Fresh077
Picked011
Done011
Total1099118
Error
0.0b
Counts
118 → 9
Alt Table
StatusErrorProgram
2.9b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 a (*.f64 27 b))))
34.8b
(/.f64 (-.f64 (*.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x))) (*.f64 (*.f64 9 (*.f64 y (*.f64 t z))) (*.f64 9 (*.f64 y (*.f64 t z))))) (+.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 y (*.f64 t z)))))
2.7b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 y (*.f64 t z))))
4.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
2.9b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 (*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))))
3.0b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 (*.f64 a 27) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))
2.7b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3)))
28.2b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (sqrt.f64 (*.f64 (*.f64 a 27) b)) (sqrt.f64 (*.f64 (*.f64 a 27) b)))))
4.9b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 (*.f64 y t) z)))
Compiler

Compiled 3311 to 1928 computations (41.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))))
0.5b
(*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))))
6.9b
(*.f64 y (*.f64 t z))
12.5b
(cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))

series2.2s (23.6%)

Counts
3 → 108
Calls

3 calls:

1.4s
(*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))))
682.0ms
(cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))
76.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))))

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
16×pow1/3_binary64
11×pow-prod-up_binary64
11×add-sqr-sqrt_binary64
10×add-exp-log_binary64
Counts
3 → 79
Calls

3 calls:

11.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))))
5.0ms
(*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))))
3.0ms
(cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))

simplify125.0ms (1.4%)

Algorithm
egg-herbie
Rules
348×fma-neg_binary64
338×unswap-sqr_binary64
298×exp-prod_binary64
282×exp-sum_binary64
275×*-commutative_binary64
Counts
187 → 137
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01863802
14213569
29183061
323932802
448072802
550792802

prune346.0ms (3.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New2601261
Fresh156
Picked011
Done022
Total2619270
Error
0.0b
Counts
270 → 9
Alt Table
StatusErrorProgram
2.9b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 a (*.f64 27 b))))
34.8b
(/.f64 (-.f64 (*.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x))) (*.f64 (*.f64 9 (*.f64 y (*.f64 t z))) (*.f64 9 (*.f64 y (*.f64 t z))))) (+.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 y (*.f64 t z)))))
2.7b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 y (*.f64 t z))))
4.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
2.9b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 (*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))))
4.4b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 9 (*.f64 t (*.f64 z y))))
3.0b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 (*.f64 a 27) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))
2.7b
(-.f64 (+.f64 (*.f64 27 (*.f64 a b)) (*.f64 2 x)) (*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3)))
28.2b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (sqrt.f64 (*.f64 (*.f64 a 27) b)) (sqrt.f64 (*.f64 (*.f64 a 27) b)))))
Compiler

Compiled 10745 to 5418 computations (49.6% saved)

regimes1.7s (18.4%)

Accuracy

Total 0.8b remaining (97.1%)

Threshold costs 0.8b (97.1%)

Counts
78 → 3
Compiler

Compiled 30459 to 22210 computations (27.1% saved)

bsearch4.0ms (0%)

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
23×*-commutative_binary64
14×+-commutative_binary64
12×distribute-rgt-neg-in_binary64
11×distribute-lft-neg-in_binary64
11×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039133
165133
287133
3111133
4130133
5138133
6140133
7139133

end54.0ms (0.6%)

Compiler

Compiled 480 to 325 computations (32.3% saved)

sample1.8s (20.2%)

Algorithm
intervals
Results
502.0ms8000×body128valid
194.0ms3012×body128invalid
Compiler

Compiled 400 to 275 computations (31.3% saved)

Profiling

Loading profile data...