Details

Time bar (total: 9.4s)

analyze2.7s (28.6%)

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)

sample74.0ms (0.8%)

Algorithm
intervals
Results
20.0ms256×body128valid
7.0ms89×body128invalid
Compiler

Compiled 53 to 41 computations (22.6% saved)

simplify55.0ms (0.6%)

Algorithm
egg-herbie
Rules
213×cancel-sign-sub-inv_binary64
172×distribute-rgt-neg-in_binary64
162×unsub-neg_binary64
99×distribute-rgt-in_binary64
94×distribute-lft-neg-in_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01825
13825
210525
326925
440925
562925
674125
792425
890425
990525
1090525
1190525
1278825

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
2.5b
Counts
1 → 1
Alt Table
StatusErrorProgram
2.5b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
Compiler

Compiled 46 to 34 computations (26.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
0.2b
(*.f64 (*.f64 y 9) z)
0.2b
(*.f64 (*.f64 a 27) b)
6.4b
(*.f64 (*.f64 (*.f64 y 9) z) t)

rewrite106.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
23×pow1_binary64
12×cbrt-unprod_binary64
12×prod-exp_binary64
Counts
4 → 72
Calls

4 calls:

5.0ms
(*.f64 (*.f64 (*.f64 y 9) z) t)
5.0ms
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
4.0ms
(*.f64 (*.f64 y 9) z)
3.0ms
(*.f64 (*.f64 a 27) b)
Compiler

Compiled 1628 to 1070 computations (34.3% saved)

series130.0ms (1.4%)

Error
0.1b
Counts
4 → 57
Calls

4 calls:

78.0ms
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
21.0ms
(*.f64 (*.f64 (*.f64 y 9) z) t)
10.0ms
(*.f64 (*.f64 y 9) z)
10.0ms
(*.f64 (*.f64 a 27) b)
Compiler

Compiled 2154 to 1582 computations (26.6% saved)

simplify107.0ms (1.1%)

Algorithm
egg-herbie
Rules
356×associate-*l*_binary64
315×exp-prod_binary64
261×log-prod_binary64
254×associate-*r*_binary64
226×distribute-rgt-in_binary64
Counts
129 → 89
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01512034
13891875
216131863
333351863
447831863
549431863

prune59.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New80989
Fresh000
Picked101
Done000
Total81990
Error
0.0b
Counts
90 → 9
Alt Table
StatusErrorProgram
35.0b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 (*.f64 9 y) (sqrt.f64 z)) (sqrt.f64 z)) t)) (*.f64 (*.f64 a 27) b))
1.6b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 9 (*.f64 y (*.f64 t z)))) (+.f64 x x))
15.1b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (cbrt.f64 (*.f64 729 (pow.f64 (*.f64 y z) 3))) t)) (*.f64 (*.f64 a 27) b))
2.5b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (pow.f64 (*.f64 9 (*.f64 y z)) 1) t)) (*.f64 (*.f64 a 27) b))
20.1b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 (*.f64 27 a) (sqrt.f64 b)) (sqrt.f64 b)))
2.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 (*.f64 27 a) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
2.8b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 9 (*.f64 y z)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))) (*.f64 (*.f64 a 27) b))
1.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y 9) (*.f64 t z))) (*.f64 (*.f64 a 27) b))
34.9b
(/.f64 (-.f64 (*.f64 (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9)) (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9))) (*.f64 a (*.f64 (*.f64 729 a) (*.f64 b b)))) (-.f64 (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9)) (*.f64 27 (*.f64 a b))))
Compiler

Compiled 1497 to 874 computations (41.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 9 (*.f64 y (*.f64 t z)))) (+.f64 x x))
0.2b
(*.f64 9 (*.f64 y (*.f64 t z)))
0.3b
(*.f64 27 (*.f64 a b))
7.9b
(*.f64 y (*.f64 t z))

rewrite108.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
23×pow1_binary64
16×add-log-exp_binary64
12×*-un-lft-identity_binary64
Counts
4 → 81
Calls

4 calls:

10.0ms
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 9 (*.f64 y (*.f64 t z)))) (+.f64 x x))
5.0ms
(*.f64 9 (*.f64 y (*.f64 t z)))
4.0ms
(*.f64 y (*.f64 t z))
3.0ms
(*.f64 27 (*.f64 a b))
Compiler

Compiled 2039 to 841 computations (58.8% saved)

series134.0ms (1.4%)

Error
0.0b
Counts
4 → 60
Calls

4 calls:

79.0ms
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 9 (*.f64 y (*.f64 t z)))) (+.f64 x x))
22.0ms
(*.f64 9 (*.f64 y (*.f64 t z)))
19.0ms
(*.f64 y (*.f64 t z))
10.0ms
(*.f64 27 (*.f64 a b))
Compiler

Compiled 2258 to 1613 computations (28.6% saved)

simplify99.0ms (1%)

Algorithm
egg-herbie
Rules
461×distribute-rgt-in_binary64
426×distribute-lft-in_binary64
262×cancel-sign-sub-inv_binary64
243×associate-*r*_binary64
214×associate-*l*_binary64
Counts
141 → 94
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01712670
14522241
215962208
346752208
450252208

prune48.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New91394
Fresh358
Picked101
Done000
Total958103
Error
0.0b
Counts
103 → 8
Alt Table
StatusErrorProgram
35.0b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 (*.f64 9 y) (sqrt.f64 z)) (sqrt.f64 z)) t)) (*.f64 (*.f64 a 27) b))
15.1b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (cbrt.f64 (*.f64 729 (pow.f64 (*.f64 y z) 3))) t)) (*.f64 (*.f64 a 27) b))
2.5b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (pow.f64 (*.f64 9 (*.f64 y z)) 1) t)) (*.f64 (*.f64 a 27) b))
20.1b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 (*.f64 27 a) (sqrt.f64 b)) (sqrt.f64 b)))
1.6b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (*.f64 y 9) (*.f64 t z))) (+.f64 x x))
1.6b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3))) (+.f64 x x))
1.7b
(+.f64 (-.f64 (*.f64 (sqrt.f64 27) (*.f64 (*.f64 a b) (sqrt.f64 27))) (*.f64 9 (*.f64 y (*.f64 t z)))) (+.f64 x x))
34.9b
(/.f64 (-.f64 (*.f64 (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9)) (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9))) (*.f64 a (*.f64 (*.f64 729 a) (*.f64 b b)))) (-.f64 (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9)) (*.f64 27 (*.f64 a b))))
Compiler

Compiled 1410 to 730 computations (48.2% saved)

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (*.f64 y 9) (*.f64 t z))) (+.f64 x x))
0.3b
(*.f64 27 (*.f64 a b))
7.9b
(*.f64 (*.f64 y 9) (*.f64 t z))

rewrite87.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
20×add-cbrt-cube_binary64
20×add-exp-log_binary64
20×pow1_binary64
15×add-log-exp_binary64
11×cbrt-unprod_binary64
Counts
3 → 64
Calls

3 calls:

9.0ms
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (*.f64 y 9) (*.f64 t z))) (+.f64 x x))
5.0ms
(*.f64 (*.f64 y 9) (*.f64 t z))
3.0ms
(*.f64 27 (*.f64 a b))
Compiler

Compiled 1723 to 810 computations (53% saved)

series121.0ms (1.3%)

Error
0.0b
Counts
3 → 51
Calls

3 calls:

78.0ms
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (*.f64 y 9) (*.f64 t z))) (+.f64 x x))
20.0ms
(*.f64 (*.f64 y 9) (*.f64 t z))
16.0ms
(*.f64 27 (*.f64 a b))
Compiler

Compiled 1861 to 1332 computations (28.4% saved)

simplify118.0ms (1.3%)

Algorithm
egg-herbie
Rules
470×distribute-rgt-in_binary64
435×distribute-lft-in_binary64
315×cancel-sign-sub-inv_binary64
251×distribute-rgt-neg-in_binary64
249×associate-*l*_binary64
Counts
115 → 78
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01632419
14532041
216322008
346332008
449922008
549962008

prune42.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New77178
Fresh167
Picked011
Done000
Total78886
Error
0.0b
Counts
86 → 8
Alt Table
StatusErrorProgram
34.9b
(/.f64 (-.f64 (*.f64 (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9)) (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9))) (*.f64 a (*.f64 (*.f64 729 a) (*.f64 b b)))) (-.f64 (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9)) (*.f64 27 (*.f64 a b))))
3.4b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (*.f64 t (*.f64 9 y)) z)) (+.f64 x x))
15.1b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (cbrt.f64 (*.f64 729 (pow.f64 (*.f64 y z) 3))) t)) (*.f64 (*.f64 a 27) b))
2.5b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (pow.f64 (*.f64 9 (*.f64 y z)) 1) t)) (*.f64 (*.f64 a 27) b))
20.1b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 (*.f64 27 a) (sqrt.f64 b)) (sqrt.f64 b)))
1.6b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (*.f64 y 9) (*.f64 t z))) (+.f64 x x))
1.6b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3))) (+.f64 x x))
1.7b
(+.f64 (-.f64 (*.f64 (sqrt.f64 27) (*.f64 (*.f64 a b) (sqrt.f64 27))) (*.f64 9 (*.f64 y (*.f64 t z)))) (+.f64 x x))
Compiler

Compiled 1219 to 645 computations (47.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3))
0.3b
(*.f64 27 (*.f64 a b))
0.3b
(*.f64 (*.f64 y (*.f64 t z)) 3)
7.9b
(*.f64 y (*.f64 t z))

rewrite110.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
37×add-cbrt-cube_binary64
37×add-exp-log_binary64
37×pow1_binary64
22×cbrt-unprod_binary64
22×prod-exp_binary64
Counts
4 → 84
Calls

4 calls:

10.0ms
(*.f64 (*.f64 y (*.f64 t z)) 3)
8.0ms
(*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3))
4.0ms
(*.f64 y (*.f64 t z))
3.0ms
(*.f64 27 (*.f64 a b))
Compiler

Compiled 1896 to 936 computations (50.6% saved)

series81.0ms (0.9%)

Error
0.0b
Counts
4 → 33
Calls

4 calls:

24.0ms
(*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3))
20.0ms
(*.f64 y (*.f64 t z))
20.0ms
(*.f64 (*.f64 y (*.f64 t z)) 3)
15.0ms
(*.f64 27 (*.f64 a b))
Compiler

Compiled 1725 to 1234 computations (28.5% saved)

simplify109.0ms (1.2%)

Algorithm
egg-herbie
Rules
575×*-commutative_binary64
328×cube-prod_binary64
307×pow-sqr_binary64
296×sqr-pow_binary64
271×associate-*l*_binary64
Counts
117 → 65
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01241481
12801175
210361175
317771175
427001175
538371175
646171175
751221175

prune34.0ms (0.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New65065
Fresh066
Picked011
Done011
Total65873
Error
0.0b
Counts
73 → 8
Alt Table
StatusErrorProgram
34.9b
(/.f64 (-.f64 (*.f64 (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9)) (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9))) (*.f64 a (*.f64 (*.f64 729 a) (*.f64 b b)))) (-.f64 (+.f64 (+.f64 x x) (*.f64 (*.f64 y (*.f64 t z)) -9)) (*.f64 27 (*.f64 a b))))
3.4b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (*.f64 t (*.f64 9 y)) z)) (+.f64 x x))
15.1b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (cbrt.f64 (*.f64 729 (pow.f64 (*.f64 y z) 3))) t)) (*.f64 (*.f64 a 27) b))
2.5b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (pow.f64 (*.f64 9 (*.f64 y z)) 1) t)) (*.f64 (*.f64 a 27) b))
20.1b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 (*.f64 27 a) (sqrt.f64 b)) (sqrt.f64 b)))
1.6b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (*.f64 y 9) (*.f64 t z))) (+.f64 x x))
1.6b
(+.f64 (-.f64 (*.f64 27 (*.f64 a b)) (*.f64 (sqrt.f64 9) (*.f64 (*.f64 y (*.f64 t z)) 3))) (+.f64 x x))
1.7b
(+.f64 (-.f64 (*.f64 (sqrt.f64 27) (*.f64 (*.f64 a b) (sqrt.f64 27))) (*.f64 9 (*.f64 y (*.f64 t z)))) (+.f64 x x))
Compiler

Compiled 814 to 448 computations (45% saved)

regimes2.1s (22%)

Accuracy

Total 1.1b remaining (97.4%)

Threshold costs 0b (0%)

Compiler

Compiled 42990 to 30923 computations (28.1% saved)

bsearch47.0ms (0.5%)

Steps
ItersRangePoint
8
1.5670357519327951e+109
9.083303842744861e+112
1.681822738427985e+109
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
18×*-commutative_binary64
12×+-commutative_binary64
10×distribute-rgt-neg-in_binary64
10×sub-neg_binary64
distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02956
15156
27856
39956
411156
511656
611756
711656

end78.0ms (0.8%)

Remove

(sort a b)

Compiler

Compiled 308 to 210 computations (31.8% saved)

sample2.8s (30.1%)

Algorithm
intervals
Results
603.0ms8000×body128valid
185.0ms2963×body128invalid
Compiler

Compiled 308 to 213 computations (30.8% saved)

Profiling

Loading profile data...