Details

Time bar (total: 10.3s)

analyze1.2s (11.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
13.2%86.5%0.2%10
17%82.8%0.2%11
18.2%81.5%0.2%12
21.7%78.1%0.2%13
32.9%66.9%0.2%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample25.0ms (0.2%)

Algorithm
intervals
Results
11.0ms256×body128valid
1.0ms26×body128invalid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify118.0ms (1.1%)

Algorithm
egg-herbie
Rules
1539×fma-neg_binary64
1346×fma-def_binary64
1046×div-sub_binary64
750×associate-/r/_binary64
420×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01116
12616
24916
39616
418316
533916
665716
7172616
8283016
9268716
10295116
11317216
12325816
13429716
14521316

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
11.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
11.0b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
Compiler

Compiled 59 to 33 computations (44.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(-.f64 t (*.f64 a z))
10.7b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

series71.0ms (0.7%)

Counts
2 → 69
Calls

2 calls:

65.0ms
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
5.0ms
(-.f64 t (*.f64 a z))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
2 → 54
Calls

2 calls:

5.0ms
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
2.0ms
(-.f64 t (*.f64 a z))

simplify132.0ms (1.3%)

Algorithm
egg-herbie
Rules
841×fma-def_binary64
684×cancel-sign-sub-inv_binary64
237×fma-neg_binary64
199×sub-neg_binary64
173×times-frac_binary64
Counts
123 → 136
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02053833
16213570
223033442
348763442
449903442
549503442

prune109.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1279136
Fresh000
Picked011
Done000
Total12710137
Error
3.9b
Counts
137 → 10
Alt Table
StatusErrorProgram
11.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
37.6b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
11.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (/.f64 (-.f64 x (*.f64 y z)) (cbrt.f64 (-.f64 t (*.f64 a z)))))
34.0b
(/.f64 (-.f64 x (*.f64 y z)) t)
38.0b
(/.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) (/.f64 (-.f64 t (*.f64 a z)) (sqrt.f64 (-.f64 x (*.f64 y z)))))
38.6b
(-.f64 (+.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)) (/.f64 y a)) (/.f64 x (*.f64 a z)))
41.2b
(/.f64 y a)
34.5b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y z) (*.f64 y z))) (*.f64 (-.f64 t (*.f64 z a)) (fma.f64 y z x)))
40.5b
(/.f64 x t)
11.0b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
Compiler

Compiled 3905 to 1153 computations (70.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z)))))
4.2b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (/.f64 (-.f64 x (*.f64 y z)) (cbrt.f64 (-.f64 t (*.f64 a z)))))
4.5b
(/.f64 (-.f64 x (*.f64 y z)) (cbrt.f64 (-.f64 t (*.f64 a z))))
8.6b
(cbrt.f64 (-.f64 t (*.f64 a z)))

series540.0ms (5.3%)

Counts
4 → 192
Calls

4 calls:

331.0ms
(/.f64 (-.f64 x (*.f64 y z)) (cbrt.f64 (-.f64 t (*.f64 a z))))
83.0ms
(/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z)))))
71.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (/.f64 (-.f64 x (*.f64 y z)) (cbrt.f64 (-.f64 t (*.f64 a z)))))
54.0ms
(cbrt.f64 (-.f64 t (*.f64 a z)))

rewrite75.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
62×add-exp-log_binary64
58×add-sqr-sqrt_binary64
54×times-frac_binary64
40×*-un-lft-identity_binary64
37×add-cube-cbrt_binary64
Counts
4 → 188
Calls

4 calls:

34.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (/.f64 (-.f64 x (*.f64 y z)) (cbrt.f64 (-.f64 t (*.f64 a z)))))
7.0ms
(/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z)))))
5.0ms
(/.f64 (-.f64 x (*.f64 y z)) (cbrt.f64 (-.f64 t (*.f64 a z))))
3.0ms
(cbrt.f64 (-.f64 t (*.f64 a z)))

simplify361.0ms (3.5%)

Algorithm
egg-herbie
Rules
908×fma-def_binary64
309×*-commutative_binary64
222×sub-neg_binary64
158×cancel-sign-sub-inv_binary64
154×+-commutative_binary64
Counts
380 → 507
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
091118293
1298017112
2483517082
3509517082

prune520.0ms (5.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New6452647
Fresh088
Picked011
Done011
Total64512657
Error
3.9b
Counts
657 → 12
Alt Table
StatusErrorProgram
38.0b
(/.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) (/.f64 (-.f64 t (*.f64 a z)) (sqrt.f64 (-.f64 x (*.f64 y z)))))
30.6b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))) x))
38.6b
(-.f64 (+.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)) (/.f64 y a)) (/.f64 x (*.f64 a z)))
46.0b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (*.f64 (pow.f64 (/.f64 1 (-.f64 t (*.f64 a z))) 1/3) x))
11.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
37.6b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
11.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (/.f64 (-.f64 x (*.f64 y z)) (cbrt.f64 (-.f64 t (*.f64 a z)))))
34.0b
(/.f64 (-.f64 x (*.f64 y z)) t)
41.2b
(/.f64 y a)
34.5b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y z) (*.f64 y z))) (*.f64 (-.f64 t (*.f64 z a)) (fma.f64 y z x)))
40.5b
(/.f64 x t)
11.0b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
Compiler

Compiled 34586 to 13008 computations (62.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
0.5b
(*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
5.4b
(cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))))
10.7b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

series2.2s (21%)

Counts
3 → 180
Calls

3 calls:

1.4s
(*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
633.0ms
(cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))))
82.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))

rewrite80.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
104×cbrt-prod_binary64
78×add-sqr-sqrt_binary64
61×times-frac_binary64
50×*-un-lft-identity_binary64
50×add-cube-cbrt_binary64
Counts
3 → 170
Calls

3 calls:

20.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
17.0ms
(*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
4.0ms
(cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))))

simplify451.0ms (4.4%)

Algorithm
egg-herbie
Rules
466×fma-def_binary64
287×associate-/l*_binary64
259×times-frac_binary64
175×sqr-pow_binary64
124×unpow1/3_binary64
Counts
350 → 446
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0300543746
1544543746

prune1.7s (16.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New103011031
Fresh189
Picked011
Done022
Total1031121043
Error
2.7b
Counts
1043 → 12
Alt Table
StatusErrorProgram
34.0b
(/.f64 (-.f64 x (*.f64 y z)) t)
37.2b
(-.f64 (+.f64 (/.f64 (*.f64 a (*.f64 z x)) (*.f64 t t)) (/.f64 x t)) (/.f64 y (/.f64 t z)))
38.0b
(/.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) (/.f64 (-.f64 t (*.f64 a z)) (sqrt.f64 (-.f64 x (*.f64 y z)))))
30.6b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))) x))
38.6b
(-.f64 (+.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)) (/.f64 y a)) (/.f64 x (*.f64 a z)))
46.0b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (*.f64 (pow.f64 (/.f64 1 (-.f64 t (*.f64 a z))) 1/3) x))
11.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
37.6b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
11.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (/.f64 (-.f64 x (*.f64 y z)) (cbrt.f64 (-.f64 t (*.f64 a z)))))
41.2b
(/.f64 y a)
34.5b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y z) (*.f64 y z))) (*.f64 (-.f64 t (*.f64 z a)) (fma.f64 y z x)))
11.0b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
Compiler

Compiled 121182 to 49445 computations (59.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z)))))
0.7b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))) x))
8.2b
(cbrt.f64 (/.f64 1 (-.f64 t (*.f64 a z))))
8.6b
(cbrt.f64 (-.f64 t (*.f64 a z)))

series109.0ms (1.1%)

Counts
2 → 84
Calls

2 calls:

63.0ms
(cbrt.f64 (/.f64 1 (-.f64 t (*.f64 a z))))
46.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))) x))

rewrite28.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
47×add-exp-log_binary64
27×prod-exp_binary64
16×add-cbrt-cube_binary64
15×associate-*l*_binary64
15×cbrt-prod_binary64
Counts
2 → 77
Calls

2 calls:

15.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))) x))
3.0ms
(cbrt.f64 (/.f64 1 (-.f64 t (*.f64 a z))))

simplify129.0ms (1.3%)

Algorithm
egg-herbie
Rules
359×associate-*r*_binary64
311×times-frac_binary64
297×associate-*l*_binary64
225×associate-/r*_binary64
200×associate-/l*_binary64
Counts
161 → 168
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03266247
19175449
238155369
349825369

prune377.0ms (3.7%)

Pruning

13 alts after pruning (9 fresh and 4 done)

PrunedKeptTotal
New4142416
Fresh178
Picked011
Done033
Total41513428
Error
2.7b
Counts
428 → 13
Alt Table
StatusErrorProgram
34.0b
(/.f64 (-.f64 x (*.f64 y z)) t)
37.2b
(-.f64 (+.f64 (/.f64 (*.f64 a (*.f64 z x)) (*.f64 t t)) (/.f64 x t)) (/.f64 y (/.f64 t z)))
58.8b
(*.f64 (+.f64 (*.f64 2/3 (/.f64 (*.f64 t (exp.f64 (*.f64 1/3 (+.f64 (*.f64 2 (log.f64 (/.f64 1 z))) (log.f64 (/.f64 1 (pow.f64 a 2))))))) (*.f64 a z))) (exp.f64 (*.f64 1/3 (+.f64 (*.f64 2 (log.f64 (/.f64 1 z))) (log.f64 (/.f64 1 (pow.f64 a 2))))))) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))) x))
51.6b
(neg.f64 (/.f64 x (*.f64 a z)))
38.0b
(/.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) (/.f64 (-.f64 t (*.f64 a z)) (sqrt.f64 (-.f64 x (*.f64 y z)))))
30.6b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))) x))
11.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
37.6b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))) (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))))
11.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))) (/.f64 (-.f64 x (*.f64 y z)) (cbrt.f64 (-.f64 t (*.f64 a z)))))
38.6b
(-.f64 (+.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)) (/.f64 y a)) (/.f64 x (*.f64 a z)))
41.2b
(/.f64 y a)
34.5b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y z) (*.f64 y z))) (*.f64 (-.f64 t (*.f64 z a)) (fma.f64 y z x)))
11.0b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
Compiler

Compiled 19476 to 9343 computations (52% saved)

regimes1.1s (10.8%)

Accuracy

Total 4.8b remaining (71.3%)

Threshold costs 0b (0%)

Counts
117 → 2
Compiler

Compiled 20348 to 10650 computations (47.7% saved)

bsearch5.0ms (0%)

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01641
12841
24541
35541
46141
56241
66241

end1.0ms (0%)

Compiler

Compiled 33 to 14 computations (57.6% saved)

sample924.0ms (9%)

Algorithm
intervals
Results
363.0ms8000×body128valid
32.0ms743×body128invalid
Compiler

Compiled 406 to 219 computations (46.1% saved)

Profiling

Loading profile data...