Details

Time bar (total: 10.3s)

analyze2.8s (27%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.5%0.5%0
0%99.5%0.5%1
0%99.5%0.5%2
0%99.5%0.5%3
0%99.5%0.5%4
0%99.5%0.5%5
0%99.5%0.5%6
0%99.5%0.5%7
0%99.5%0.5%8
0%99.5%0.5%9
0%99.5%0.5%10
0%99.5%0.5%11
0%99.5%0.5%12
0%99.5%0.5%13
0%99.5%0.5%14
Compiler

Compiled 42 to 30 computations (28.6% saved)

sample3.6s (34.6%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results
1.7s8300×body128invalid
1.7s8256×body128valid
Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify346.0ms (3.4%)

Algorithm
egg-herbie
Rules
6437×fma-neg_binary64
684×unsub-neg_binary64
621×distribute-rgt-neg-in_binary64
515×distribute-rgt-in_binary64
434×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02943
17737
225535
377335
4171135
5277735
6347435
7347035
8349335
9351635
10353435
11353435
12352635
13354935
14354935
15354935
16363935
17413135
18367535
19367535
20367535
21938435

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
6.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
4.6b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
Compiler

Compiled 218 to 148 computations (32.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))
0.1b
(fma.f64 -27 (*.f64 j k) (*.f64 b c))
2.8b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
4.7b
(*.f64 y (*.f64 z t))

series132.0ms (1.3%)

Counts
4 → 252
Calls

4 calls:

100.0ms
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
13.0ms
(fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))
10.0ms
(fma.f64 -27 (*.f64 j k) (*.f64 b c))
8.0ms
(*.f64 y (*.f64 z t))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
4 → 50
Calls

4 calls:

4.0ms
(*.f64 y (*.f64 z t))
0.0ms
(fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))
0.0ms
(fma.f64 -27 (*.f64 j k) (*.f64 b c))
0.0ms
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))

simplify167.0ms (1.6%)

Algorithm
egg-herbie
Rules
856×fma-neg_binary64
688×associate-*l*_binary64
535×associate-*r*_binary64
523×cancel-sign-sub-inv_binary64
490×exp-prod_binary64
Counts
302 → 121
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01356517
13115980
29245783
328655781
448605781
551495781

prune175.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1156121
Fresh011
Picked101
Done000
Total1167123
Error
0.0b
Counts
123 → 7
Alt Table
StatusErrorProgram
4.6b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
4.4b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
46.5b
(cbrt.f64 (pow.f64 (fma.f64 c b (fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4)))) 3))
5.4b
(fma.f64 x (fma.f64 18 (*.f64 (*.f64 y z) t) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
6.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
5.8b
(fma.f64 c b (fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
5.2b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (*.f64 (*.f64 (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c)))) (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
Compiler

Compiled 3901 to 1865 computations (52.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
0.3b
(*.f64 27 (*.f64 k j))
4.3b
(*.f64 y (*.f64 t (*.f64 z x)))
6.1b
(*.f64 t (*.f64 z x))

series61.0ms (0.6%)

Counts
4 → 0
Calls

4 calls:

23.0ms
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
18.0ms
(*.f64 t (*.f64 z x))
16.0ms
(*.f64 y (*.f64 t (*.f64 z x)))
4.0ms
(*.f64 27 (*.f64 k j))

rewrite27.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
37×add-cbrt-cube_binary64
37×add-exp-log_binary64
37×pow1_binary64
22×cbrt-unprod_binary64
22×prod-exp_binary64
Counts
4 → 89
Calls

4 calls:

6.0ms
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
5.0ms
(*.f64 y (*.f64 t (*.f64 z x)))
4.0ms
(*.f64 t (*.f64 z x))
3.0ms
(*.f64 27 (*.f64 k j))

simplify73.0ms (0.7%)

Algorithm
egg-herbie
Rules
620×unswap-sqr_binary64
594×*-commutative_binary64
389×associate-/l/_binary64
385×sqr-pow_binary64
333×associate-/r/_binary64
Counts
89 → 104
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01311275
1288990
21009990
31695990
42239990
53346990
65183990

prune170.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New995104
Fresh246
Picked101
Done000
Total1029111
Error
0.0b
Counts
111 → 9
Alt Table
StatusErrorProgram
4.4b
(-.f64 (+.f64 (*.f64 c b) (*.f64 (*.f64 18 y) (*.f64 t (*.f64 z x)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
4.6b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
5.4b
(fma.f64 x (fma.f64 18 (*.f64 (*.f64 y z) t) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
6.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
5.8b
(fma.f64 c b (fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
4.4b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (*.f64 27 k) j))))
4.4b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (sqrt.f64 27) (*.f64 (sqrt.f64 27) (*.f64 k j))))))
30.9b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (sqrt.f64 (*.f64 27 (*.f64 k j))) (sqrt.f64 (*.f64 27 (*.f64 k j)))))))
2.9b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 (*.f64 t z) x)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
Compiler

Compiled 4601 to 2122 computations (53.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 18 (*.f64 y (*.f64 (*.f64 t z) x)))
0.3b
(*.f64 27 (*.f64 k j))
3.0b
(*.f64 (*.f64 t z) x)
4.3b
(*.f64 y (*.f64 (*.f64 t z) x))

series46.0ms (0.4%)

Counts
3 → 132
Calls

3 calls:

19.0ms
(*.f64 y (*.f64 (*.f64 t z) x))
18.0ms
(*.f64 18 (*.f64 y (*.f64 (*.f64 t z) x)))
9.0ms
(*.f64 (*.f64 t z) x)

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
31×add-cbrt-cube_binary64
31×add-exp-log_binary64
31×pow1_binary64
19×cbrt-unprod_binary64
19×prod-exp_binary64
Counts
3 → 69
Calls

3 calls:

7.0ms
(*.f64 y (*.f64 (*.f64 t z) x))
6.0ms
(*.f64 18 (*.f64 y (*.f64 (*.f64 t z) x)))
4.0ms
(*.f64 (*.f64 t z) x)

simplify110.0ms (1.1%)

Algorithm
egg-herbie
Rules
746×unswap-sqr_binary64
549×*-commutative_binary64
415×sqr-pow_binary64
251×associate-*r*_binary64
224×associate-*l*_binary64
Counts
201 → 93
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0982426
12202177
29172177
316152177
422922177
534702177
654062177

prune222.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1121113
Fresh088
Picked011
Done000
Total11210122
Error
0.0b
Counts
122 → 10
Alt Table
StatusErrorProgram
4.4b
(-.f64 (+.f64 (*.f64 c b) (*.f64 (*.f64 18 y) (*.f64 t (*.f64 z x)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
4.6b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
5.4b
(fma.f64 x (fma.f64 18 (*.f64 (*.f64 y z) t) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
6.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
5.8b
(fma.f64 c b (fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
4.4b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (*.f64 27 k) j))))
4.4b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (sqrt.f64 27) (*.f64 (sqrt.f64 27) (*.f64 k j))))))
4.6b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 (*.f64 y (*.f64 t z)) x))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
30.9b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (sqrt.f64 (*.f64 27 (*.f64 k j))) (sqrt.f64 (*.f64 27 (*.f64 k j)))))))
2.9b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 (*.f64 t z) x)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
Compiler

Compiled 4945 to 2277 computations (54% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
0.2b
(*.f64 (*.f64 27 k) j)
4.3b
(*.f64 y (*.f64 t (*.f64 z x)))
6.1b
(*.f64 t (*.f64 z x))

series5.0ms (0%)

Counts
1 → 24
Calls

1 calls:

5.0ms
(*.f64 (*.f64 27 k) j)

rewrite4.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
associate-*r*_binary64
cbrt-unprod_binary64
Counts
1 → 20
Calls

1 calls:

4.0ms
(*.f64 (*.f64 27 k) j)

simplify71.0ms (0.7%)

Algorithm
egg-herbie
Rules
537×associate-*l*_binary64
367×associate-*r*_binary64
353×*-commutative_binary64
340×cube-div_binary64
340×log-div_binary64
Counts
44 → 27
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
044380
197344
2352344
3971344
41135344
51335344
61591344
72659344
84026344
94880344

prune200.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1110111
Fresh088
Picked011
Done011
Total11110121
Error
0.0b
Counts
121 → 10
Alt Table
StatusErrorProgram
4.4b
(-.f64 (+.f64 (*.f64 c b) (*.f64 (*.f64 18 y) (*.f64 t (*.f64 z x)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
4.6b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
5.4b
(fma.f64 x (fma.f64 18 (*.f64 (*.f64 y z) t) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
6.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
5.8b
(fma.f64 c b (fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
4.4b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (*.f64 27 k) j))))
4.4b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (sqrt.f64 27) (*.f64 (sqrt.f64 27) (*.f64 k j))))))
4.6b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 (*.f64 y (*.f64 t z)) x))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
30.9b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (sqrt.f64 (*.f64 27 (*.f64 k j))) (sqrt.f64 (*.f64 27 (*.f64 k j)))))))
2.9b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 (*.f64 t z) x)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
Compiler

Compiled 4520 to 2092 computations (53.7% saved)

regimes1.5s (14.7%)

Accuracy

Total 1.6b remaining (99.1%)

Threshold costs 0b (0%)

Counts
65 → 3
Compiler

Compiled 37865 to 26944 computations (28.8% saved)

bsearch91.0ms (0.9%)

Steps
ItersRangePoint
8
1.7301765299175992e-97
7.926753054258356e-94
4.479382283497473e-94
2
-2.5637548541739587e-17
-2.3215903512825172e-17
-2.5334842913125285e-17
Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
46×*-commutative_binary64
30×+-commutative_binary64
24×distribute-rgt-neg-in_binary64
24×sub-neg_binary64
20×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
062139
1106139
2154139
3193139
4238139
5264139
6271139
7273139
8271139

end425.0ms (4.1%)

Remove

(sort j k)

(sort b c)

Compiler

Compiled 1454 to 934 computations (35.8% saved)

Profiling

Loading profile data...