Details

Time bar (total: 9.8s)

analyze2.7s (27.7%)

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)

sample169.0ms (1.7%)

Algorithm
intervals
Symmetry

(sort y z)

(sort b c)

(sort j k)

Results
27.0ms256×body128valid
27.0ms255×body128invalid
Compiler

Compiled 93 to 69 computations (25.8% saved)

simplify334.0ms (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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.6b
(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))))
7.2b
(-.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))
Compiler

Compiled 218 to 148 computations (32.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 x 18) y)
0.5b
(*.f64 (*.f64 j 27) k)
5.3b
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)
5.9b
(*.f64 (*.f64 (*.f64 x 18) y) z)

series39.0ms (0.4%)

Counts
4 → 132
Calls

4 calls:

19.0ms
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)
10.0ms
(*.f64 (*.f64 (*.f64 x 18) y) z)
5.0ms
(*.f64 (*.f64 x 18) y)
4.0ms
(*.f64 (*.f64 j 27) k)

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:

7.0ms
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)
6.0ms
(*.f64 (*.f64 (*.f64 x 18) y) z)
4.0ms
(*.f64 (*.f64 j 27) k)
4.0ms
(*.f64 (*.f64 x 18) y)

simplify111.0ms (1.1%)

Algorithm
egg-herbie
Rules
708×unswap-sqr_binary64
612×sqr-pow_binary64
463×associate-*l*_binary64
289×associate-*r*_binary64
215×pow-sqr_binary64
Counts
221 → 127
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01502582
13512318
214072318
318312318
425852318
539632318
657602318

prune226.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1216127
Fresh011
Picked101
Done000
Total1227129
Error
0.0b
Counts
129 → 7
Alt Table
StatusErrorProgram
7.6b
(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))))
6.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
6.1b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
5.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 18 (*.f64 y (*.f64 z x))) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
7.4b
(-.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 (*.f64 j 27) (*.f64 (cbrt.f64 k) (cbrt.f64 k))) (cbrt.f64 k)))
6.9b
(-.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 j (*.f64 27 k)))
23.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 (*.f64 z x) t)))) (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 (*.f64 z x) t))))) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
Compiler

Compiled 5258 to 3071 computations (41.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 18 (*.f64 y (*.f64 z x)))
0.5b
(*.f64 (*.f64 j 27) k)
5.3b
(*.f64 (*.f64 18 (*.f64 y (*.f64 z x))) t)
6.0b
(*.f64 y (*.f64 z x))

series40.0ms (0.4%)

Counts
3 → 48
Calls

3 calls:

21.0ms
(*.f64 (*.f64 18 (*.f64 y (*.f64 z x))) t)
11.0ms
(*.f64 18 (*.f64 y (*.f64 z x)))
8.0ms
(*.f64 y (*.f64 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 (*.f64 18 (*.f64 y (*.f64 z x))) t)
6.0ms
(*.f64 18 (*.f64 y (*.f64 z x)))
4.0ms
(*.f64 y (*.f64 z x))

simplify85.0ms (0.9%)

Algorithm
egg-herbie
Rules
632×unswap-sqr_binary64
527×*-commutative_binary64
465×sqr-pow_binary64
240×associate-*l*_binary64
221×associate-*r*_binary64
Counts
117 → 75
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0981685
12281448
28971448
315961448
422511448
535161448
652041448

prune173.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1050105
Fresh066
Picked011
Done000
Total1057112
Error
0.0b
Counts
112 → 7
Alt Table
StatusErrorProgram
7.6b
(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))))
6.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
6.1b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
5.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 18 (*.f64 y (*.f64 z x))) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
7.4b
(-.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 (*.f64 j 27) (*.f64 (cbrt.f64 k) (cbrt.f64 k))) (cbrt.f64 k)))
6.9b
(-.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 j (*.f64 27 k)))
23.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 (*.f64 z x) t)))) (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 (*.f64 z x) t))))) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
Compiler

Compiled 4450 to 2402 computations (46% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) t) (*.f64 (*.f64 a 4) t))
0.5b
(*.f64 (*.f64 j 27) k)
4.1b
(*.f64 (*.f64 x 18) (*.f64 y z))
5.3b
(*.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) t)

series61.0ms (0.6%)

Counts
3 → 144
Calls

3 calls:

29.0ms
(-.f64 (*.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) t) (*.f64 (*.f64 a 4) t))
20.0ms
(*.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) t)
12.0ms
(*.f64 (*.f64 x 18) (*.f64 y z))

rewrite24.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
33×add-cbrt-cube_binary64
33×add-exp-log_binary64
33×pow1_binary64
21×cbrt-unprod_binary64
21×prod-exp_binary64
Counts
3 → 70
Calls

3 calls:

7.0ms
(*.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) t)
7.0ms
(-.f64 (*.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) t) (*.f64 (*.f64 a 4) t))
5.0ms
(*.f64 (*.f64 x 18) (*.f64 y z))

simplify142.0ms (1.4%)

Algorithm
egg-herbie
Rules
529×fma-def_binary64
516×fma-neg_binary64
367×associate-*l*_binary64
297×associate-*r*_binary64
292×cancel-sign-sub-inv_binary64
Counts
214 → 102
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01363320
13583032
214813015
331943013
447683013
549983013
648863013

prune215.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1302132
Fresh055
Picked011
Done011
Total1309139
Error
0.0b
Counts
139 → 9
Alt Table
StatusErrorProgram
7.6b
(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))))
6.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
6.1b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
5.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 18 (*.f64 y (*.f64 z x))) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
7.4b
(-.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 (*.f64 j 27) (*.f64 (cbrt.f64 k) (cbrt.f64 k))) (cbrt.f64 k)))
6.9b
(-.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 j (*.f64 27 k)))
7.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 18) (*.f64 (*.f64 y z) t)) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
39.4b
(-.f64 (-.f64 (+.f64 (/.f64 (*.f64 t (*.f64 t (fma.f64 x (*.f64 (*.f64 324 x) (*.f64 (*.f64 y z) (*.f64 y z))) (*.f64 (*.f64 a a) -16)))) (*.f64 t (fma.f64 18 (*.f64 y (*.f64 z x)) (*.f64 a 4)))) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
23.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 (*.f64 z x) t)))) (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 (*.f64 z x) t))))) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
Compiler

Compiled 5676 to 3181 computations (44% 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))))
0.5b
(*.f64 (*.f64 j 27) k)
4.5b
(*.f64 t (*.f64 z x))
8.4b
(*.f64 y (*.f64 t (*.f64 z x)))

series49.0ms (0.5%)

Counts
3 → 0
Calls

3 calls:

22.0ms
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
19.0ms
(*.f64 y (*.f64 t (*.f64 z x)))
8.0ms
(*.f64 t (*.f64 z x))

rewrite19.0ms (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 18 (*.f64 y (*.f64 t (*.f64 z x))))
5.0ms
(*.f64 y (*.f64 t (*.f64 z x)))
4.0ms
(*.f64 t (*.f64 z x))

simplify81.0ms (0.8%)

Algorithm
egg-herbie
Rules
598×unswap-sqr_binary64
466×*-commutative_binary64
399×associate-/l/_binary64
390×associate-/l*_binary64
369×associate-/r/_binary64
Counts
69 → 75
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0921065
1205816
2757816
31333816
41806816
52847816
64884816
75035816

prune187.0ms (1.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1041105
Fresh066
Picked011
Done022
Total10410114
Error
0.0b
Counts
114 → 10
Alt Table
StatusErrorProgram
6.5b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 18) (*.f64 (sqrt.f64 18) (*.f64 y (*.f64 t (*.f64 z x))))) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
7.6b
(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))))
6.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
6.1b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x 18) (*.f64 y z)) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
5.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 18 (*.f64 y (*.f64 z x))) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
7.4b
(-.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 (*.f64 j 27) (*.f64 (cbrt.f64 k) (cbrt.f64 k))) (cbrt.f64 k)))
6.9b
(-.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 j (*.f64 27 k)))
7.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 18) (*.f64 (*.f64 y z) t)) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
39.4b
(-.f64 (-.f64 (+.f64 (/.f64 (*.f64 t (*.f64 t (fma.f64 x (*.f64 (*.f64 324 x) (*.f64 (*.f64 y z) (*.f64 y z))) (*.f64 (*.f64 a a) -16)))) (*.f64 t (fma.f64 18 (*.f64 y (*.f64 z x)) (*.f64 a 4)))) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
23.2b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 (*.f64 z x) t)))) (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 (*.f64 z x) t))))) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
Compiler

Compiled 4347 to 2228 computations (48.7% saved)

regimes1.6s (16.2%)

Accuracy

Total 1.1b remaining (97.5%)

Threshold costs 0b (0%)

Counts
42 → 3
Compiler

Compiled 34221 to 23937 computations (30.1% saved)

bsearch3.0ms (0%)

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
36×*-commutative_binary64
22×+-commutative_binary64
20×sub-neg_binary64
16×distribute-rgt-neg-in_binary64
14×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057211
1105211
2155211
3187211
4207211
5213211
6211211

end199.0ms (2%)

Remove

(sort b c)

Compiler

Compiled 1683 to 1034 computations (38.6% saved)

sample3.2s (32.7%)

Algorithm
intervals
Results
841.0ms8091×body128invalid
823.0ms8000×body128valid
Compiler

Compiled 652 to 441 computations (32.4% saved)

Profiling

Loading profile data...