Details

Time bar (total: 11.2s)

analyze2.7s (24.4%)

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 (32.2%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results
1.7s8388×body128invalid
1.7s8256×body128valid
Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify336.0ms (3%)

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
0.6b
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))))
5.4b
(-.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 j 27) k))
Compiler

Compiled 218 to 148 computations (32.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 j 27) k)
0.2b
(*.f64 (*.f64 x 18) y)
4.7b
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)
5.1b
(*.f64 (*.f64 (*.f64 x 18) y) z)

series40.0ms (0.4%)

Counts
4 → 132
Calls

4 calls:

20.0ms
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)
10.0ms
(*.f64 (*.f64 (*.f64 x 18) y) z)
5.0ms
(*.f64 (*.f64 j 27) k)
4.0ms
(*.f64 (*.f64 x 18) y)

rewrite25.0ms (0.2%)

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

simplify126.0ms (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

prune176.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1207127
Fresh011
Picked101
Done000
Total1218129
Error
0.0b
Counts
129 → 8
Alt Table
StatusErrorProgram
7.1b
(-.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))
5.6b
(-.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)))
7.6b
(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))))
5.6b
(-.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)))
5.1b
(-.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))
5.6b
(-.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 (cbrt.f64 (*.f64 (*.f64 j 27) k)) (cbrt.f64 (*.f64 (*.f64 j 27) k))) (cbrt.f64 (*.f64 (*.f64 j 27) k))))
22.7b
(-.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)) (cbrt.f64 (*.f64 19683 (pow.f64 (*.f64 k j) 3))))
6.1b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) (*.f64 z t)) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
Compiler

Compiled 5352 to 3147 computations (41.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 j 27) k)
0.2b
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
4.0b
(*.f64 t (*.f64 z x))
7.2b
(*.f64 y (*.f64 t (*.f64 z x)))

series46.0ms (0.4%)

Counts
3 → 0
Calls

3 calls:

20.0ms
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
17.0ms
(*.f64 y (*.f64 t (*.f64 z x)))
8.0ms
(*.f64 t (*.f64 z x))

rewrite22.0ms (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:

10.0ms
(*.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))

simplify73.0ms (0.6%)

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

prune195.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1041105
Fresh077
Picked011
Done000
Total1049113
Error
0.0b
Counts
113 → 9
Alt Table
StatusErrorProgram
7.1b
(-.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))
5.6b
(-.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)))
5.6b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 18 (*.f64 (*.f64 y 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))))
5.6b
(-.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)))
5.1b
(-.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))
5.6b
(-.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 (cbrt.f64 (*.f64 (*.f64 j 27) k)) (cbrt.f64 (*.f64 (*.f64 j 27) k))) (cbrt.f64 (*.f64 (*.f64 j 27) k))))
22.7b
(-.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)) (cbrt.f64 (*.f64 19683 (pow.f64 (*.f64 k j) 3))))
6.1b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) (*.f64 z t)) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
Compiler

Compiled 4635 to 2438 computations (47.4% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (*.f64 (*.f64 j 27) k)) (cbrt.f64 (*.f64 (*.f64 j 27) k)))
4.7b
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)
5.1b
(*.f64 (*.f64 (*.f64 x 18) y) z)
8.4b
(cbrt.f64 (*.f64 (*.f64 j 27) k))

series1.1s (9.4%)

Counts
2 → 48
Calls

2 calls:

657.0ms
(*.f64 (cbrt.f64 (*.f64 (*.f64 j 27) k)) (cbrt.f64 (*.f64 (*.f64 j 27) k)))
394.0ms
(cbrt.f64 (*.f64 (*.f64 j 27) k))

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
pow1_binary64
add-sqr-sqrt_binary64
pow1/3_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
2 → 44
Calls

2 calls:

5.0ms
(*.f64 (cbrt.f64 (*.f64 (*.f64 j 27) k)) (cbrt.f64 (*.f64 (*.f64 j 27) k)))
2.0ms
(cbrt.f64 (*.f64 (*.f64 j 27) k))

simplify99.0ms (0.9%)

Algorithm
egg-herbie
Rules
692×fma-neg_binary64
372×associate-*l*_binary64
332×exp-prod_binary64
289×fma-def_binary64
277×associate-*r*_binary64
Counts
92 → 82
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01191742
12431575
25101318
317321135
440141073
548861073
649321073

prune395.0ms (3.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1990199
Fresh077
Picked011
Done011
Total1999208
Error
0.0b
Counts
208 → 9
Alt Table
StatusErrorProgram
7.1b
(-.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))
5.6b
(-.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)))
5.6b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 18 (*.f64 (*.f64 y 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))))
5.6b
(-.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)))
5.1b
(-.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))
5.6b
(-.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 (cbrt.f64 (*.f64 (*.f64 j 27) k)) (cbrt.f64 (*.f64 (*.f64 j 27) k))) (cbrt.f64 (*.f64 (*.f64 j 27) k))))
22.7b
(-.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)) (cbrt.f64 (*.f64 19683 (pow.f64 (*.f64 k j) 3))))
6.1b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) (*.f64 z t)) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
Compiler

Compiled 10833 to 6932 computations (36% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 x 18) y)
0.4b
(*.f64 j (*.f64 27 k))
4.7b
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)
5.1b
(*.f64 (*.f64 (*.f64 x 18) y) z)

series5.0ms (0%)

Counts
1 → 24
Calls

1 calls:

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

rewrite5.0ms (0%)

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

1 calls:

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

simplify62.0ms (0.6%)

Algorithm
egg-herbie
Rules
525×associate-/r/_binary64
451×associate-*l*_binary64
384×associate-/l*_binary64
372×*-commutative_binary64
301×associate-*r*_binary64
Counts
44 → 30
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
042378
190342
2302342
3821342
41011342
51137342
62002342
74806342
84922342

prune237.0ms (2.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1270127
Fresh066
Picked011
Done022
Total1279136
Error
0.0b
Counts
136 → 9
Alt Table
StatusErrorProgram
7.1b
(-.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))
5.6b
(-.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)))
5.6b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 18 (*.f64 (*.f64 y 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))))
5.6b
(-.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)))
5.1b
(-.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))
5.6b
(-.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 (cbrt.f64 (*.f64 (*.f64 j 27) k)) (cbrt.f64 (*.f64 (*.f64 j 27) k))) (cbrt.f64 (*.f64 (*.f64 j 27) k))))
22.7b
(-.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)) (cbrt.f64 (*.f64 19683 (pow.f64 (*.f64 k j) 3))))
6.1b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) (*.f64 z t)) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
Compiler

Compiled 5046 to 2931 computations (41.9% saved)

regimes1.2s (11%)

Accuracy

Total 1.1b remaining (96.6%)

Threshold costs 0b (0%)

Counts
32 → 3
Compiler

Compiled 26340 to 18767 computations (28.8% saved)

bsearch4.0ms (0%)

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
32×*-commutative_binary64
20×+-commutative_binary64
18×sub-neg_binary64
12×distribute-rgt-neg-in_binary64
12×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055185
1101185
2144185
3168185
4186185
5192185
6190185

end614.0ms (5.5%)

Remove

(sort b c)

Compiler

Compiled 2008 to 1293 computations (35.6% saved)

Profiling

Loading profile data...