Details

Time bar (total: 9.6s)

analyze2.8s (29.2%)

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)

sample195.0ms (2%)

Algorithm
intervals
Symmetry

(sort y z)

(sort b c)

(sort j k)

Results
31.0ms262×body128invalid
29.0ms256×body128valid
Compiler

Compiled 93 to 69 computations (25.8% saved)

simplify338.0ms (3.5%)

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
4.7b
(-.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)) (*.f64 (*.f64 j 27) k))
5.9b
(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)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 x 18) y)
0.4b
(*.f64 (*.f64 j 27) k)
4.0b
(*.f64 (*.f64 (*.f64 x 18) y) z)
4.9b
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)

series42.0ms (0.4%)

Counts
4 → 132
Calls

4 calls:

20.0ms
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)
13.0ms
(*.f64 (*.f64 (*.f64 x 18) y) z)
5.0ms
(*.f64 (*.f64 x 18) y)
5.0ms
(*.f64 (*.f64 j 27) k)

rewrite26.0ms (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:

9.0ms
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)
5.0ms
(*.f64 (*.f64 (*.f64 x 18) y) z)
4.0ms
(*.f64 (*.f64 j 27) k)
4.0ms
(*.f64 (*.f64 x 18) y)

simplify119.0ms (1.2%)

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

prune221.0ms (2.3%)

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
4.7b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 18 y)) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
21.0b
(-.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) (sqrt.f64 k)) (sqrt.f64 k)))
4.4b
(-.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 j (*.f64 27 k)))
21.7b
(-.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))))
5.2b
(-.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))
22.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (sqrt.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 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))
5.9b
(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 5340 to 3133 computations (41.3% saved)

localize59.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 x 18) y)
0.2b
(*.f64 j (*.f64 27 k))
4.0b
(*.f64 (*.f64 (*.f64 x 18) y) z)
4.9b
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)

series6.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

6.0ms
(*.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))

simplify68.0ms (0.7%)

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

prune218.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1261127
Fresh077
Picked011
Done000
Total1269135
Error
0.0b
Counts
135 → 9
Alt Table
StatusErrorProgram
4.4b
(-.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 j (*.f64 27 k)))
4.7b
(-.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)) (*.f64 (*.f64 (cbrt.f64 j) (cbrt.f64 j)) (*.f64 (cbrt.f64 j) (*.f64 27 k))))
4.7b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 18 y)) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
21.0b
(-.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) (sqrt.f64 k)) (sqrt.f64 k)))
21.7b
(-.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))))
5.2b
(-.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))
22.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (sqrt.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 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))
5.9b
(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 5395 to 3167 computations (41.3% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 j) (cbrt.f64 j))
0.5b
(cbrt.f64 j)
4.0b
(*.f64 (*.f64 (*.f64 x 18) y) z)
4.9b
(*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t)

series70.0ms (0.7%)

Counts
2 → 24
Calls

2 calls:

36.0ms
(*.f64 (cbrt.f64 j) (cbrt.f64 j))
34.0ms
(cbrt.f64 j)

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64
19×cbrt-prod_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
pow1_binary64
Counts
2 → 55
Calls

2 calls:

4.0ms
(*.f64 (cbrt.f64 j) (cbrt.f64 j))
1.0ms
(cbrt.f64 j)

simplify65.0ms (0.7%)

Algorithm
egg-herbie
Rules
577×distribute-rgt-in_binary64
561×log-prod_binary64
538×distribute-lft-in_binary64
525×unswap-sqr_binary64
384×fma-def_binary64
Counts
79 → 74
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
058610
198554
2296516
3769502
41799410
54642410
64805410

prune533.0ms (5.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1770177
Fresh077
Picked011
Done011
Total1779186
Error
0.0b
Counts
186 → 9
Alt Table
StatusErrorProgram
4.4b
(-.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 j (*.f64 27 k)))
4.7b
(-.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)) (*.f64 (*.f64 (cbrt.f64 j) (cbrt.f64 j)) (*.f64 (cbrt.f64 j) (*.f64 27 k))))
4.7b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 18 y)) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
21.0b
(-.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) (sqrt.f64 k)) (sqrt.f64 k)))
21.7b
(-.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))))
5.2b
(-.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))
22.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (sqrt.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 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))
5.9b
(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 8299 to 4343 computations (47.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 x (*.f64 18 y))
0.4b
(*.f64 (*.f64 j 27) k)
4.0b
(*.f64 (*.f64 x (*.f64 18 y)) z)
4.9b
(*.f64 (*.f64 (*.f64 x (*.f64 18 y)) z) t)

series37.0ms (0.4%)

Counts
3 → 108
Calls

3 calls:

21.0ms
(*.f64 (*.f64 (*.f64 x (*.f64 18 y)) z) t)
11.0ms
(*.f64 (*.f64 x (*.f64 18 y)) z)
5.0ms
(*.f64 x (*.f64 18 y))

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

simplify167.0ms (1.7%)

Algorithm
egg-herbie
Rules
660×*-commutative_binary64
536×sqr-pow_binary64
400×associate-/l/_binary64
346×associate-*l*_binary64
346×unswap-sqr_binary64
Counts
177 → 98
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01052203
12511975
211071975
318111975
425311975
539911975
652591975

prune254.0ms (2.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1280128
Fresh066
Picked011
Done022
Total1289137
Error
0.0b
Counts
137 → 9
Alt Table
StatusErrorProgram
4.4b
(-.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 j (*.f64 27 k)))
4.7b
(-.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)) (*.f64 (*.f64 (cbrt.f64 j) (cbrt.f64 j)) (*.f64 (cbrt.f64 j) (*.f64 27 k))))
4.7b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 18 y)) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
21.0b
(-.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) (sqrt.f64 k)) (sqrt.f64 k)))
21.7b
(-.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))))
5.2b
(-.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))
22.4b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (sqrt.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 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))
5.9b
(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 5078 to 2945 computations (42% saved)

regimes729.0ms (7.6%)

Accuracy

Total 1.0b remaining (93.9%)

Threshold costs 1.0b (93.9%)

Counts
17 → 3
Compiler

Compiled 15182 to 10687 computations (29.6% saved)

bsearch1.0ms (0%)

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify9.0ms (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

end73.0ms (0.8%)

Remove

(sort b c)

(sort y z)

Compiler

Compiled 1377 to 846 computations (38.6% saved)

sample3.4s (35.9%)

Algorithm
intervals
Results
898.0ms8333×body128invalid
847.0ms8000×body128valid
Compiler

Compiled 594 to 403 computations (32.2% saved)

Profiling

Loading profile data...