Details

Time bar (total: 10.3s)

analyze1.2s (11.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%99.9%0.1%8
0%99.9%0.1%9
9.4%89.3%1.3%10
13.3%84.6%2.1%11
15.2%82.3%2.5%12
21.1%73.9%5%13
23.1%71.1%5.9%14
Compiler

Compiled 15 to 10 computations (33.3% saved)

sample2.1s (20.5%)

Symmetry

(sort x y)

Results
983.0ms8256×body128valid
834.0ms1389×body8192exit
88.0ms772×body128invalid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify103.0ms (1%)

Algorithm
egg-herbie
Rules
826×associate-*r/_binary64
769×associate-/l/_binary64
660×associate-*l/_binary64
522×associate-/l*_binary64
421×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01016
13016
27814
319514
431414
538314
642614
763114
8100914
9220414
10286814
11296714
12307914
13319314
14305814
15371214
16498814
17482414

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
4.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.5b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
11.0b
(/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1)))
Compiler

Compiled 78 to 45 computations (42.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 y (fma.f64 z z z)) z)
5.0b
(/.f64 y (fma.f64 z z z))
6.6b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series196.0ms (1.9%)

Counts
3 → 84
Calls

3 calls:

103.0ms
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
55.0ms
(/.f64 (/.f64 y (fma.f64 z z z)) z)
37.0ms
(/.f64 y (fma.f64 z z z))

rewrite34.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
153×times-frac_binary64
98×add-sqr-sqrt_binary64
89×*-un-lft-identity_binary64
89×add-cube-cbrt_binary64
43×associate-*r*_binary64
Counts
3 → 168
Calls

3 calls:

10.0ms
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
4.0ms
(/.f64 (/.f64 y (fma.f64 z z z)) z)
2.0ms
(/.f64 y (fma.f64 z z z))

simplify166.0ms (1.6%)

Algorithm
egg-herbie
Rules
805×fma-def_binary64
353×fma-neg_binary64
351×*-commutative_binary64
341×associate-/r/_binary64
275×sub-neg_binary64
Counts
252 → 296
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02874846
16874599
223044515
336074509
448174509
549634509

prune390.0ms (3.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New28115296
Fresh101
Picked101
Done000
Total28315298
Error
1.4b
Counts
298 → 15
Alt Table
StatusErrorProgram
37.4b
(*.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 (cbrt.f64 y) (hypot.f64 z (sqrt.f64 z))) z)))
12.9b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
5.0b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
5.0b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
9.7b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) z))
7.5b
(*.f64 x (/.f64 (*.f64 1 (/.f64 y (fma.f64 z z z))) z))
7.3b
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
10.9b
(/.f64 (*.f64 y x) (*.f64 z (fma.f64 z z z)))
6.0b
(*.f64 (*.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 z)))
10.9b
(*.f64 (*.f64 x (/.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
3.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
11.6b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 y (*.f64 z (fma.f64 z z z))) (cbrt.f64 x)))
11.6b
(*.f64 x (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (*.f64 z (fma.f64 z z z)))))
20.6b
(*.f64 x (-.f64 (/.f64 y (pow.f64 z 3)) (/.f64 y (pow.f64 z 4))))
11.3b
(*.f64 (*.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
Compiler

Compiled 6534 to 1573 computations (75.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.9b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
3.9b
(/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
4.6b
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
23.7b
(cbrt.f64 (fma.f64 z z z))

series2.5s (24.6%)

Counts
4 → 108
Calls

4 calls:

1.7s
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
708.0ms
(/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
119.0ms
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
6.0ms
(cbrt.f64 (fma.f64 z z z))

rewrite104.0ms (1%)

Algorithm
rewrite-expression-head
Rules
231×times-frac_binary64
129×associate-*r*_binary64
127×add-exp-log_binary64
126×add-sqr-sqrt_binary64
123×*-un-lft-identity_binary64
Counts
4 → 244
Calls

4 calls:

28.0ms
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
8.0ms
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
6.0ms
(/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
1.0ms
(cbrt.f64 (fma.f64 z z z))

simplify295.0ms (2.9%)

Algorithm
egg-herbie
Rules
696×associate-*l/_binary64
421×associate-/l*_binary64
312×associate-/r*_binary64
291×times-frac_binary64
270×fma-def_binary64
Counts
352 → 431
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
056216302
1167012076
2496112036
3510212036

prune631.0ms (6.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New4901491
Fresh11314
Picked011
Done000
Total49115506
Error
1.4b
Counts
506 → 15
Alt Table
StatusErrorProgram
3.0b
(*.f64 (*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (*.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) 1) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
11.6b
(*.f64 x (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (*.f64 z (fma.f64 z z z)))))
37.4b
(*.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 (cbrt.f64 y) (hypot.f64 z (sqrt.f64 z))) z)))
12.9b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
5.0b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
5.0b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
9.7b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) z))
7.5b
(*.f64 x (/.f64 (*.f64 1 (/.f64 y (fma.f64 z z z))) z))
7.3b
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
10.9b
(/.f64 (*.f64 y x) (*.f64 z (fma.f64 z z z)))
6.0b
(*.f64 (*.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 z)))
3.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
11.6b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 y (*.f64 z (fma.f64 z z z))) (cbrt.f64 x)))
20.6b
(*.f64 x (-.f64 (/.f64 y (pow.f64 z 3)) (/.f64 y (pow.f64 z 4))))
11.3b
(*.f64 (*.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
Compiler

Compiled 21711 to 4437 computations (79.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 (cbrt.f64 y))
3.9b
(/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
4.6b
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
23.7b
(cbrt.f64 (fma.f64 z z z))

series257.0ms (2.5%)

Counts
1 → 12
Calls

1 calls:

257.0ms
(cbrt.f64 (cbrt.f64 y))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
cbrt-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
1 → 16
Calls

1 calls:

1.0ms
(cbrt.f64 (cbrt.f64 y))

simplify103.0ms (1%)

Algorithm
egg-herbie
Rules
952×unswap-sqr_binary64
687×sqr-pow_binary64
466×*-commutative_binary64
325×cube-prod_binary64
311×associate-/l/_binary64
Counts
28 → 21
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
033234
151234
289234
3160230
4410226
5652226
61364226
71508226
81713226
91972226
102408226
113558226
123799226
134679226
144777226

prune468.0ms (4.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New2790279
Fresh01313
Picked011
Done011
Total27915294
Error
1.4b
Counts
294 → 15
Alt Table
StatusErrorProgram
3.0b
(*.f64 (*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (*.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) 1) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
11.6b
(*.f64 x (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (*.f64 z (fma.f64 z z z)))))
37.4b
(*.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 (cbrt.f64 y) (hypot.f64 z (sqrt.f64 z))) z)))
12.9b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
5.0b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
5.0b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
9.7b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) z))
7.5b
(*.f64 x (/.f64 (*.f64 1 (/.f64 y (fma.f64 z z z))) z))
7.3b
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
10.9b
(/.f64 (*.f64 y x) (*.f64 z (fma.f64 z z z)))
6.0b
(*.f64 (*.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 z)))
3.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
11.6b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 y (*.f64 z (fma.f64 z z z))) (cbrt.f64 x)))
20.6b
(*.f64 x (-.f64 (/.f64 y (pow.f64 z 3)) (/.f64 y (pow.f64 z 4))))
11.3b
(*.f64 (*.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
Compiler

Compiled 16715 to 4621 computations (72.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.5b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
5.0b
(/.f64 y (fma.f64 z z z))
5.7b
(*.f64 x (/.f64 y (fma.f64 z z z)))

series178.0ms (1.7%)

Counts
2 → 72
Calls

2 calls:

105.0ms
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
72.0ms
(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
13×associate-*r*_binary64
13×times-frac_binary64
Counts
2 → 60
Calls

2 calls:

8.0ms
(*.f64 x (/.f64 y (fma.f64 z z z)))
4.0ms
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

simplify85.0ms (0.8%)

Algorithm
egg-herbie
Rules
604×fma-neg_binary64
483×associate-*l*_binary64
433×associate-/r*_binary64
417×associate-*r*_binary64
378×associate-/r/_binary64
Counts
132 → 124
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01532289
13972096
215391990
344391990
449681990

prune202.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1705175
Fresh7512
Picked101
Done202
Total18010190
Error
1.4b
Counts
190 → 10
Alt Table
StatusErrorProgram
7.1b
(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
7.3b
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
11.6b
(*.f64 x (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (*.f64 z (fma.f64 z z z)))))
44.6b
(/.f64 (*.f64 x (*.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))))) z)
7.5b
(*.f64 x (/.f64 (*.f64 1 (/.f64 y (fma.f64 z z z))) z))
5.0b
(/.f64 1 (/.f64 z (*.f64 x (/.f64 y (fma.f64 z z z)))))
4.0b
(/.f64 (*.f64 (/.f64 x (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (/.f64 y (cbrt.f64 (fma.f64 z z z)))) z)
5.0b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
20.6b
(*.f64 x (-.f64 (/.f64 y (pow.f64 z 3)) (/.f64 y (pow.f64 z 4))))
7.2b
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
Compiler

Compiled 3135 to 853 computations (72.8% saved)

regimes936.0ms (9.1%)

Accuracy

Total 2.0b remaining (58.7%)

Threshold costs 0b (0%)

Counts
174 → 1
Compiler

Compiled 24924 to 11959 computations (52% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01768
11968
21968

end259.0ms (2.5%)

Compiler

Compiled 365 to 158 computations (56.7% saved)

Profiling

Loading profile data...