Details

Time bar (total: 21.0s)

analyze307.0ms (1.5%)

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
49.9%49.9%0.1%4
49.9%49.9%0.1%5
49.9%49.9%0.1%6
74.9%25%0.1%7
74.9%25%0.1%8
74.9%25%0.1%9
74.9%25%0.1%10
74.9%25%0.1%11
74.9%25%0.1%12
87.4%12.5%0.1%13
87.4%12.5%0.1%14
Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (6.6%)

Symmetry

(sort x y)

Results
1.1s8256×body128valid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify175.0ms (0.8%)

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

prune6.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
3.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
6.4b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
9.2b
(/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1)))
Compiler

Compiled 78 to 45 computations (42.3% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 y (fma.f64 z z z)) z)
3.5b
(/.f64 y (fma.f64 z z z))
6.1b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series309.0ms (1.5%)

Counts
3 → 84
Calls

3 calls:

160.0ms
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
87.0ms
(/.f64 (/.f64 y (fma.f64 z z z)) z)
62.0ms
(/.f64 y (fma.f64 z z z))

rewrite60.0ms (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:

20.0ms
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
13.0ms
(/.f64 y (fma.f64 z z z))
8.0ms
(/.f64 (/.f64 y (fma.f64 z z z)) z)

simplify267.0ms (1.3%)

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

prune570.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2879296
Fresh101
Picked011
Done000
Total28810298
Error
0.5b
Counts
298 → 10
Alt Table
StatusErrorProgram
2.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
54.3b
(*.f64 (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))))
22.9b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
3.5b
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
34.5b
(*.f64 (*.f64 x (/.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (sqrt.f64 z))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) (sqrt.f64 z)))
16.7b
(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
6.6b
(*.f64 x (/.f64 1 (/.f64 z (/.f64 y (fma.f64 z z z)))))
6.4b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
3.6b
(*.f64 (/.f64 x (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 y (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
10.6b
(*.f64 x (*.f64 (/.f64 y 1) (/.f64 (/.f64 1 (fma.f64 z z z)) z)))
Compiler

Compiled 6347 to 1464 computations (76.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(cbrt.f64 y)
1.2b
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
1.2b
(/.f64 (cbrt.f64 y) (fma.f64 z z z))
1.6b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))

series2.6s (12.5%)

Counts
4 → 108
Calls

4 calls:

2.2s
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
220.0ms
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
186.0ms
(/.f64 (cbrt.f64 y) (fma.f64 z z z))
63.0ms
(cbrt.f64 y)

rewrite195.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
260×times-frac_binary64
148×add-sqr-sqrt_binary64
145×*-un-lft-identity_binary64
145×add-cube-cbrt_binary64
141×associate-*r*_binary64
Counts
4 → 274
Calls

4 calls:

65.0ms
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
16.0ms
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
7.0ms
(/.f64 (cbrt.f64 y) (fma.f64 z z z))
1.0ms
(cbrt.f64 y)

simplify397.0ms (1.9%)

Algorithm
egg-herbie
Rules
590×associate-*l/_binary64
563×associate-*r/_binary64
460×associate-/l*_binary64
264×times-frac_binary64
225×associate-/l/_binary64
Counts
382 → 456
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
049713084
113899752
249269726
351119726

prune936.0ms (4.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New4882490
Fresh178
Picked011
Done101
Total49010500
Error
0.5b
Counts
500 → 10
Alt Table
StatusErrorProgram
2.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
54.3b
(*.f64 (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))))
22.9b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
3.5b
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
16.7b
(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
6.6b
(*.f64 x (/.f64 1 (/.f64 z (/.f64 y (fma.f64 z z z)))))
10.6b
(*.f64 x (*.f64 (/.f64 y 1) (/.f64 (/.f64 1 (fma.f64 z z z)) z)))
1.9b
(*.f64 (*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))))) (/.f64 (/.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 (cbrt.f64 z))))
3.6b
(*.f64 (/.f64 x (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 y (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
17.0b
(*.f64 (*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 (cbrt.f64 z))))
Compiler

Compiled 17809 to 3052 computations (82.9% saved)

localize64.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.0b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z)))))
1.2b
(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
1.7b
(/.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
14.3b
(cbrt.f64 (fma.f64 z z z))

series6.6s (31.5%)

Counts
3 → 72
Calls

3 calls:

4.8s
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z)))))
1.8s
(/.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
11.0ms
(cbrt.f64 (fma.f64 z z z))

rewrite161.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
273×add-exp-log_binary64
136×cbrt-unprod_binary64
136×prod-exp_binary64
129×add-cbrt-cube_binary64
90×cbrt-undiv_binary64
Counts
3 → 150
Calls

3 calls:

41.0ms
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z)))))
9.0ms
(/.f64 (cbrt.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))

simplify418.0ms (2%)

Algorithm
egg-herbie
Rules
798×fma-def_binary64
460×associate-*l*_binary64
351×associate-*r*_binary64
287×fma-neg_binary64
275×associate-*r/_binary64
Counts
222 → 247
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043115337
111909872
240779654
349799654

prune876.0ms (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3660366
Fresh088
Picked011
Done011
Total36610376
Error
0.5b
Counts
376 → 10
Alt Table
StatusErrorProgram
2.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
54.3b
(*.f64 (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))))
22.9b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
3.5b
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
16.7b
(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
6.6b
(*.f64 x (/.f64 1 (/.f64 z (/.f64 y (fma.f64 z z z)))))
10.6b
(*.f64 x (*.f64 (/.f64 y 1) (/.f64 (/.f64 1 (fma.f64 z z z)) z)))
1.9b
(*.f64 (*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))))) (/.f64 (/.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 (cbrt.f64 z))))
3.6b
(*.f64 (/.f64 x (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 y (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
17.0b
(*.f64 (*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 (cbrt.f64 z))))
Compiler

Compiled 25330 to 4309 computations (83% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
0.6b
(cbrt.f64 z)
2.7b
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
3.4b
(*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series2.0s (9.3%)

Counts
4 → 96
Calls

4 calls:

1.6s
(*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
214.0ms
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
80.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
58.0ms
(cbrt.f64 z)

rewrite133.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
136×times-frac_binary64
105×add-exp-log_binary64
97×add-sqr-sqrt_binary64
95×associate-*r*_binary64
85×*-un-lft-identity_binary64
Counts
4 → 215
Calls

4 calls:

47.0ms
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
14.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
10.0ms
(*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
1.0ms
(cbrt.f64 z)

simplify305.0ms (1.4%)

Algorithm
egg-herbie
Rules
505×fma-def_binary64
423×associate-*l*_binary64
293×associate-*r*_binary64
238×associate-*r/_binary64
206×associate-*l/_binary64
Counts
311 → 337
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02777018
16975127
232774884
339894869
448424869
549434869

prune776.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3721373
Fresh167
Picked011
Done112
Total3749383
Error
0.5b
Counts
383 → 9
Alt Table
StatusErrorProgram
2.1b
(*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
54.3b
(*.f64 (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))))
3.5b
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
4.6b
(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
22.9b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
16.7b
(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
6.6b
(*.f64 x (/.f64 1 (/.f64 z (/.f64 y (fma.f64 z z z)))))
10.6b
(*.f64 x (*.f64 (/.f64 y 1) (/.f64 (/.f64 1 (fma.f64 z z z)) z)))
17.0b
(*.f64 (*.f64 (*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 (cbrt.f64 z))))
Compiler

Compiled 10436 to 3522 computations (66.3% saved)

regimes1.8s (8.4%)

Accuracy

Total 1.6b remaining (56.4%)

Threshold costs 0b (0%)

Counts
162 → 1
Compiler

Compiled 24414 to 12077 computations (50.5% saved)

simplify8.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01446
11646
21646

end627.0ms (3%)

Compiler

Compiled 326 to 152 computations (53.4% saved)

Profiling

Loading profile data...