Details

Time bar (total: 8.7s)

analyze355.0ms (4.1%)

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
25%74.9%0.1%6
25%74.9%0.1%7
43.7%56.2%0.1%8
62.4%37.4%0.1%9
65.5%34.3%0.1%10
71.8%27.7%0.5%11
79.2%19.7%1.1%12
80.2%18.7%1.1%13
82.8%15%2.2%14
Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.1s (12.4%)

Symmetry

(sort x y)

Results
977.0ms8256×body128valid
56.0ms471×body128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
44×fma-def_binary64
37×associate-*l*_binary64
36×associate-*r*_binary64
20×*-commutative_binary64
19×distribute-lft-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01016
12414
24114
39414
412214
514914
615314
714614

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
7.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
7.7b
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
Compiler

Compiled 50 to 34 computations (32% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
4.0b
(*.f64 y (fma.f64 z z 1))
5.0b
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

series96.0ms (1.1%)

Counts
2 → 60
Calls

2 calls:

87.0ms
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
9.0ms
(*.f64 y (fma.f64 z z 1))

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
31×times-frac_binary64
26×add-exp-log_binary64
20×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64
18×add-cube-cbrt_binary64
Counts
2 → 74
Calls

2 calls:

12.0ms
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
3.0ms
(*.f64 y (fma.f64 z z 1))

simplify117.0ms (1.3%)

Algorithm
egg-herbie
Rules
469×associate-/r*_binary64
453×associate-*l*_binary64
414×associate-/l*_binary64
336×associate-/l/_binary64
297×associate-*r*_binary64
Counts
134 → 132
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01542203
13301967
211071965
339561963
444821963
548061963
649381963

prune122.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1257132
Fresh000
Picked101
Done000
Total1267133
Error
3.8b
Counts
133 → 7
Alt Table
StatusErrorProgram
7.7b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
7.0b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
21.2b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
6.8b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
27.5b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1))) (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
8.3b
(/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 (/.f64 1 x))))
6.8b
(*.f64 (/.f64 1 y) (/.f64 1 (*.f64 x (fma.f64 z z 1))))
Compiler

Compiled 2496 to 1444 computations (42.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
0.6b
(cbrt.f64 (/.f64 1 x))
2.4b
(/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))
4.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))

series261.0ms (3%)

Counts
4 → 84
Calls

4 calls:

107.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
88.0ms
(/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))
36.0ms
(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
29.0ms
(cbrt.f64 (/.f64 1 x))

rewrite70.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
240×times-frac_binary64
205×add-sqr-sqrt_binary64
190×cbrt-prod_binary64
147×*-un-lft-identity_binary64
135×add-cube-cbrt_binary64
Counts
4 → 290
Calls

4 calls:

21.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
10.0ms
(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
4.0ms
(/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))
2.0ms
(cbrt.f64 (/.f64 1 x))

simplify236.0ms (2.7%)

Algorithm
egg-herbie
Rules
539×unswap-sqr_binary64
472×fma-def_binary64
333×fma-neg_binary64
304×associate-*l*_binary64
295×cancel-sign-sub-inv_binary64
Counts
374 → 446
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03048811
17247584
228997460
338537377
452417377

prune607.0ms (7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New4946500
Fresh156
Picked101
Done000
Total49611507
Error
2.5b
Counts
507 → 11
Alt Table
StatusErrorProgram
27.5b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1))) (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
7.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y)) (cbrt.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y))) (*.f64 (cbrt.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y)) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))))
4.8b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
7.3b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))) y)
7.7b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
7.0b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
21.2b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
50.4b
(*.f64 (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)))
6.8b
(*.f64 (/.f64 1 y) (/.f64 1 (*.f64 x (fma.f64 z z 1))))
7.0b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))) (cbrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))))) (cbrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))))
5.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 (*.f64 (cbrt.f64 (cbrt.f64 (/.f64 1 x))) (cbrt.f64 (cbrt.f64 (/.f64 1 x)))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (cbrt.f64 (/.f64 1 x))) (hypot.f64 1 z))))
Compiler

Compiled 15812 to 11327 computations (28.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y)
0.5b
(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
0.6b
(cbrt.f64 (/.f64 1 x))
4.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))

series603.0ms (7%)

Counts
2 → 60
Calls

2 calls:

475.0ms
(/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y)
128.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))

rewrite40.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
130×add-exp-log_binary64
61×prod-exp_binary64
58×add-cbrt-cube_binary64
44×div-exp_binary64
33×cbrt-unprod_binary64
Counts
2 → 95
Calls

2 calls:

17.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
6.0ms
(/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y)

simplify142.0ms (1.6%)

Algorithm
egg-herbie
Rules
687×times-frac_binary64
445×associate-/l/_binary64
433×*-commutative_binary64
427×associate-/r*_binary64
355×fma-def_binary64
Counts
155 → 149
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02095464
15322954
215032851
341842795
449622795
549952795

prune479.0ms (5.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New3427349
Fresh5510
Picked101
Done000
Total34812360
Error
0.0b
Counts
360 → 12
Alt Table
StatusErrorProgram
1.4b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (*.f64 1 (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z)))) (*.f64 y (hypot.f64 1 z)))
6.8b
(*.f64 (/.f64 1 y) (/.f64 1 (*.f64 x (fma.f64 z z 1))))
4.8b
(*.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (/.f64 y (cbrt.f64 (/.f64 1 x)))) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
7.7b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
7.0b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
21.2b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
24.3b
(*.f64 (/.f64 (cbrt.f64 (/.f64 1 (*.f64 x x))) (*.f64 y (hypot.f64 1 z))) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z)))
3.4b
(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))
50.4b
(*.f64 (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)))
0.7b
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
5.1b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))) (cbrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z)))))) (cbrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))))
5.0b
(*.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 y))) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
Compiler

Compiled 12149 to 9173 computations (24.5% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 1 z)
0.0b
(*.f64 y (hypot.f64 1 z))
0.1b
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
0.7b
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))

series182.0ms (2.1%)

Counts
4 → 96
Calls

4 calls:

114.0ms
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
45.0ms
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
14.0ms
(*.f64 y (hypot.f64 1 z))
9.0ms
(hypot.f64 1 z)

rewrite39.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
250×times-frac_binary64
120×add-sqr-sqrt_binary64
118×*-un-lft-identity_binary64
118×add-cube-cbrt_binary64
56×associate-/l*_binary64
Counts
4 → 220
Calls

4 calls:

10.0ms
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
4.0ms
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
3.0ms
(*.f64 y (hypot.f64 1 z))
0.0ms
(hypot.f64 1 z)

simplify220.0ms (2.5%)

Algorithm
egg-herbie
Rules
657×fma-def_binary64
529×associate-*l/_binary64
499×associate-/r/_binary64
246×associate-/r*_binary64
229×fma-neg_binary64
Counts
316 → 377
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03456931
18666209
226145885
344745881
449995881
549365881

prune569.0ms (6.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New4074411
Fresh5611
Picked101
Done000
Total41310423
Error
0b
Counts
423 → 10
Alt Table
StatusErrorProgram
16.8b
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 (sqrt.f64 (*.f64 y (hypot.f64 1 z))) (sqrt.f64 (*.f64 y (hypot.f64 1 z)))))
1.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z))) (cbrt.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)))) y) (/.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z))) (hypot.f64 1 z)))
3.4b
(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))
0.7b
(/.f64 (/.f64 1 (*.f64 x (hypot.f64 1 z))) (*.f64 y (hypot.f64 1 z)))
7.0b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
1.1b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 z))) y) (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (hypot.f64 1 z))) (hypot.f64 1 z)))
24.3b
(*.f64 (/.f64 (cbrt.f64 (/.f64 1 (*.f64 x x))) (*.f64 y (hypot.f64 1 z))) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z)))
4.8b
(*.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (/.f64 y (cbrt.f64 (/.f64 1 x)))) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
5.1b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))) (cbrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z)))))) (cbrt.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))))
5.0b
(*.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 y))) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
Compiler

Compiled 9534 to 6611 computations (30.7% saved)

regimes3.0s (34.9%)

Accuracy

Total 1.6b remaining (97.9%)

Threshold costs 0b (0%)

Counts
239 → 1
Compiler

Compiled 50352 to 37689 computations (25.1% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01019
11219
21119

end354.0ms (4.1%)

Compiler

Compiled 368 to 282 computations (23.4% saved)

Profiling

Loading profile data...