Details

Time bar (total: 5.8s)

analyze142.0ms (2.5%)

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
25%74.9%0.1%4
37.4%62.4%0.1%5
56.2%43.7%0.1%6
56.2%43.7%0.1%7
65.5%34.3%0.1%8
76.5%23.4%0.1%9
76.5%23.4%0.1%10
81.9%17.9%0.1%11
87.8%12.1%0.1%12
87.8%12.1%0.1%13
90.7%9.2%0.1%14
Compiler

Compiled 15 to 11 computations (26.7% saved)

sample767.0ms (13.3%)

Symmetry

(sort x y)

Results
722.0ms8256×body128valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify10.0ms (0.2%)

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 (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
6.4b
Counts
3 → 1
Alt Table
StatusErrorProgram
6.4b
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
Compiler

Compiled 50 to 34 computations (32% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
3.2b
(*.f64 y (fma.f64 z z 1))
4.3b
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

series102.0ms (1.8%)

Counts
2 → 60
Calls

2 calls:

89.0ms
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
13.0ms
(*.f64 y (fma.f64 z z 1))

rewrite12.0ms (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:

5.0ms
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
3.0ms
(*.f64 y (fma.f64 z z 1))

simplify118.0ms (2%)

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

prune142.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1239132
Fresh000
Picked101
Done000
Total1249133
Error
3.2b
Counts
133 → 9
Alt Table
StatusErrorProgram
5.7b
(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
7.1b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1))))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
19.9b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
6.0b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
6.0b
(*.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)))
6.0b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
6.8b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (fma.f64 y (*.f64 z z) y) (cbrt.f64 x)))
6.4b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
26.3b
(/.f64 (/.f64 1 x) y)
Compiler

Compiled 2534 to 1464 computations (42.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
3.1b
(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
3.5b
(/.f64 (/.f64 1 x) (fma.f64 z z 1))

series129.0ms (2.2%)

Counts
2 → 60
Calls

2 calls:

93.0ms
(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
36.0ms
(/.f64 (/.f64 1 x) (fma.f64 z z 1))

rewrite41.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
173×times-frac_binary64
126×add-sqr-sqrt_binary64
93×*-un-lft-identity_binary64
86×add-cube-cbrt_binary64
76×add-exp-log_binary64
Counts
2 → 182
Calls

2 calls:

16.0ms
(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
4.0ms
(/.f64 (/.f64 1 x) (fma.f64 z z 1))

simplify142.0ms (2.5%)

Algorithm
egg-herbie
Rules
758×fma-def_binary64
687×times-frac_binary64
610×associate-/l*_binary64
504×fma-neg_binary64
455×associate-/r*_binary64
Counts
242 → 303
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02315183
15734561
216384502
340924490
451074490

prune306.0ms (5.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2985303
Fresh448
Picked101
Done000
Total3039312
Error
1.5b
Counts
312 → 9
Alt Table
StatusErrorProgram
4.0b
(*.f64 (/.f64 1 y) (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
6.0b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
6.0b
(/.f64 1 (*.f64 (*.f64 x (fma.f64 z z 1)) y))
6.8b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (fma.f64 y (*.f64 z z) y) (cbrt.f64 x)))
6.4b
(/.f64 (*.f64 1 (/.f64 1 x)) (*.f64 y (fma.f64 z z 1)))
19.9b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
3.4b
(*.f64 (/.f64 1 y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
7.1b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1))))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
19.5b
(*.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 (sqrt.f64 (/.f64 1 y)) (/.f64 (/.f64 1 x) (fma.f64 z z 1))))
Compiler

Compiled 7034 to 4706 computations (33.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 1 z))
0.1b
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
0.3b
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
3.1b
(*.f64 (/.f64 1 y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))

series203.0ms (3.5%)

Counts
4 → 96
Calls

4 calls:

105.0ms
(*.f64 (/.f64 1 y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
50.0ms
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
44.0ms
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
3.0ms
(/.f64 1 (hypot.f64 1 z))

rewrite82.0ms (1.4%)

Algorithm
rewrite-expression-head
Rules
451×add-exp-log_binary64
220×div-exp_binary64
191×times-frac_binary64
184×prod-exp_binary64
143×add-sqr-sqrt_binary64
Counts
4 → 346
Calls

4 calls:

18.0ms
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
13.0ms
(*.f64 (/.f64 1 y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
5.0ms
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
2.0ms
(/.f64 1 (hypot.f64 1 z))

simplify255.0ms (4.4%)

Algorithm
egg-herbie
Rules
834×fma-def_binary64
475×*-commutative_binary64
339×fma-neg_binary64
298×associate-/r/_binary64
256×associate-*r*_binary64
Counts
442 → 521
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03879628
19408532
226138250
342078242
449468242

prune569.0ms (9.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New5174521
Fresh448
Picked011
Done000
Total5219530
Error
0.0b
Counts
530 → 9
Alt Table
StatusErrorProgram
3.4b
(*.f64 (/.f64 1 y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
3.8b
(*.f64 (/.f64 1 y) (*.f64 (/.f64 (/.f64 1 (hypot.f64 1 z)) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z))))
3.5b
(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))
1.9b
(/.f64 (*.f64 1 (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 1 x))) (*.f64 y (hypot.f64 1 z)))
7.1b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1))))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
19.9b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
1.9b
(/.f64 (*.f64 (/.f64 1 y) (*.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z)))) (hypot.f64 1 z))
6.0b
(/.f64 1 (*.f64 (*.f64 x (fma.f64 z z 1)) y))
19.5b
(*.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 (sqrt.f64 (/.f64 1 y)) (/.f64 (/.f64 1 x) (fma.f64 z z 1))))
Compiler

Compiled 13802 to 10325 computations (25.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 1 z))
0.0b
(*.f64 y (hypot.f64 1 z))
0.4b
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 1 x))
1.6b
(/.f64 (*.f64 1 (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 1 x))) (*.f64 y (hypot.f64 1 z)))

series173.0ms (3%)

Counts
3 → 84
Calls

3 calls:

112.0ms
(/.f64 (*.f64 1 (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 1 x))) (*.f64 y (hypot.f64 1 z)))
44.0ms
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 1 x))
17.0ms
(*.f64 y (hypot.f64 1 z))

rewrite49.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
350×add-exp-log_binary64
184×prod-exp_binary64
150×div-exp_binary64
74×1-exp_binary64
73×add-cbrt-cube_binary64
Counts
3 → 193
Calls

3 calls:

10.0ms
(/.f64 (*.f64 1 (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 1 x))) (*.f64 y (hypot.f64 1 z)))
8.0ms
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 1 x))
3.0ms
(*.f64 y (hypot.f64 1 z))

simplify213.0ms (3.7%)

Algorithm
egg-herbie
Rules
869×times-frac_binary64
491×fma-neg_binary64
353×sub-neg_binary64
332×fma-def_binary64
300×associate-/r*_binary64
Counts
277 → 313
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
03045656
17624654
226234135
338594117
447064081
549684078
649344078

prune383.0ms (6.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3673370
Fresh347
Picked101
Done011
Total3718379
Error
0b
Counts
379 → 8
Alt Table
StatusErrorProgram
2.1b
(/.f64 (*.f64 1 (/.f64 1 (hypot.f64 1 z))) (*.f64 (*.f64 y (hypot.f64 1 z)) x))
19.9b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
3.4b
(*.f64 (/.f64 1 y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
3.8b
(*.f64 (/.f64 1 y) (*.f64 (/.f64 (/.f64 1 (hypot.f64 1 z)) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z))))
19.5b
(*.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 (sqrt.f64 (/.f64 1 y)) (/.f64 (/.f64 1 x) (fma.f64 z z 1))))
1.7b
(/.f64 (*.f64 1 (/.f64 (/.f64 1 (hypot.f64 1 z)) x)) (*.f64 y (hypot.f64 1 z)))
6.4b
(/.f64 (*.f64 1 (*.f64 1 (/.f64 1 x))) (fma.f64 y (*.f64 z z) y))
7.1b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1))))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
Compiler

Compiled 9046 to 6689 computations (26.1% saved)

regimes1.6s (27.9%)

Accuracy

Total 1.4b remaining (97.4%)

Threshold costs 0b (0%)

Counts
160 → 1
Compiler

Compiled 24330 to 17678 computations (27.3% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01225
11625
21525

end290.0ms (5%)

Compiler

Compiled 259 to 195 computations (24.7% saved)

Profiling

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