Details

Time bar (total: 7.4s)

analyze327.0ms (4.4%)

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)

sample964.0ms (13%)

Symmetry

(sort x y)

Results
873.0ms8256×body128valid
52.0ms450×body128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify18.0ms (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%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
5.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
5.9b
(/.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
3.9b
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
4.0b
(*.f64 y (fma.f64 z z 1))

series93.0ms (1.3%)

Counts
2 → 60
Calls

2 calls:

84.0ms
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
9.0ms
(*.f64 y (fma.f64 z z 1))

rewrite13.0ms (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))

simplify116.0ms (1.6%)

Algorithm
egg-herbie
Rules
469×associate-/r*_binary64
451×associate-*l*_binary64
414×associate-/l*_binary64
336×associate-/l/_binary64
296×associate-*r*_binary64
Counts
134 → 122
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01542203
13301967
211071965
339561963
444821963
548061963
649381963

prune175.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1148122
Fresh000
Picked101
Done000
Total1158123
Error
3.8b
Counts
123 → 8
Alt Table
StatusErrorProgram
6.3b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
5.9b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
6.0b
(*.f64 (/.f64 1 y) (/.f64 1 (*.f64 (fma.f64 z z 1) x)))
25.6b
(*.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
6.4b
(*.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)))))
18.5b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
25.4b
(/.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 (*.f64 y (fma.f64 z z 1)) 3)))
5.7b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
Compiler

Compiled 2376 to 1489 computations (37.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.5b
(/.f64 1 (*.f64 y x))
5.3b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))

series138.0ms (1.9%)

Counts
2 → 36
Calls

2 calls:

129.0ms
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
9.0ms
(/.f64 1 (*.f64 y x))

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
36×times-frac_binary64
32×add-exp-log_binary64
20×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
Counts
2 → 84
Calls

2 calls:

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

simplify134.0ms (1.8%)

Algorithm
egg-herbie
Rules
519×fma-def_binary64
468×fma-neg_binary64
445×times-frac_binary64
368×associate-/r*_binary64
345×cancel-sign-sub-inv_binary64
Counts
120 → 121
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01482243
13322008
29002006
332702000
444212000
547932000
649852000
749292000

prune129.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1174121
Fresh347
Picked011
Done000
Total1209129
Error
0.0b
Counts
129 → 9
Alt Table
StatusErrorProgram
6.0b
(*.f64 (/.f64 1 y) (/.f64 1 (*.f64 (fma.f64 z z 1) x)))
5.9b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
25.6b
(*.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
3.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 (*.f64 y x))) (cbrt.f64 (/.f64 1 (*.f64 y x)))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 (*.f64 y x))) (hypot.f64 1 z)))
6.3b
(/.f64 1 (*.f64 y (fma.f64 (*.f64 z z) x x)))
5.9b
(/.f64 1 (*.f64 (fma.f64 z z 1) (*.f64 y x)))
25.4b
(/.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 (*.f64 y (fma.f64 z z 1)) 3)))
5.7b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
1.7b
(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
Compiler

Compiled 2427 to 1429 computations (41.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 1 y) (hypot.f64 1 z))
0.1b
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
1.7b
(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))

series420.0ms (5.7%)

Counts
3 → 84
Calls

3 calls:

326.0ms
(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
50.0ms
(/.f64 (/.f64 1 y) (hypot.f64 1 z))
43.0ms
(/.f64 (/.f64 1 x) (hypot.f64 1 z))

rewrite81.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
322×times-frac_binary64
221×add-sqr-sqrt_binary64
165×*-un-lft-identity_binary64
157×add-cube-cbrt_binary64
121×add-exp-log_binary64
Counts
3 → 298
Calls

3 calls:

31.0ms
(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
7.0ms
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
4.0ms
(/.f64 (/.f64 1 y) (hypot.f64 1 z))

simplify258.0ms (3.5%)

Algorithm
egg-herbie
Rules
591×fma-def_binary64
385×associate-/r/_binary64
376×sub-neg_binary64
361×associate-*l/_binary64
344×associate-*r/_binary64
Counts
382 → 480
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03629105
19998238
228248132
341958128
451008128

prune587.0ms (7.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4773480
Fresh437
Picked011
Done011
Total4818489
Error
0.0b
Counts
489 → 8
Alt Table
StatusErrorProgram
15.7b
(*.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) 1) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
25.4b
(/.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 (*.f64 y (fma.f64 z z 1)) 3)))
6.0b
(*.f64 (/.f64 1 y) (/.f64 1 (*.f64 (fma.f64 z z 1) x)))
3.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 (*.f64 y x))) (cbrt.f64 (/.f64 1 (*.f64 y x)))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 (*.f64 y x))) (hypot.f64 1 z)))
2.3b
(*.f64 (/.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (sqrt.f64 (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (sqrt.f64 (hypot.f64 1 z))))
1.3b
(/.f64 (*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 1 x)) (hypot.f64 1 z))
5.7b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
1.7b
(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
Compiler

Compiled 12841 to 9286 computations (27.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 1 y) (hypot.f64 1 z))
0.5b
(/.f64 (*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 1 x)) (hypot.f64 1 z))
3.7b
(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 1 x))

series211.0ms (2.9%)

Counts
2 → 72
Calls

2 calls:

106.0ms
(/.f64 (*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 1 x)) (hypot.f64 1 z))
105.0ms
(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 1 x))

rewrite46.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
154×add-exp-log_binary64
101×times-frac_binary64
89×div-exp_binary64
86×add-sqr-sqrt_binary64
53×*-un-lft-identity_binary64
Counts
2 → 160
Calls

2 calls:

14.0ms
(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 1 x))
11.0ms
(/.f64 (*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 1 x)) (hypot.f64 1 z))

simplify165.0ms (2.2%)

Algorithm
egg-herbie
Rules
583×fma-neg_binary64
488×associate-/r/_binary64
378×*-commutative_binary64
376×sub-neg_binary64
280×fma-def_binary64
Counts
232 → 280
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02755200
17364438
222194347
338814317
446944317
549544317

prune431.0ms (5.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New3940394
Fresh055
Picked011
Done022
Total3948402
Error
0.0b
Counts
402 → 8
Alt Table
StatusErrorProgram
15.7b
(*.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) 1) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
25.4b
(/.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 (*.f64 y (fma.f64 z z 1)) 3)))
6.0b
(*.f64 (/.f64 1 y) (/.f64 1 (*.f64 (fma.f64 z z 1) x)))
3.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 (*.f64 y x))) (cbrt.f64 (/.f64 1 (*.f64 y x)))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 (*.f64 y x))) (hypot.f64 1 z)))
2.3b
(*.f64 (/.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (sqrt.f64 (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (sqrt.f64 (hypot.f64 1 z))))
1.3b
(/.f64 (*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 1 x)) (hypot.f64 1 z))
5.7b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
1.7b
(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
Compiler

Compiled 9886 to 7022 computations (29% saved)

regimes2.9s (38.9%)

Accuracy

Total 1.4b remaining (96%)

Threshold costs 0b (0%)

Counts
204 → 1
Compiler

Compiled 36190 to 26940 computations (25.6% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
*-rgt-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
11419
21319

end166.0ms (2.2%)

Remove

(sort x y)

Compiler

Compiled 225 to 169 computations (24.9% saved)

Profiling

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