Details

Time bar (total: 9.8s)

analyze252.0ms (2.6%)

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)

sample1.2s (12.7%)

Symmetry

(sort x y)

Results
1.2s8256×body128valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify24.0ms (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

prune14.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
6.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
6.5b
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
Compiler

Compiled 50 to 34 computations (32% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
3.0b
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
3.5b
(*.f64 y (fma.f64 z z 1))

series173.0ms (1.8%)

Counts
2 → 60
Calls

2 calls:

155.0ms
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
18.0ms
(*.f64 y (fma.f64 z z 1))

rewrite41.0ms (0.4%)

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:

24.0ms
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
10.0ms
(*.f64 y (fma.f64 z z 1))

simplify196.0ms (2%)

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

prune226.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1157122
Fresh000
Picked101
Done000
Total1167123
Error
3.6b
Counts
123 → 7
Alt Table
StatusErrorProgram
6.4b
(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
6.5b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
7.2b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
6.6b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
23.9b
(/.f64 (/.f64 1 x) y)
7.1b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
17.9b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
Compiler

Compiled 2272 to 1413 computations (37.8% saved)

localize27.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
3.2b
(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
4.4b
(/.f64 (/.f64 1 x) (fma.f64 z z 1))

series214.0ms (2.2%)

Counts
2 → 60
Calls

2 calls:

153.0ms
(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
60.0ms
(/.f64 (/.f64 1 x) (fma.f64 z z 1))

rewrite82.0ms (0.8%)

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:

39.0ms
(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
9.0ms
(/.f64 (/.f64 1 x) (fma.f64 z z 1))

simplify306.0ms (3.1%)

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

prune493.0ms (5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2985303
Fresh246
Picked011
Done000
Total30010310
Error
1.3b
Counts
310 → 10
Alt Table
StatusErrorProgram
7.1b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
7.1b
(*.f64 (*.f64 (/.f64 1 y) (/.f64 1 x)) (/.f64 1 (fma.f64 z z 1)))
48.9b
(*.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)))
6.4b
(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
7.2b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
3.2b
(*.f64 (/.f64 1 y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
6.6b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
49.1b
(*.f64 (/.f64 1 y) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
3.8b
(*.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))))
17.9b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
Compiler

Compiled 7045 to 4723 computations (33% saved)

localize18.0ms (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)))
0.1b
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
3.2b
(*.f64 (/.f64 1 y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))

series364.0ms (3.7%)

Counts
4 → 96
Calls

4 calls:

194.0ms
(*.f64 (/.f64 1 y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
84.0ms
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
79.0ms
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
6.0ms
(/.f64 1 (hypot.f64 1 z))

rewrite125.0ms (1.3%)

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:

27.0ms
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
26.0ms
(*.f64 (/.f64 1 y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
12.0ms
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
3.0ms
(/.f64 1 (hypot.f64 1 z))

simplify424.0ms (4.3%)

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

prune1.6s (16.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New5156521
Fresh448
Picked101
Done101
Total52110531
Error
0.0b
Counts
531 → 10
Alt Table
StatusErrorProgram
7.1b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
7.1b
(*.f64 (*.f64 (/.f64 1 y) (/.f64 1 x)) (/.f64 1 (fma.f64 z z 1)))
0.7b
(/.f64 (*.f64 1 (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 1 x))) (*.f64 y (hypot.f64 1 z)))
0.7b
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
17.3b
(*.f64 (/.f64 1 (sqrt.f64 y)) (/.f64 (/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (hypot.f64 1 z)) (sqrt.f64 y)))
7.2b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
6.6b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
3.5b
(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))
1.4b
(/.f64 (*.f64 (/.f64 1 y) (*.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z)))) (hypot.f64 1 z))
3.1b
(/.f64 (/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (hypot.f64 1 z)) y)
Compiler

Compiled 13788 to 10315 computations (25.2% saved)

localize14.0ms (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)))

series208.0ms (2.1%)

Counts
3 → 72
Calls

3 calls:

174.0ms
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
25.0ms
(*.f64 y (hypot.f64 1 z))
8.0ms
(hypot.f64 1 z)

rewrite64.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
175×times-frac_binary64
77×add-sqr-sqrt_binary64
75×*-un-lft-identity_binary64
75×add-cube-cbrt_binary64
43×associate-/l*_binary64
Counts
3 → 146
Calls

3 calls:

21.0ms
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
6.0ms
(*.f64 y (hypot.f64 1 z))
1.0ms
(hypot.f64 1 z)

simplify232.0ms (2.4%)

Algorithm
egg-herbie
Rules
805×associate-/l*_binary64
575×fma-def_binary64
472×associate-*l/_binary64
439×associate-/r/_binary64
229×associate-/r*_binary64
Counts
218 → 267
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02944922
17224369
222424049
346694045
449514045

prune989.0ms (10.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New4065411
Fresh549
Picked101
Done000
Total4129421
Error
0.0b
Counts
421 → 9
Alt Table
StatusErrorProgram
7.2b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
0.9b
(/.f64 1 (/.f64 (*.f64 y (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
15.8b
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
7.2b
(*.f64 (/.f64 1 (*.f64 y x)) (/.f64 1 (fma.f64 z z 1)))
1.4b
(/.f64 (*.f64 (/.f64 1 y) (*.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z)))) (hypot.f64 1 z))
0.7b
(/.f64 (/.f64 1 (*.f64 (hypot.f64 1 z) x)) (*.f64 y (hypot.f64 1 z)))
7.1b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
0.7b
(/.f64 (*.f64 (/.f64 1 x) (/.f64 1 (hypot.f64 1 z))) (*.f64 y (hypot.f64 1 z)))
3.1b
(/.f64 (/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (hypot.f64 1 z)) y)
Compiler

Compiled 9385 to 6490 computations (30.8% saved)

regimes2.0s (19.9%)

Accuracy

Total 1.2b remaining (83.7%)

Threshold costs 0b (0%)

Counts
146 → 1
Compiler

Compiled 21186 to 15541 computations (26.6% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11722
21622

end502.0ms (5.1%)

Compiler

Compiled 228 to 170 computations (25.4% saved)

Profiling

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