Details

Time bar (total: 1.6s)

analyze153.0ms (9.8%)

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
25%74.9%0.1%5
25%62.4%12.6%6
25%46.8%28.2%7
31.2%35.9%32.9%8
39%25%36%9
42.9%18.7%38.3%10
47.2%12.9%39.9%11
49.4%9.6%41.1%12
51.6%6.5%41.9%13
52.7%4.8%42.4%14
Compiler

Compiled 16 to 10 computations (37.5% saved)

sample885.0ms (56.7%)

Symmetry

(sort x y)

Results
819.0ms8256×body128valid
25.0ms220×body128invalid
Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify7.0ms (0.4%)

Algorithm
egg-herbie
Rules
33×fma-def_binary64
*-commutative_binary64
+-commutative_binary64
associate-+r+_binary64
associate-+l+_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01017
11914
24512
36812
47012
57012

prune3.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.0b
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
Compiler

Compiled 46 to 24 computations (47.8% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

series6.0ms (0.4%)

Counts
1 → 24
Calls

1 calls:

6.0ms
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

0.0ms
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

simplify39.0ms (2.5%)

Algorithm
egg-herbie
Rules
824×associate-+l+_binary64
820×associate-+r+_binary64
311×distribute-lft-in_binary64
310×distribute-rgt-in_binary64
296×distribute-rgt-out_binary64
Counts
34 → 28
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
025473
148376
292373
3310367
41673367
55874367

prune20.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New26228
Fresh000
Picked011
Done000
Total26329
Error
0b
Counts
29 → 3
Alt Table
StatusErrorProgram
0.0b
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
0.0b
(fma.f64 y (fma.f64 2 x y) (*.f64 x x))
0.0b
(+.f64 (*.f64 2 (*.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
Compiler

Compiled 407 to 198 computations (51.4% saved)

localize8.0ms (0.5%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
0.0b
(*.f64 2 (*.f64 y x))
0.0b
(+.f64 (*.f64 2 (*.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))

series22.0ms (1.4%)

Counts
3 → 18
Calls

3 calls:

13.0ms
(+.f64 (*.f64 2 (*.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
6.0ms
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
4.0ms
(*.f64 2 (*.f64 y x))

rewrite19.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-log-exp_binary64
fma-def_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
3 → 59
Calls

3 calls:

8.0ms
(+.f64 (*.f64 2 (*.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
5.0ms
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
3.0ms
(*.f64 2 (*.f64 y x))

simplify60.0ms (3.8%)

Algorithm
egg-herbie
Rules
662×fma-neg_binary64
654×associate-*l*_binary64
513×associate-*r*_binary64
471×fma-def_binary64
319×distribute-rgt-neg-in_binary64
Counts
77 → 95
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
088905
1248787
2837728
33406728
45028728

prune67.0ms (4.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New94195
Fresh101
Picked101
Done011
Total96298
Error
0b
Counts
98 → 2
Alt Table
StatusErrorProgram
0.0b
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
0.0b
(+.f64 (*.f64 y (+.f64 (*.f64 x 2) y)) (pow.f64 x 2))
Compiler

Compiled 1783 to 1083 computations (39.3% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(*.f64 y (+.f64 (*.f64 x 2) y))
0.0b
(+.f64 (*.f64 y (+.f64 (*.f64 x 2) y)) (pow.f64 x 2))

series12.0ms (0.8%)

Counts
2 → 48
Calls

2 calls:

6.0ms
(+.f64 (*.f64 y (+.f64 (*.f64 x 2) y)) (pow.f64 x 2))
5.0ms
(*.f64 y (+.f64 (*.f64 x 2) y))

rewrite15.0ms (1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
2 → 40
Calls

2 calls:

8.0ms
(*.f64 y (+.f64 (*.f64 x 2) y))
6.0ms
(+.f64 (*.f64 y (+.f64 (*.f64 x 2) y)) (pow.f64 x 2))

simplify77.0ms (4.9%)

Algorithm
egg-herbie
Rules
493×distribute-rgt-in_binary64
478×distribute-lft-in_binary64
458×sub-neg_binary64
448×fma-def_binary64
309×+-commutative_binary64
Counts
88 → 79
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
076964
1236934
2839917
32874917
44399917
55053917

prune52.0ms (3.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New79079
Fresh000
Picked011
Done011
Total79281
Error
0b
Counts
81 → 2
Alt Table
StatusErrorProgram
0.0b
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
0.0b
(+.f64 (*.f64 y (+.f64 (*.f64 x 2) y)) (pow.f64 x 2))
Compiler

Compiled 1335 to 820 computations (38.6% saved)

regimes49.0ms (3.1%)

Accuracy

Total 0.0b remaining (73.8%)

Threshold costs 0.0b (73.8%)

Counts
16 → 1
Compiler

Compiled 498 to 323 computations (35.1% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
11316
21316

end51.0ms (3.2%)

Remove

(sort x y)

Compiler

Compiled 76 to 51 computations (32.9% saved)

Profiling

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