Details

Time bar (total: 1.4s)

analyze90.0ms (6.3%)

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%56.2%18.8%6
25%40.6%34.4%7
31.2%31.2%37.6%8
39%21.1%39.9%9
42.9%16%41.1%10
47.2%10.7%42%11
49.4%8.1%42.5%12
51.6%5.4%43%13
52.7%4.1%43.2%14
Compiler

Compiled 10 to 5 computations (50% saved)

sample690.0ms (48.3%)

Symmetry

(sort x y)

Results
646.0ms8256×body128valid
9.0ms106×body128invalid
Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify9.0ms (0.6%)

Algorithm
egg-herbie
Rules
70×fma-def_binary64
24×associate-+l+_binary64
18×associate-+r+_binary64
10×distribute-rgt-in_binary64
*-commutative_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0510
11210
22610
34610
48110
510110
611710
713010
813210
913210

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.0b
(*.f64 (+.f64 x y) (+.f64 x y))
Compiler

Compiled 27 to 12 computations (55.6% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0.4%)

Counts
1 → 24
Calls

1 calls:

5.0ms
(*.f64 (+.f64 x y) (+.f64 x y))

rewrite8.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity_binary64
pow1_binary64
add-sqr-sqrt_binary64
distribute-lft-out_binary64
swap-sqr_binary64
Counts
1 → 42
Calls

1 calls:

6.0ms
(*.f64 (+.f64 x y) (+.f64 x y))

simplify48.0ms (3.4%)

Algorithm
egg-herbie
Rules
728×associate-+l+_binary64
594×unswap-sqr_binary64
430×distribute-rgt-in_binary64
422×distribute-lft-in_binary64
327×fma-def_binary64
Counts
66 → 64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
068994
1200853
2739757
32462692
45240692

prune36.0ms (2.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New62264
Fresh000
Picked101
Done000
Total63265
Error
0b
Counts
65 → 2
Alt Table
StatusErrorProgram
0.0b
(+.f64 (*.f64 x (+.f64 x y)) (*.f64 y (+.f64 x y)))
0.0b
(+.f64 (*.f64 2 (*.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
Compiler

Compiled 939 to 291 computations (69% saved)

localize5.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series17.0ms (1.2%)

Counts
3 → 72
Calls

3 calls:

8.0ms
(+.f64 (*.f64 x (+.f64 x y)) (*.f64 y (+.f64 x y)))
5.0ms
(*.f64 y (+.f64 x y))
5.0ms
(*.f64 x (+.f64 x y))

rewrite17.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
12×associate-*r/_binary64
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
associate-*r*_binary64
flip-+_binary64
Counts
3 → 73
Calls

3 calls:

5.0ms
(*.f64 x (+.f64 x y))
5.0ms
(+.f64 (*.f64 x (+.f64 x y)) (*.f64 y (+.f64 x y)))
4.0ms
(*.f64 y (+.f64 x y))

simplify86.0ms (6%)

Algorithm
egg-herbie
Rules
873×fma-neg_binary64
401×*-commutative_binary64
387×associate-+l+_binary64
371×cancel-sign-sub-inv_binary64
370×associate-+r+_binary64
Counts
145 → 130
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01201613
13801512
215361408
333001408
448691408
549581408

prune60.0ms (4.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1300130
Fresh011
Picked011
Done000
Total1302132
Error
0b
Counts
132 → 2
Alt Table
StatusErrorProgram
0.0b
(+.f64 (*.f64 x (+.f64 x y)) (*.f64 y (+.f64 x y)))
0.0b
(+.f64 (*.f64 2 (*.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
Compiler

Compiled 2323 to 513 computations (77.9% saved)

localize7.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

series18.0ms (1.3%)

Counts
3 → 18
Calls

3 calls:

7.0ms
(+.f64 (*.f64 2 (*.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
7.0ms
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
4.0ms
(*.f64 2 (*.f64 y x))

rewrite18.0ms (1.3%)

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))

simplify58.0ms (4%)

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

prune61.0ms (4.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New95095
Fresh000
Picked011
Done011
Total95297
Error
0b
Counts
97 → 2
Alt Table
StatusErrorProgram
0.0b
(+.f64 (*.f64 x (+.f64 x y)) (*.f64 y (+.f64 x y)))
0.0b
(+.f64 (*.f64 2 (*.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
Compiler

Compiled 1774 to 1076 computations (39.3% saved)

regimes143.0ms (10%)

Accuracy

Total 0.0b remaining (60.6%)

Threshold costs 0.0b (60.6%)

Counts
41 → 1
Compiler

Compiled 2034 to 1096 computations (46.1% saved)

simplify2.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0716
11116
21116

end44.0ms (3.1%)

Remove

(sort x y)

Compiler

Compiled 80 to 41 computations (48.8% saved)

Profiling

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