Details

Time bar (total: 1.9s)

analyze98.0ms (5.2%)

Algorithm
1×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)

sample747.0ms (39.8%)

Symmetry

(sort x y)

Results
705.0ms8256×body128valid
7.0ms85×body128invalid
Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify13.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
70×fma-def_binary64
24×associate-+l+_binary64
18×associate-+r+_binary64
10×distribute-rgt-in_binary64
8×*-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)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0.3%)

Counts
1 → 24
Calls

1 calls:

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

rewrite46.0ms (2.4%)

Algorithm
2×batch-egg-rewrite
Rules
682×prod-diff_binary64
618×log1p-expm1-u_binary64
618×expm1-log1p-u_binary64
60×add-sqr-sqrt_binary64
57×add-log-exp_binary64
Counts
1 → 29
Calls

1 calls:

44.0ms
(*.f64 (+.f64 x y) (+.f64 x y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11157
215147
350277
000
100

simplify159.0ms (8.5%)

Algorithm
1×egg-herbie
Rules
968×sqr-pow_binary64
615×fma-def_binary64
579×fabs-mul_binary64
537×cube-prod_binary64
464×*-commutative_binary64
Counts
53 → 39
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
012294
132267
262222
3129216
4318216
51005216
61665216
71886216
82020216
92235216
102469216
112722216
122890216
133334216
143914216
154267216
164546216
174648216
184677216
194689216
205141216

prune25.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New37239
Fresh000
Picked011
Done000
Total37340
Error
0b
Counts
40 → 3
Alt Table
StatusErrorProgram
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)))
✓0.0b
(*.f64 (+.f64 x y) (+.f64 x y))
Compiler

Compiled 557 to 216 computations (61.2% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series16.0ms (0.9%)

Counts
2 → 18
Calls

2 calls:

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

rewrite71.0ms (3.8%)

Algorithm
2×batch-egg-rewrite
Rules
576×fma-def_binary64
535×log-prod_binary64
299×fma-neg_binary64
193×expm1-udef_binary64
193×log1p-udef_binary64
Counts
2 → 144
Calls

2 calls:

68.0ms
(+.f64 (*.f64 2 (*.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
68.0ms
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01027
122821
2281421
3570221
000
100

simplify147.0ms (7.8%)

Algorithm
1×egg-herbie
Rules
968×sqr-pow_binary64
579×fabs-mul_binary64
537×cube-prod_binary64
474×fma-def_binary64
464×*-commutative_binary64
Counts
162 → 152
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
010114
126111
249102
311096
428496
594996
6155896
7175396
8188796
9210296
10233696
11259796
12277396
13321696
14379696
15414996
16442896
17453096
18455996
19457196
20502396

prune86.0ms (4.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1511152
Fresh101
Picked101
Done011
Total1532155
Error
0b
Counts
155 → 2
Alt Table
StatusErrorProgram
▶0.0b
(fma.f64 y y (fma.f64 x x (*.f64 2 (*.f64 y x))))
✓0.0b
(*.f64 (+.f64 x y) (+.f64 x y))
Compiler

Compiled 2718 to 1363 computations (49.9% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series18.0ms (0.9%)

Counts
2 → 48
Calls

2 calls:

11.0ms
(fma.f64 x x (*.f64 2 (*.f64 y x)))
6.0ms
(fma.f64 y y (fma.f64 x x (*.f64 2 (*.f64 y x))))

rewrite52.0ms (2.8%)

Algorithm
2×batch-egg-rewrite
Rules
697×log1p-expm1-u_binary64
697×expm1-log1p-u_binary64
214×prod-diff_binary64
144×log1p-udef_binary64
80×add-sqr-sqrt_binary64
Counts
2 → 49
Calls

2 calls:

50.0ms
(fma.f64 y y (fma.f64 x x (*.f64 2 (*.f64 y x))))
50.0ms
(fma.f64 x x (*.f64 2 (*.f64 y x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0826
116124
2182724
3498524
000
100

simplify171.0ms (9.1%)

Algorithm
1×egg-herbie
Rules
968×sqr-pow_binary64
615×fma-def_binary64
579×fabs-mul_binary64
537×cube-prod_binary64
464×*-commutative_binary64
Counts
97 → 60
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
012525
132480
262399
3129393
4318393
51005393
61665393
71886393
82020393
92235393
102469393
112722393
122890393
133334393
143914393
154267393
164546393
174648393
184677393
194689393
205141393

prune38.0ms (2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New60060
Fresh000
Picked011
Done011
Total60262
Error
0b
Counts
62 → 2
Alt Table
StatusErrorProgram
✓0.0b
(fma.f64 y y (fma.f64 x x (*.f64 2 (*.f64 y x))))
✓0.0b
(*.f64 (+.f64 x y) (+.f64 x y))
Compiler

Compiled 876 to 478 computations (45.4% saved)

regimes112.0ms (6%)

Accuracy

Total 0.0b remaining (82%)

Threshold costs 0.0b (82%)

Counts
27 → 1
Compiler

Compiled 1118 to 703 computations (37.1% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
11114
21114

end54.0ms (2.9%)

Remove

(sort x y)

Compiler

Compiled 70 to 39 computations (44.3% saved)

Profiling

Loading profile data...