Details

Time bar (total: 2.9s)

analyze65.0ms (2.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
25%25%50%4
25%25%50%5
31.2%18.7%50%6
34.3%15.6%50%7
39%10.9%50%8
40.6%8.6%50.8%9
42.9%5.9%51.2%10
43.7%4.5%51.8%11
44.9%3%52.1%12
45.3%2.3%52.4%13
45.9%1.5%52.6%14
Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.2s (41.2%)

Results
951.0ms8256×body128valid
12.0ms90×body128invalid
Compiler

Compiled 50 to 41 computations (18% saved)

simplify35.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
474×fma-neg_binary64
309×fma-def_binary64
228×cancel-sign-sub-inv_binary64
83×associate-/l*_binary64
72×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01321
12718
25618
311218
420116
533916
660816
785616
889216
990716
1093016
1183716

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.2b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
▶0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
Compiler

Compiled 85 to 66 computations (22.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 1 (/.f64 1 (*.f64 x 9)))
✓0.2b
(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓0.3b
(*.f64 3 (sqrt.f64 x))
✓0.6b
(/.f64 1 (*.f64 x 9))

series30.0ms (1%)

Counts
4 → 36
Calls

4 calls:

20.0ms
(/.f64 y (*.f64 3 (sqrt.f64 x)))
7.0ms
(*.f64 3 (sqrt.f64 x))
1.0ms
(/.f64 1 (*.f64 x 9))
1.0ms
(-.f64 1 (/.f64 1 (*.f64 x 9)))

rewrite72.0ms (2.4%)

Algorithm
2×batch-egg-rewrite
Rules
566×log-prod_binary64
206×expm1-udef_binary64
205×log1p-udef_binary64
184×log-pow_binary64
178×prod-diff_binary64
Counts
4 → 136
Calls

4 calls:

68.0ms
(-.f64 1 (/.f64 1 (*.f64 x 9)))
68.0ms
(/.f64 y (*.f64 3 (sqrt.f64 x)))
68.0ms
(*.f64 3 (sqrt.f64 x))
68.0ms
(/.f64 1 (*.f64 x 9))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01232
125626
2297826
3538226
000
100

simplify20.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
16×fma-def_binary64
11×sub-neg_binary64
9×*-commutative_binary64
6×+-commutative_binary64
4×associate-+l-_binary64
Counts
172 → 141
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015261
128261
243261
359261
471261
589261
6103261
7112261
8119261
989261

prune432.0ms (14.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1347141
Fresh011
Picked101
Done000
Total1358143
Error
0.0b
Counts
143 → 8
Alt Table
StatusErrorProgram
0.5b
(-.f64 (-.f64 1 (pow.f64 (cbrt.f64 (/.f64 1/9 x)) 3)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
▶0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (sqrt.f64 (*.f64 x 9))))
0.2b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
0.2b
(-.f64 (-.f64 1 (*.f64 1/9 (/.f64 1 x))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
27.4b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (pow.f64 (sqrt.f64 (/.f64 y (*.f64 3 (sqrt.f64 x)))) 2))
0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 1/3 (/.f64 y (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (pow.f64 (/.f64 1/3 (sqrt.f64 x)) 2)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
Compiler

Compiled 2801 to 2069 computations (26.1% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 1 (/.f64 1 (*.f64 x 9)))
✓0.2b
(/.f64 y (sqrt.f64 (*.f64 x 9)))
✓0.6b
(sqrt.f64 (*.f64 x 9))
0.6b
(/.f64 1 (*.f64 x 9))

series24.0ms (0.8%)

Counts
2 → 12
Calls

2 calls:

18.0ms
(/.f64 y (sqrt.f64 (*.f64 x 9)))
6.0ms
(sqrt.f64 (*.f64 x 9))

rewrite52.0ms (1.8%)

Algorithm
2×batch-egg-rewrite
Rules
672×log1p-expm1-u_binary64
672×expm1-log1p-u_binary64
357×log-prod_binary64
126×expm1-udef_binary64
126×log1p-udef_binary64
Counts
2 → 71
Calls

2 calls:

51.0ms
(/.f64 y (sqrt.f64 (*.f64 x 9)))
51.0ms
(sqrt.f64 (*.f64 x 9))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
114615
2175215
3534115
000
100

simplify12.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
5×*-commutative_binary64
3×associate-*r*_binary64
3×associate-*l*_binary64
1×1-exp_binary64
Counts
83 → 72
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09144
115144
221144
321144
420144

prune205.0ms (6.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1472149
Fresh257
Picked101
Done000
Total1507157
Error
0.0b
Counts
157 → 7
Alt Table
StatusErrorProgram
0.2b
(-.f64 (-.f64 1 (*.f64 1/9 (/.f64 1 x))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 y (pow.f64 (*.f64 x 9) -1/2)))
27.4b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (pow.f64 (sqrt.f64 (/.f64 y (*.f64 3 (sqrt.f64 x)))) 2))
0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 1/3 (/.f64 y (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (pow.f64 (/.f64 1/3 (sqrt.f64 x)) 2)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.5b
(-.f64 (-.f64 1 (pow.f64 (cbrt.f64 (/.f64 1/9 x)) 3)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
▶0.2b
(-.f64 (-.f64 1 (/.f64 1/9 x)) (/.f64 y (sqrt.f64 (*.f64 x 9))))
Compiler

Compiled 2926 to 2313 computations (21% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 1 (/.f64 1/9 x))
0.2b
(/.f64 y (sqrt.f64 (*.f64 x 9)))
✓0.3b
(/.f64 1/9 x)
0.6b
(sqrt.f64 (*.f64 x 9))

series3.0ms (0.1%)

Counts
2 → 12
Calls

2 calls:

2.0ms
(/.f64 1/9 x)
1.0ms
(-.f64 1 (/.f64 1/9 x))

rewrite76.0ms (2.6%)

Algorithm
2×batch-egg-rewrite
Rules
607×log1p-expm1-u_binary64
607×expm1-log1p-u_binary64
255×log-prod_binary64
244×prod-diff_binary64
111×expm1-udef_binary64
Counts
2 → 72
Calls

2 calls:

74.0ms
(-.f64 1 (/.f64 1/9 x))
74.0ms
(/.f64 1/9 x)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
113211
2155311
3508111
000
100

simplify13.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
16×fma-def_binary64
11×sub-neg_binary64
6×+-commutative_binary64
4×*-commutative_binary64
4×associate-+l-_binary64
Counts
84 → 75
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0969
11969
22869
34469
45669
57469
68869
79769
810469
97469

prune153.0ms (5.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1443147
Fresh336
Picked101
Done000
Total1486154
Error
0.0b
Counts
154 → 6
Alt Table
StatusErrorProgram
0.2b
(-.f64 (fma.f64 -1/9 (/.f64 1 x) 1) (/.f64 y (sqrt.f64 (*.f64 x 9))))
▶0.2b
(-.f64 (-.f64 1 (/.f64 1/9 x)) (*.f64 (pow.f64 (*.f64 x 9) -1/2) y))
27.1b
(-.f64 (-.f64 1 (/.f64 1/9 x)) (pow.f64 (sqrt.f64 (/.f64 y (sqrt.f64 (*.f64 x 9)))) 2))
0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 1/3 (/.f64 y (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (pow.f64 (/.f64 1/3 (sqrt.f64 x)) 2)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.5b
(-.f64 (-.f64 1 (pow.f64 (cbrt.f64 (/.f64 1/9 x)) 3)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
Compiler

Compiled 2687 to 2071 computations (22.9% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 1 (/.f64 1/9 x))
✓0.3b
(*.f64 (pow.f64 (*.f64 x 9) -1/2) y)
0.3b
(/.f64 1/9 x)
✓0.6b
(pow.f64 (*.f64 x 9) -1/2)

series48.0ms (1.6%)

Counts
2 → 24
Calls

2 calls:

30.0ms
(pow.f64 (*.f64 x 9) -1/2)
17.0ms
(*.f64 (pow.f64 (*.f64 x 9) -1/2) y)

rewrite49.0ms (1.7%)

Algorithm
2×batch-egg-rewrite
Rules
696×log1p-expm1-u_binary64
696×expm1-log1p-u_binary64
372×log-prod_binary64
144×expm1-udef_binary64
144×log1p-udef_binary64
Counts
2 → 42
Calls

2 calls:

48.0ms
(*.f64 (pow.f64 (*.f64 x 9) -1/2) y)
48.0ms
(pow.f64 (*.f64 x 9) -1/2)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
117017
2183917
3533117
000
100

simplify45.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
780×unswap-sqr_binary64
612×fma-def_binary64
538×div-sub_binary64
400×fma-neg_binary64
205×sub-neg_binary64
Counts
66 → 48
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
028300
157300
292264
3203228
4465228
51055204
62590204
749204

prune117.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1230123
Fresh055
Picked011
Done000
Total1236129
Error
0.0b
Counts
129 → 6
Alt Table
StatusErrorProgram
0.2b
(-.f64 (fma.f64 -1/9 (/.f64 1 x) 1) (/.f64 y (sqrt.f64 (*.f64 x 9))))
✓0.2b
(-.f64 (-.f64 1 (/.f64 1/9 x)) (*.f64 (pow.f64 (*.f64 x 9) -1/2) y))
27.1b
(-.f64 (-.f64 1 (/.f64 1/9 x)) (pow.f64 (sqrt.f64 (/.f64 y (sqrt.f64 (*.f64 x 9)))) 2))
0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 1/3 (/.f64 y (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (pow.f64 (/.f64 1/3 (sqrt.f64 x)) 2)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.5b
(-.f64 (-.f64 1 (pow.f64 (cbrt.f64 (/.f64 1/9 x)) 3)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
Compiler

Compiled 2307 to 1839 computations (20.3% saved)

regimes145.0ms (4.9%)

Accuracy

Total 0.2b remaining (86.2%)

Threshold costs 0.2b (86.2%)

Counts
46 → 1
Compiler

Compiled 2222 to 1777 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
5×+-commutative_binary64
5×sub-neg_binary64
4×*-commutative_binary64
3×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01218
11918
23118
33718
44118
54218
64018

end96.0ms (3.3%)

Compiler

Compiled 125 to 100 computations (20% saved)

Profiling

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