Details

Time bar (total: 5.7s)

analyze58.0ms (1%)

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 (21.7%)

Results
978.0ms8256×body128valid
10.0ms92×body128invalid
Compiler

Compiled 50 to 41 computations (18% saved)

simplify34.0ms (0.6%)

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

prune4.0ms (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
0.3b
(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 (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
✓0.2b
(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓0.3b
(*.f64 3 (sqrt.f64 x))
✓0.4b
(/.f64 1 (*.f64 x 9))

series51.0ms (0.9%)

Counts
4 → 38
Calls

4 calls:

24.0ms
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
19.0ms
(/.f64 y (*.f64 3 (sqrt.f64 x)))
7.0ms
(*.f64 3 (sqrt.f64 x))
1.0ms
(/.f64 1 (*.f64 x 9))

rewrite38.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
89×*-un-lft-identity_binary64
80×add-sqr-sqrt_binary64
70×prod-diff_binary64
50×add-cube-cbrt_binary64
42×times-frac_binary64
Counts
4 → 190
Calls

4 calls:

13.0ms
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
4.0ms
(*.f64 3 (sqrt.f64 x))
3.0ms
(/.f64 y (*.f64 3 (sqrt.f64 x)))
3.0ms
(/.f64 1 (*.f64 x 9))

simplify154.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
834×fma-def_binary64
276×fma-neg_binary64
266×exp-prod_binary64
243×cancel-sign-sub-inv_binary64
236×distribute-rgt-in_binary64
Counts
228 → 236
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02715841
16093520
218622992
343542992
448592992
547692992

prune307.0ms (5.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2306236
Fresh011
Picked101
Done000
Total2317238
Error
0.0b
Counts
238 → 7
Alt Table
StatusErrorProgram
▶0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.5b
(-.f64 (-.f64 1 (*.f64 (*.f64 (cbrt.f64 (/.f64 1/9 x)) (cbrt.f64 (/.f64 1/9 x))) (cbrt.f64 (/.f64 1/9 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.4b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 (*.f64 (cbrt.f64 (/.f64 y (*.f64 3 (sqrt.f64 x)))) (cbrt.f64 (/.f64 y (*.f64 3 (sqrt.f64 x))))) (cbrt.f64 (/.f64 y (*.f64 3 (sqrt.f64 x))))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (sqrt.f64 x)))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 (sqrt.f64 (*.f64 3 (sqrt.f64 x))) (sqrt.f64 (*.f64 3 (sqrt.f64 x))))))
0.3b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
Compiler

Compiled 6900 to 4987 computations (27.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 3 (/.f64 y (sqrt.f64 x)))
✓0.3b
(/.f64 y (sqrt.f64 x))
0.4b
(/.f64 1 (*.f64 x 9))
✓1.0b
(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))

series49.0ms (0.9%)

Counts
3 → 36
Calls

3 calls:

22.0ms
(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
17.0ms
(/.f64 y (sqrt.f64 x))
10.0ms
(/.f64 3 (/.f64 y (sqrt.f64 x)))

rewrite80.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Rules
849×times-frac_binary64
413×*-un-lft-identity_binary64
413×add-sqr-sqrt_binary64
413×add-cube-cbrt_binary64
156×sqrt-prod_binary64
Counts
3 → 463
Calls

3 calls:

14.0ms
(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
5.0ms
(/.f64 3 (/.f64 y (sqrt.f64 x)))
3.0ms
(/.f64 y (sqrt.f64 x))

simplify646.0ms (11.4%)

Algorithm
1×egg-herbie
Rules
594×fma-neg_binary64
473×*-commutative_binary64
345×fabs-mul_binary64
344×associate-/r/_binary64
295×fma-def_binary64
Counts
499 → 582
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032011015
161510136
2186410009
3226710009
4266910009
5297010009
6381710009
7463910009
8450210009
9480810009
10493110009
11484010009

prune1.0s (18.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New6203623
Fresh336
Picked101
Done000
Total6246630
Error
0.0b
Counts
630 → 6
Alt Table
StatusErrorProgram
0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.5b
(-.f64 (-.f64 1 (*.f64 (*.f64 (cbrt.f64 (/.f64 1/9 x)) (cbrt.f64 (/.f64 1/9 x))) (cbrt.f64 (/.f64 1/9 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (sqrt.f64 1) (*.f64 3 (/.f64 (sqrt.f64 x) y))))
0.3b
(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 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (/.f64 y (sqrt.f64 x)) (cbrt.f64 3))))
▶0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (*.f64 1/3 y) (sqrt.f64 x)))
Compiler

Compiled 17261 to 10850 computations (37.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (*.f64 1/3 y) (sqrt.f64 x)))
✓0.3b
(*.f64 1/3 y)
✓0.4b
(/.f64 (*.f64 1/3 y) (sqrt.f64 x))
0.4b
(/.f64 1 (*.f64 x 9))

series44.0ms (0.8%)

Counts
3 → 26
Calls

3 calls:

22.0ms
(/.f64 (*.f64 1/3 y) (sqrt.f64 x))
20.0ms
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (*.f64 1/3 y) (sqrt.f64 x)))
2.0ms
(*.f64 1/3 y)

rewrite41.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
110×*-un-lft-identity_binary64
96×add-sqr-sqrt_binary64
91×prod-diff_binary64
66×times-frac_binary64
59×add-cube-cbrt_binary64
Counts
3 → 186
Calls

3 calls:

14.0ms
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (*.f64 1/3 y) (sqrt.f64 x)))
4.0ms
(/.f64 (*.f64 1/3 y) (sqrt.f64 x))
3.0ms
(*.f64 1/3 y)

simplify238.0ms (4.2%)

Algorithm
1×egg-herbie
Rules
733×times-frac_binary64
290×fma-neg_binary64
244×cancel-sign-sub-inv_binary64
229×distribute-rgt-in_binary64
227×exp-prod_binary64
Counts
212 → 220
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02577045
15724210
217543639
343263621
448573621
549813621
649943621
747383621

prune314.0ms (5.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2610261
Fresh055
Picked011
Done000
Total2616267
Error
0.0b
Counts
267 → 6
Alt Table
StatusErrorProgram
0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.5b
(-.f64 (-.f64 1 (*.f64 (*.f64 (cbrt.f64 (/.f64 1/9 x)) (cbrt.f64 (/.f64 1/9 x))) (cbrt.f64 (/.f64 1/9 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
▶0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (sqrt.f64 1) (*.f64 3 (/.f64 (sqrt.f64 x) y))))
0.3b
(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 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (/.f64 y (sqrt.f64 x)) (cbrt.f64 3))))
✓0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (*.f64 1/3 y) (sqrt.f64 x)))
Compiler

Compiled 7717 to 5386 computations (30.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 3 (/.f64 (sqrt.f64 x) y))
✓0.3b
(/.f64 (sqrt.f64 x) y)
0.4b
(/.f64 1 (*.f64 x 9))
✓1.0b
(/.f64 (sqrt.f64 1) (*.f64 3 (/.f64 (sqrt.f64 x) y)))

series39.0ms (0.7%)

Counts
3 → 36
Calls

3 calls:

18.0ms
(/.f64 (sqrt.f64 1) (*.f64 3 (/.f64 (sqrt.f64 x) y)))
10.0ms
(/.f64 (sqrt.f64 x) y)
10.0ms
(*.f64 3 (/.f64 (sqrt.f64 x) y))

rewrite23.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
44×times-frac_binary64
44×add-sqr-sqrt_binary64
36×*-un-lft-identity_binary64
36×add-cube-cbrt_binary64
28×sqrt-prod_binary64
Counts
3 → 117
Calls

3 calls:

6.0ms
(*.f64 3 (/.f64 (sqrt.f64 x) y))
6.0ms
(/.f64 (sqrt.f64 1) (*.f64 3 (/.f64 (sqrt.f64 x) y)))
5.0ms
(/.f64 (sqrt.f64 x) y)

simplify122.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
710×fma-neg_binary64
294×div-sub_binary64
286×times-frac_binary64
236×associate-/l*_binary64
220×fma-def_binary64
Counts
153 → 156
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01401984
12721729
26701701
322701701
424951662
528671662
640541662
750331662

prune218.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1970197
Fresh044
Picked011
Done011
Total1976203
Error
0.0b
Counts
203 → 6
Alt Table
StatusErrorProgram
0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.5b
(-.f64 (-.f64 1 (*.f64 (*.f64 (cbrt.f64 (/.f64 1/9 x)) (cbrt.f64 (/.f64 1/9 x))) (cbrt.f64 (/.f64 1/9 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
✓0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (sqrt.f64 1) (*.f64 3 (/.f64 (sqrt.f64 x) y))))
0.3b
(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 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (/.f64 y (sqrt.f64 x)) (cbrt.f64 3))))
✓0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (*.f64 1/3 y) (sqrt.f64 x)))
Compiler

Compiled 4545 to 3062 computations (32.6% saved)

regimes822.0ms (14.4%)

Accuracy

Total 0.2b remaining (88.5%)

Threshold costs 0.2b (88.5%)

Counts
220 → 1
Compiler

Compiled 14627 to 11971 computations (18.2% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01321
12421
23821
34921
45421
55521
65221

end104.0ms (1.8%)

Compiler

Compiled 146 to 120 computations (17.8% saved)

Profiling

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