Details

Time bar (total: 4.8s)

analyze59.0ms (1.2%)

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 (25.4%)

Results
948.0ms8256×body128valid
11.0ms102×body128invalid
Compiler

Compiled 50 to 41 computations (18% saved)

simplify37.0ms (0.8%)

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
0.2b
(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)

localize9.0ms (0.2%)

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))
✓0.5b
(/.f64 1 (*.f64 x 9))

series61.0ms (1.3%)

Counts
4 → 38
Calls

4 calls:

26.0ms
(/.f64 y (*.f64 3 (sqrt.f64 x)))
26.0ms
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
7.0ms
(*.f64 3 (sqrt.f64 x))
2.0ms
(/.f64 1 (*.f64 x 9))

rewrite39.0ms (0.8%)

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:

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

simplify155.0ms (3.3%)

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

prune275.0ms (5.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2315236
Fresh011
Picked101
Done000
Total2326238
Error
0.0b
Counts
238 → 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
(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 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
0.3b
(-.f64 (-.f64 1 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 x 9))) (sqrt.f64 (/.f64 1 (*.f64 x 9))))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
Compiler

Compiled 6826 to 4933 computations (27.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(sqrt.f64 (/.f64 1 x))
✓0.3b
(*.f64 y (sqrt.f64 (/.f64 1 x)))
✓0.4b
(*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))))
0.5b
(/.f64 1 (*.f64 x 9))

series36.0ms (0.8%)

Counts
3 → 0
Calls

3 calls:

18.0ms
(*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))))
13.0ms
(*.f64 y (sqrt.f64 (/.f64 1 x)))
5.0ms
(sqrt.f64 (/.f64 1 x))

rewrite28.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64
29×sqrt-prod_binary64
22×times-frac_binary64
22×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
Counts
3 → 88
Calls

3 calls:

16.0ms
(*.f64 y (sqrt.f64 (/.f64 1 x)))
6.0ms
(*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))))
2.0ms
(sqrt.f64 (/.f64 1 x))

simplify107.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
460×associate-/l*_binary64
395×associate-*l*_binary64
354×*-commutative_binary64
326×associate-*l/_binary64
301×associate-/r*_binary64
Counts
88 → 99
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0921020
1154963
2403962
3939962
41338962
52435962
63031962
73633962
84923962
94922962

prune149.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1391140
Fresh145
Picked101
Done000
Total1415146
Error
0.0b
Counts
146 → 5
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))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
0.3b
(-.f64 (-.f64 1 (*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) (*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
0.2b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
Compiler

Compiled 3165 to 2537 computations (19.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series33.0ms (0.7%)

Counts
2 → 26
Calls

2 calls:

31.0ms
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
2.0ms
(/.f64 (/.f64 1 x) 9)

rewrite168.0ms (3.5%)

Algorithm
1×rewrite-expression-head
Rules
458×times-frac_binary64
423×add-sqr-sqrt_binary64
330×*-un-lft-identity_binary64
261×add-cube-cbrt_binary64
213×prod-diff_binary64
Counts
2 → 370
Calls

2 calls:

40.0ms
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
4.0ms
(/.f64 (/.f64 1 x) 9)

simplify312.0ms (6.5%)

Algorithm
1×egg-herbie
Rules
957×fma-neg_binary64
780×times-frac_binary64
216×associate-*r/_binary64
196×associate-*l/_binary64
179×*-commutative_binary64
Counts
396 → 542
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037814432
19769574
226738625
344038501
448778501

prune857.0ms (18%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New5971598
Fresh044
Picked101
Done000
Total5985603
Error
0b
Counts
603 → 5
Alt Table
StatusErrorProgram
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
0.3b
(-.f64 (-.f64 1 (*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) (*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
▶0.2b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
0.5b
(-.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) 3) (/.f64 (cbrt.f64 (/.f64 1 x)) 3))) (/.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))))
Compiler

Compiled 23898 to 17809 computations (25.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
✓0.4b
(/.f64 1/9 x)
✓0.4b
(/.f64 -1/3 (sqrt.f64 x))

series45.0ms (0.9%)

Counts
3 → 14
Calls

3 calls:

28.0ms
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
15.0ms
(/.f64 -1/3 (sqrt.f64 x))
2.0ms
(/.f64 1/9 x)

rewrite8.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
27×times-frac_binary64
26×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
26×add-cube-cbrt_binary64
12×sqrt-prod_binary64
Counts
3 → 80
Calls

3 calls:

3.0ms
(/.f64 -1/3 (sqrt.f64 x))
2.0ms
(/.f64 1/9 x)
0.0ms
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))

simplify102.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
824×fma-def_binary64
571×associate-*l/_binary64
541×times-frac_binary64
427×associate-/l/_binary64
395×associate-*r/_binary64
Counts
94 → 101
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01361257
12181162
24431162
310921161
439261143
545381143
649781143

prune103.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1001101
Fresh134
Picked011
Done000
Total1015106
Error
0b
Counts
106 → 5
Alt Table
StatusErrorProgram
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
0.3b
(-.f64 (-.f64 1 (*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) (*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
✓0.2b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
0.5b
(-.f64 (-.f64 1 (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) 3) (/.f64 (cbrt.f64 (/.f64 1 x)) 3))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (*.f64 (/.f64 (*.f64 (cbrt.f64 1/9) (cbrt.f64 1/9)) (sqrt.f64 x)) (/.f64 (cbrt.f64 1/9) (sqrt.f64 x)))))
Compiler

Compiled 1758 to 1180 computations (32.9% saved)

regimes833.0ms (17.5%)

Accuracy

Total 0.3b remaining (86%)

Threshold costs 0.3b (86%)

Counts
247 → 1
Compiler

Compiled 14882 to 12064 computations (18.9% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01324
12524
23724
35324
46324
56924
67124
76824

end98.0ms (2.1%)

Compiler

Compiled 142 to 115 computations (19% saved)

Profiling

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