Details

Time bar (total: 6.1s)

analyze60.0ms (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)

sample1.3s (21.8%)

Results
1.1s8256×body128valid
12.0ms106×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
▶0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
Compiler

Compiled 85 to 66 computations (22.4% saved)

localize9.0ms (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))))
✓0.3b
(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓0.3b
(/.f64 1 (*.f64 x 9))
✓0.3b
(*.f64 3 (sqrt.f64 x))

series96.0ms (1.6%)

Counts
4 → 38
Calls

4 calls:

41.0ms
(*.f64 3 (sqrt.f64 x))
28.0ms
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
25.0ms
(/.f64 y (*.f64 3 (sqrt.f64 x)))
1.0ms
(/.f64 1 (*.f64 x 9))

rewrite43.0ms (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:

12.0ms
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
7.0ms
(/.f64 y (*.f64 3 (sqrt.f64 x)))
4.0ms
(*.f64 3 (sqrt.f64 x))
3.0ms
(/.f64 1 (*.f64 x 9))

simplify163.0ms (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

prune336.0ms (5.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2288236
Fresh011
Picked101
Done000
Total2299238
Error
0.0b
Counts
238 → 9
Alt Table
StatusErrorProgram
0.2b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y)))
0.6b
(-.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 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
14.7b
(/.f64 (-.f64 (*.f64 (-.f64 (*.f64 1 1) (*.f64 (/.f64 1 (*.f64 x 9)) (/.f64 1 (*.f64 x 9)))) (*.f64 3 (sqrt.f64 x))) (*.f64 (+.f64 1 (/.f64 1 (*.f64 x 9))) y)) (*.f64 (+.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 3 (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (*.f64 (/.f64 1 x) 1/9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 3) (sqrt.f64 x)))))
0.3b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
Compiler

Compiled 6980 to 5059 computations (27.5% saved)

localize9.0ms (0.1%)

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 (/.f64 1 x) 9)
0.3b
(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b
(*.f64 3 (sqrt.f64 x))

series31.0ms (0.5%)

Counts
2 → 26
Calls

2 calls:

29.0ms
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
2.0ms
(/.f64 (/.f64 1 x) 9)

rewrite105.0ms (1.7%)

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:

33.0ms
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
4.0ms
(/.f64 (/.f64 1 x) 9)

simplify314.0ms (5.2%)

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

prune914.0ms (15%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New5953598
Fresh628
Picked101
Done000
Total6025607
Error
0b
Counts
607 → 5
Alt Table
StatusErrorProgram
▶0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1/3 x) (sqrt.f64 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1/9 (sqrt.f64 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 3) (sqrt.f64 x)))))
Compiler

Compiled 23870 to 17785 computations (25.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 3 (/.f64 y (sqrt.f64 x)))
0.2b
(/.f64 (/.f64 1 x) 9)
✓0.3b
(/.f64 y (sqrt.f64 x))
✓0.9b
(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))

series70.0ms (1.1%)

Counts
3 → 36
Calls

3 calls:

32.0ms
(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
23.0ms
(/.f64 y (sqrt.f64 x))
15.0ms
(/.f64 3 (/.f64 y (sqrt.f64 x)))

rewrite88.0ms (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:

15.0ms
(/.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))

simplify694.0ms (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

prune757.0ms (12.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New6830683
Fresh044
Picked011
Done000
Total6835688
Error
0b
Counts
688 → 5
Alt Table
StatusErrorProgram
✓0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
▶0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1/3 x) (sqrt.f64 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1/9 (sqrt.f64 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 3) (sqrt.f64 x)))))
Compiler

Compiled 18800 to 11925 computations (36.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series3.0ms (0.1%)

Counts
2 → 12
Calls

2 calls:

2.0ms
(/.f64 1/3 x)
2.0ms
(/.f64 (/.f64 1/3 x) (sqrt.f64 9))

rewrite21.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
150×times-frac_binary64
87×*-un-lft-identity_binary64
87×add-sqr-sqrt_binary64
87×add-cube-cbrt_binary64
42×sqrt-prod_binary64
Counts
2 → 143
Calls

2 calls:

8.0ms
(/.f64 (/.f64 1/3 x) (sqrt.f64 9))
2.0ms
(/.f64 1/3 x)

simplify225.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
1117×fma-neg_binary64
544×associate-*r/_binary64
539×associate-/r/_binary64
355×*-commutative_binary64
335×associate-/l/_binary64
Counts
155 → 207
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01962468
13862352
27992352
317962352
422252352
525362352
631292352
737192352
839232352
942422352
1046222352
1147272352

prune288.0ms (4.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2630263
Fresh033
Picked011
Done011
Total2635268
Error
0b
Counts
268 → 5
Alt Table
StatusErrorProgram
✓0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
✓0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1/3 x) (sqrt.f64 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1/9 (sqrt.f64 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (*.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
0.3b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 y (*.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 3) (sqrt.f64 x)))))
Compiler

Compiled 6148 to 4595 computations (25.3% saved)

regimes345.0ms (5.7%)

Accuracy

Total 0.2b remaining (85.1%)

Threshold costs 0.2b (85.1%)

Counts
100 → 1
Compiler

Compiled 5654 to 4555 computations (19.4% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01321
12021
23121
34121
44721
54921
64721

end114.0ms (1.9%)

Compiler

Compiled 125 to 101 computations (19.2% saved)

Profiling

Loading profile data...