Details

Time bar (total: 6.2s)

analyze411.0ms (6.6%)

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)

sample41.0ms (0.7%)

Algorithm
1×intervals
Results
27.0ms256×body128valid
0.0ms5×body128invalid
Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify87.0ms (1.4%)

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

prune7.0ms (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)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite47.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
34×add-sqr-sqrt_binary64
31×*-un-lft-identity_binary64
27×add-cube-cbrt_binary64
22×add-exp-log_binary64
21×prod-diff_binary64
Counts
4 → 125
Calls

4 calls:

11.0ms
(-.f64 1 (/.f64 1 (*.f64 x 9)))
9.0ms
(/.f64 y (*.f64 3 (sqrt.f64 x)))
7.0ms
(*.f64 3 (sqrt.f64 x))
6.0ms
(/.f64 1 (*.f64 x 9))

series119.0ms (1.9%)

Counts
4 → 36
Calls

4 calls:

90.0ms
(/.f64 y (*.f64 3 (sqrt.f64 x)))
11.0ms
(*.f64 3 (sqrt.f64 x))
10.0ms
(/.f64 1 (*.f64 x 9))
8.0ms
(-.f64 1 (/.f64 1 (*.f64 x 9)))

simplify160.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
612×associate-/l*_binary64
514×fma-def_binary64
439×associate-*l/_binary64
356×associate-/r*_binary64
323×associate-/l/_binary64
Counts
161 → 263
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01721803
13281417
210161288
345911288
448731288

prune352.0ms (5.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2585263
Fresh011
Picked101
Done000
Total2596265
Error
0b
Counts
265 → 6
Alt Table
StatusErrorProgram
0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 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)))
0.4b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
0.5b
(-.f64 (-.f64 1 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (*.f64 x 9))) (cbrt.f64 (/.f64 1 (*.f64 x 9)))) (cbrt.f64 (/.f64 1 (*.f64 x 9))))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.4b
(-.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 (/.f64 (*.f64 3 (sqrt.f64 x)) y)))
Compiler

Compiled 3694 to 2828 computations (23.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite24.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
36×times-frac_binary64
28×add-exp-log_binary64
20×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
Counts
2 → 81
Calls

2 calls:

9.0ms
(/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y))
6.0ms
(/.f64 (*.f64 3 (sqrt.f64 x)) y)

series131.0ms (2.1%)

Counts
2 → 24
Calls

2 calls:

82.0ms
(/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y))
48.0ms
(/.f64 (*.f64 3 (sqrt.f64 x)) y)

simplify234.0ms (3.8%)

Algorithm
1×egg-herbie
Rules
744×div-sub_binary64
432×*-commutative_binary64
368×associate-/l*_binary64
281×sub-neg_binary64
275×associate-/r*_binary64
Counts
105 → 190
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01011477
11981284
26221265
322871265
427021265
530411265
639541265
742311265
849361265
948331265

prune358.0ms (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2900290
Fresh055
Picked011
Done000
Total2906296
Error
0b
Counts
296 → 6
Alt Table
StatusErrorProgram
▶0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 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)))
0.4b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
0.5b
(-.f64 (-.f64 1 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (*.f64 x 9))) (cbrt.f64 (/.f64 1 (*.f64 x 9)))) (cbrt.f64 (/.f64 1 (*.f64 x 9))))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.4b
(-.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 (/.f64 (*.f64 3 (sqrt.f64 x)) y)))
Compiler

Compiled 4092 to 2995 computations (26.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite101.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Rules
349×times-frac_binary64
248×add-sqr-sqrt_binary64
236×*-un-lft-identity_binary64
228×add-cube-cbrt_binary64
129×prod-diff_binary64
Counts
2 → 271
Calls

2 calls:

37.0ms
(-.f64 1 (/.f64 (/.f64 1 x) 9))
9.0ms
(/.f64 (/.f64 1 x) 9)

series18.0ms (0.3%)

Counts
2 → 24
Calls

2 calls:

10.0ms
(/.f64 (/.f64 1 x) 9)
8.0ms
(-.f64 1 (/.f64 (/.f64 1 x) 9))

simplify386.0ms (6.2%)

Algorithm
1×egg-herbie
Rules
619×associate-/l*_binary64
528×times-frac_binary64
393×fma-def_binary64
379×associate-/l/_binary64
204×distribute-neg-frac_binary64
Counts
295 → 562
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02477339
16294850
216493779
348203779
446903779

prune915.0ms (14.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New6731674
Fresh134
Picked011
Done011
Total6746680
Error
0b
Counts
680 → 6
Alt Table
StatusErrorProgram
✓0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 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)))
0.4b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
0.4b
(-.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 (/.f64 (*.f64 3 (sqrt.f64 x)) y)))
0.3b
(-.f64 (-.f64 1 (*.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (sqrt.f64 (/.f64 1 x)) 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
Compiler

Compiled 13515 to 10473 computations (22.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 1 (/.f64 1/9 x))
✓0.1b
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
✓0.3b
(/.f64 1/9 x)
✓0.4b
(/.f64 -1/3 (sqrt.f64 x))

rewrite43.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
77×add-sqr-sqrt_binary64
73×*-un-lft-identity_binary64
69×add-cube-cbrt_binary64
65×times-frac_binary64
39×prod-diff_binary64
Counts
4 → 153
Calls

4 calls:

15.0ms
(-.f64 1 (/.f64 1/9 x))
5.0ms
(/.f64 -1/3 (sqrt.f64 x))
4.0ms
(/.f64 1/9 x)
1.0ms
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))

series131.0ms (2.1%)

Counts
4 → 26
Calls

4 calls:

84.0ms
(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
27.0ms
(/.f64 -1/3 (sqrt.f64 x))
12.0ms
(/.f64 1/9 x)
8.0ms
(-.f64 1 (/.f64 1/9 x))

simplify222.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
618×associate-*r/_binary64
433×fma-def_binary64
371×associate-/l*_binary64
234×fma-neg_binary64
220×log-div_binary64
Counts
179 → 292
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02442593
15012154
212901895
344771895
447701895

prune398.0ms (6.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New2920292
Fresh033
Picked011
Done022
Total2926298
Error
0b
Counts
298 → 6
Alt Table
StatusErrorProgram
✓0.2b
(-.f64 (-.f64 1 (/.f64 (/.f64 1 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)))
0.4b
(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
0.4b
(-.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 (/.f64 (*.f64 3 (sqrt.f64 x)) y)))
0.3b
(-.f64 (-.f64 1 (*.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (sqrt.f64 (/.f64 1 x)) 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
Compiler

Compiled 4350 to 3033 computations (30.3% saved)

regimes418.0ms (6.7%)

Accuracy

Total 0.2b remaining (85.8%)

Threshold costs 0.2b (85.8%)

Compiler

Compiled 3737 to 2998 computations (19.8% saved)

simplify8.0ms (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
33921
44521
54821
64921
74721

end1.0ms (0%)

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.5s (24.6%)

Algorithm
1×intervals
Results
864.0ms8000×body128valid
10.0ms96×body128invalid
Compiler

Compiled 140 to 115 computations (17.9% saved)

Profiling

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