Details

Time bar (total: 3.7s)

analyze805.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%48.6%51.4%0
0%48.6%51.4%1
24.3%24.3%51.4%2
24.3%24.3%51.4%3
30.4%18.2%51.4%4
30.4%18.2%51.4%5
33.4%15.2%51.4%6
33.4%15.2%51.4%7
34.6%14.1%51.4%8
34.8%13.9%51.4%9
35.4%13.2%51.4%10
35.6%13.1%51.4%11
35.9%12.7%51.4%12
36%12.6%51.4%13
36.2%12.4%51.4%14

sample39.0ms

Algorithm
intervals
Results
10.0ms193×body80valid
10.0ms31×body2560valid
5.0ms19×body1280valid
5.0ms256×pre80true
1.0ms5×body640valid
1.0ms5×body320valid
0.0ms3×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
03717
13717

prune5.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 13.6b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))))
0.0b
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))
0.8b
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))
15.4b
(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity_binary64
21×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
18×times-frac_binary64
16×sqrt-prod_binary64
8×pow1_binary64
6×associate-/r*_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64
4×flip3-+_binary64 flip-+_binary64
3×sqrt-pow1_binary64 associate-/l*_binary64
2×pow1/2_binary64 associate-*r/_binary64 associate-/r/_binary64
1×pow-prod-down_binary64 distribute-lft-out_binary64 cbrt-undiv_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 81
Calls
4 calls:
15.0ms
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))))
12.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))
14.0ms
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))
6.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))

series55.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))))
10.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))
12.0ms
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))
7.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))

simplify104.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (93.0ms)

IterNodesCost
054241453

prune150.0ms

Filtered
74 candidates to 93 candidates (-25.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New821193
Fresh000
Picked101
Done000
Total831194

Merged error: 13.4b

Counts
94 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
0.8b
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
15.4b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
15.4b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
8×add-log-exp_binary64 add-sqr-sqrt_binary64
6×pow1_binary64 add-cube-cbrt_binary64 sqrt-prod_binary64
4×flip3-+_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip-+_binary64 sqrt-div_binary64
2×pow1/2_binary64 distribute-lft-out_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 54
Calls
4 calls:
14.0ms
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
14.0ms
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
6.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
6.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

series42.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
12.0ms
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
9.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
7.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

simplify82.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
04847864
14847864

prune128.0ms

Filtered
60 candidates to 66 candidates (-10.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New66066
Fresh01010
Picked011
Done000
Total661177

Merged error: 13.4b

Counts
77 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
8.1b
(+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))))
15.4b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
15.4b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod_binary64
30×add-sqr-sqrt_binary64
28×*-un-lft-identity_binary64 add-cube-cbrt_binary64
27×times-frac_binary64
9×associate-/r*_binary64
8×sqrt-div_binary64
6×add-log-exp_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
4×flip3-+_binary64 flip-+_binary64
3×associate-/l*_binary64
2×pow1/2_binary64 associate-/r/_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
1×cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 94
Calls
4 calls:
11.0ms
(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
4.0ms
(+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))))
6.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
6.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

series52.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
13.0ms
(+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))) (/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))))
7.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
8.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
049461751
149461751

prune355.0ms

Filtered
80 candidates to 106 candidates (-32.5%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1042106
Fresh189
Picked011
Done011
Total10512117

Merged error: 13.4b

Counts
117 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.f64 x (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
5.9b
(+.f64 1 (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))) (/.f64 x (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))))
16.2b
(cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
16.2b
(cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
27×times-frac_binary64
24×sqrt-prod_binary64
18×cbrt-prod_binary64
9×associate-/r*_binary64
6×cbrt-div_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
4×flip3-+_binary64 pow1_binary64 flip-+_binary64
3×associate-/l*_binary64
2×pow1/3_binary64 associate-/r/_binary64 sqrt-div_binary64
1×cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 90
Calls
4 calls:
14.0ms
(/.f64 x (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
4.0ms
(+.f64 1 (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))) (/.f64 x (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))))
6.0ms
(cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
6.0ms
(cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

series153.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/.f64 x (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
79.0ms
(+.f64 1 (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))) (/.f64 x (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))))
21.0ms
(cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
21.0ms
(cbrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

simplify73.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
050182037

prune161.0ms

Filtered
82 candidates to 102 candidates (-24.4%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New975102
Fresh369
Picked101
Done022
Total10113114

Merged error: 13.4b

Counts
114 → 13

regimes150.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 13.0b and baseline of 13.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02234
12234

end0.0ms

sample1.1s

Algorithm
intervals
Results
303.0ms6028×body80valid
264.0ms832×body2560valid
163.0ms650×body1280valid
138.0ms8000×pre80true
55.0ms267×body640valid
24.0ms167×body320valid
7.0ms56×body160valid

Profiling

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