Details

Time bar (total: 3.1s)

analyze802.0ms

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

sample34.0ms

Algorithm
intervals
Results
11.0ms208×body80valid
4.0ms256×pre80true
4.0ms12×body2560valid
3.0ms10×body1280valid
3.0ms16×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
03717
13717

prune4.0ms

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: 10.6b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))
0.0b
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))
0.5b
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))
15.9b
(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity_binary64
21×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
18×times-frac_binary64
15×sqrt-prod_binary64
8×add-log-exp_binary64
6×associate-/r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
5×pow1_binary64
4×flip3-+_binary64 flip-+_binary64 sqrt-div_binary64
3×associate-/l*_binary64
2×associate-/r/_binary64 +-commutative_binary64 sum-log_binary64
1×pow1/2_binary64 distribute-lft-out_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
4 → 79
Calls
4 calls:
7.0ms
(+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))
12.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))
15.0ms
(+.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)))

series37.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))
10.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))
13.0ms
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))))
8.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))

simplify69.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049221364
149221364

prune109.0ms

Filtered
71 candidates to 91 candidates (-28.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New791291
Fresh000
Picked101
Done000
Total801292

Merged error: 10.2b

Counts
92 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))
0.2b
(*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
3.1b
(+.f64 1 (*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))
15.9b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt_binary64
24×associate-*r*_binary64
22×times-frac_binary64
21×*-un-lft-identity_binary64
19×add-cube-cbrt_binary64
14×sqrt-prod_binary64
13×add-exp-log_binary64
9×add-cbrt-cube_binary64
8×add-log-exp_binary64
7×pow1_binary64
5×unswap-sqr_binary64
4×flip3-+_binary64 prod-exp_binary64 flip-+_binary64 sqrt-div_binary64
3×associate-*l*_binary64
2×cbrt-unprod_binary64 associate-/r/_binary64 div-exp_binary64 +-commutative_binary64 sum-log_binary64
1×pow-prod-down_binary64 pow1/2_binary64 1-exp_binary64 cbrt-undiv_binary64 associate-*r/_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 rec-exp_binary64 un-div-inv_binary64 div-inv_binary64 *-commutative_binary64
Counts
4 → 86
Calls
4 calls:
6.0ms
(+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))
15.0ms
(*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
4.0ms
(+.f64 1 (*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))
6.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

series37.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))
10.0ms
(*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
13.0ms
(+.f64 1 (*.f64 x (/.f64 1 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x))))))
8.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

simplify53.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049391275
149391275

prune94.0ms

Filtered
71 candidates to 98 candidates (-38.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New96298
Fresh3811
Picked011
Done000
Total9911110

Merged error: 10.2b

Counts
110 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
5.5b
(+.f64 1 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))))
15.9b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
15.9b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod_binary64
50×add-sqr-sqrt_binary64
34×sqrt-pow1_binary64
29×pow1_binary64
28×sqrt-div_binary64
20×*-un-lft-identity_binary64
18×pow1/2_binary64 add-cube-cbrt_binary64
15×swap-sqr_binary64
9×flip3-+_binary64 associate-*r*_binary64 pow-prod-up_binary64 associate-*l*_binary64 unswap-sqr_binary64 flip-+_binary64
6×add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
5×pow-prod-down_binary64 pow-sqr_binary64
4×frac-times_binary64
2×associate-*r/_binary64 rem-sqrt-square_binary64 associate-*l/_binary64
1×cbrt-unprod_binary64 distribute-lft-out_binary64 rem-square-sqrt_binary64 pow-plus_binary64 sqrt-unprod_binary64 prod-exp_binary64 +-commutative_binary64 pow2_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 125
Calls
4 calls:
20.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
11.0ms
(+.f64 1 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x 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)))

series39.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
13.0ms
(+.f64 1 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))))
10.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
8.0ms
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))

simplify78.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049521842
149521842

prune112.0ms

Filtered
83 candidates to 137 candidates (-65.1%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1361137
Fresh099
Picked011
Done011
Total13612148

Merged error: 10.2b

Counts
148 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.f64 x (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))))
5.8b
(+.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)))))))
15.9b
(sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))
15.9b
(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)))

series54.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/.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)))

simplify51.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049461751
149461751

prune107.0ms

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

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1051106
Fresh189
Picked101
Done022
Total10711118

Merged error: 10.2b

Counts
118 → 11

regimes94.0ms

Accuracy

0% (0.5b remaining)

Error of 13.3b against oracle of 12.8b and baseline of 13.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02219
12219

end0.0ms

sample1.1s

Algorithm
intervals
Results
313.0ms6041×body80valid
249.0ms791×body2560valid
156.0ms609×body1280valid
135.0ms8000×pre80true
62.0ms314×body640valid
24.0ms156×body320valid
9.0ms89×body160valid

Profiling

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