Details

Time bar (total: 3.9s)

analyze267.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14

sample52.0ms

Algorithm
intervals
Results
18.0ms111×body320valid
9.0ms99×body160valid
8.0ms286×pre80true
3.0ms18×body640valid
1.0ms30×body80nan
1.0ms28×body80valid

simplify228.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (226.0ms)

IterNodesCost
0183316
1183316

prune7.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 52.8b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
28.1b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
13×*-un-lft-identity_binary64
9×add-exp-log_binary64 add-cbrt-cube_binary64
8×add-log-exp_binary64
7×add-cube-cbrt_binary64
6×difference-of-squares_binary64 associate-/l*_binary64 times-frac_binary64 sqrt-prod_binary64
5×pow1_binary64
4×flip3--_binary64 flip--_binary64
3×distribute-lft-out--_binary64
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 cbrt-undiv_binary64 div-exp_binary64 sqrt-div_binary64
1×associate-/r*_binary64 pow1/2_binary64 cbrt-unprod_binary64 sqrt-pow1_binary64 div-sub_binary64 rem-sqrt-square_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-inv_binary64
Counts
4 → 70
Calls
4 calls:
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
14.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

series68.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
9.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
27.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
17.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

simplify65.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049001294
149001294

prune93.0ms

Filtered
62 candidates to 82 candidates (-32.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh000
Picked101
Done000
Total80383

Merged error: 0.1b

Counts
83 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.3b
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.3b
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log_binary64 add-cbrt-cube_binary64
22×times-frac_binary64
20×*-un-lft-identity_binary64
17×cbrt-undiv_binary64 div-exp_binary64
13×cbrt-unprod_binary64 prod-exp_binary64
11×associate-/l*_binary64
10×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
8×add-log-exp_binary64
6×associate-/r/_binary64
5×associate-/r*_binary64 distribute-lft-out_binary64
4×flip3-+_binary64 pow1_binary64 div-inv_binary64 flip-+_binary64
2×clear-num_binary64 frac-2neg_binary64
1×associate-/l/_binary64 sub-neg_binary64 flip3--_binary64 diff-log_binary64 +-commutative_binary64 flip--_binary64 sum-log_binary64
Counts
4 → 98
Calls
4 calls:
6.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
12.0ms
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
15.0ms
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))

series142.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
9.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
63.0ms
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
51.0ms
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))

simplify52.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
049492008
149492008

prune131.0ms

Filtered
75 candidates to 110 candidates (-46.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1055110
Fresh202
Picked101
Done000
Total1085113

Merged error: 0b

Counts
113 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
0.1b
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
0.1b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
14×add-cube-cbrt_binary64
12×times-frac_binary64
8×add-log-exp_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
5×pow1_binary64 distribute-lft-out_binary64
4×associate-/r*_binary64
3×associate-/l*_binary64 sqrt-prod_binary64
2×flip3-+_binary64 flip3--_binary64 associate-/r/_binary64 flip--_binary64 flip-+_binary64 sqrt-div_binary64
1×sub-neg_binary64 pow1/2_binary64 diff-log_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 71
Calls
4 calls:
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
8.0ms
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
7.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

series94.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
51.0ms
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
18.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
9.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

simplify69.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049041292
149041292

prune95.0ms

Filtered
64 candidates to 83 candidates (-29.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New83083
Fresh044
Picked011
Done000
Total83588

Merged error: 0b

Counts
88 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (*.f64 c -4) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))) 3)))
0.3b
(+.f64 (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))) (*.f64 a (*.f64 c -4)))
0.3b
(*.f64 (/.f64 (*.f64 c -4) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))) 3))) (/.f64 (+.f64 (*.f64 b b) (+.f64 (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))) (*.f64 a (*.f64 c -4)))) 2))
28.1b
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity_binary64
30×add-exp-log_binary64 add-cbrt-cube_binary64
28×times-frac_binary64
24×add-sqr-sqrt_binary64
15×distribute-lft-out_binary64 add-cube-cbrt_binary64 associate-*l*_binary64
13×associate-*r*_binary64
12×unpow-prod-down_binary64 cube-prod_binary64
9×associate-/r*_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64
8×add-log-exp_binary64
6×pow1_binary64
4×associate-/r/_binary64
3×flip3-+_binary64 sub-neg_binary64 sum-cubes_binary64 div-inv_binary64 flip-+_binary64
2×associate-+l+_binary64 unswap-sqr_binary64 difference-of-squares_binary64
1×pow-prod-down_binary64 flip3--_binary64 diff-log_binary64 associate-*r/_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 distribute-lft-out--_binary64 +-commutative_binary64 flip--_binary64 sqrt-prod_binary64 frac-times_binary64 associate-*l/_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 116
Calls
4 calls:
24.0ms
(/.f64 (*.f64 c -4) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))) 3)))
12.0ms
(+.f64 (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))) (*.f64 a (*.f64 c -4)))
38.0ms
(*.f64 (/.f64 (*.f64 c -4) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))) 3))) (/.f64 (+.f64 (*.f64 b b) (+.f64 (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))) (*.f64 a (*.f64 c -4)))) 2))
7.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/.f64 (*.f64 c -4) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))) 3)))
25.0ms
(+.f64 (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))) (*.f64 a (*.f64 c -4)))
267.0ms
(*.f64 (/.f64 (*.f64 c -4) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))) 3))) (/.f64 (+.f64 (*.f64 b b) (+.f64 (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))) (*.f64 a (*.f64 c -4)))) 2))
16.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))

simplify77.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049453955
149453955

prune196.0ms

Filtered
87 candidates to 128 candidates (-47.1%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1280128
Fresh033
Picked011
Done011
Total1285133

Merged error: 0b

Counts
133 → 5

regimes155.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06216
16216

end0.0ms

sample1.5s

Algorithm
intervals
Results
519.0ms3640×body320valid
280.0ms2928×body160valid
252.0ms8823×pre80true
99.0ms530×body640valid
48.0ms902×body80valid
41.0ms823×body80nan

Profiling

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