Details

analyze499.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample44.0ms

Algorithm

intervals

Results

12.0ms	37×	body	2560	valid
9.0ms	165×	body	80	valid
5.0ms	20×	body	1280	valid
4.0ms	21×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	15×	body	80	nan
1.0ms	11×	body	80	invalid
1.0ms	5×	body	160	valid

simplify206.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (204.0ms)

Iter	Nodes	Cost
0	1801	16
1	1801	16

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 35.8b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite31.0ms

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:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4895	1297
1	4895	1297

prune138.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 7.0b

Counts

83 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.4b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
11.5b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`distribute-lft-out_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 101

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
12.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series139.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
48.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
64.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5324	2082

prune208.0ms

Filtered

75 candidates to 113 candidates (-50.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	113	12	125

Merged error: 7.0b

Counts

125 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64` `times-frac_binary64`
3×	`distribute-lft-out_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 63

Calls

4 calls:

10.0ms	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
17.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5000	1102

prune117.0ms

Filtered

58 candidates to 75 candidates (-29.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	74	13	87

Merged error: 6.9b

Counts

87 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.5b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
14.4b	(+.f64 b (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`log-prod_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `log-pow_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `exp-diff_binary64` `log-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 60

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
7.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
9.0ms	(+.f64 b (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
16.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
18.0ms	(+.f64 b (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5101	936

prune86.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	71	14	85

Merged error: 6.9b

Counts

85 → 14

regimes388.0ms

Accuracy

94.6% (1.3b remaining)

Error of 7.1b against oracle of 5.7b and baseline of 30.0b

bsearch104.0ms

Steps

Iters	Range	Point
8	6.255575132316487e+116	2.9549336768798837e+119	1.7451134981590885e+117
11	8.584401684241317e-280	8.198110145387442e-253	2.4133286600301676e-279
8	-1.9879111548891986e+99	-6.631864365660487e+94	-1.7028086930165435e+99

Iters

Range

Point

6.255575132316487e+116

2.9549336768798837e+119

1.7451134981590885e+117

8.584401684241317e-280

8.198110145387442e-253

2.4133286600301676e-279

-1.9879111548891986e+99

-6.631864365660487e+94

-1.7028086930165435e+99

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	123	64
1	123	64

end0.0ms

sample1.3s

Algorithm

intervals

Results

338.0ms	1034×	body	2560	valid
300.0ms	5203×	body	80	valid
239.0ms	890×	body	1280	valid
97.0ms	438×	body	640	valid
41.0ms	104×	body	5120	valid
36.0ms	636×	body	80	nan
35.0ms	223×	body	320	valid
21.0ms	371×	body	80	invalid
11.0ms	108×	body	160	valid

Details

analyze499.0ms

sample44.0ms

simplify206.0ms

prune9.0ms

localize9.0ms

rewrite31.0ms

series71.0ms

simplify72.0ms

prune138.0ms

localize13.0ms

rewrite39.0ms

series139.0ms

simplify51.0ms

prune208.0ms

localize13.0ms

rewrite28.0ms

series101.0ms

simplify44.0ms

prune117.0ms

localize17.0ms

rewrite27.0ms

series60.0ms

simplify51.0ms

prune86.0ms

regimes388.0ms

bsearch104.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling