Details

analyze462.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample42.0ms

Algorithm

intervals

Results

11.0ms	181×	body	80	valid
7.0ms	28×	body	1280	valid
7.0ms	23×	body	2560	valid
3.0ms	16×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	25×	body	80	nan
1.0ms	17×	body	80	invalid
0.0ms	3×	body	160	valid
0.0ms	2×	body	320	valid

simplify245.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (242.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune7.0ms

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: 31.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite30.0ms

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:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5121	1298

prune123.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 6.4b

Counts

83 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b) 2.0)
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 82

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b) 2.0)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b) 2.0)
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4902	1622
1	4902	1622

prune116.0ms

Filtered

72 candidates to 94 candidates (-30.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	93	9	102

Merged error: 6.4b

Counts

102 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
1.4b	(/.f64 a (/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) 2.0))
12.7b	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac_binary64`
528×	`*-un-lft-identity_binary64`
369×	`add-sqr-sqrt_binary64`
368×	`add-cube-cbrt_binary64`
98×	`associate-/r*_binary64`
80×	`distribute-lft-out_binary64`
53×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
27×	`associate-/r/_binary64`
18×	`div-inv_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
9×	`associate-/l*_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
3×	`sqrt-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `distribute-frac-neg_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 473

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
26.0ms	(/.f64 a (/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) 2.0))
10.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
28.0ms	(/.f64 a (/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) 2.0))
73.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify159.0ms

Algorithm

egg-herbie

Counts

485 → 485

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4987	17207
1	4987	17207

prune1.2s

Filtered

369 candidates to 485 candidates (-31.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	483	2	485
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	484	10	494

Merged error: 6.4b

Counts

494 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.f64 1 (/.f64 (/.f64 a (neg.f64 (.f64 4.0 a))) (/.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) 2.0)))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

21043×	`times-frac_binary64`
8981×	`*-un-lft-identity_binary64`
7396×	`add-sqr-sqrt_binary64`
7395×	`add-cube-cbrt_binary64`
1281×	`associate-/r*_binary64`
793×	`distribute-lft-out_binary64`
696×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
589×	`div-inv_binary64`
533×	`associate-/r/_binary64`
265×	`flip3-+_binary64` `flip-+_binary64`
77×	`add-exp-log_binary64`
59×	`div-exp_binary64`
33×	`add-cbrt-cube_binary64`
22×	`cbrt-undiv_binary64`
8×	`add-log-exp_binary64`
7×	`1-exp_binary64` `rec-exp_binary64`
6×	`pow1_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 5206

Calls

4 calls:

220.0ms	(/.f64 1 (/.f64 (/.f64 a (neg.f64 (.f64 4.0 a))) (/.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) 2.0)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/.f64 1 (/.f64 (/.f64 a (neg.f64 (.f64 4.0 a))) (/.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) 2.0)))
7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
15.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify1.4s

Algorithm

egg-herbie

Counts

5218 → 5218

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	6015	255566

prune56.1s

Filtered

2930 candidates to 5218 candidates (-78.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	5216	2	5218
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	5219	9	5228

Merged error: 6.4b

Counts

5228 → 9

regimes290.0ms

Accuracy

96% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 34.5b

bsearch87.0ms

Steps

Iters	Range	Point
7	1.5706979261724853e+101	1.1623289505261668e+103	2.1921691367601414e+102
11	-8.710184335992647e-265	-1.439150348421662e-297	-6.989967742266468e-286
6	-4.8905778942266995e+118	-6.972514559688472e+117	-4.266218223523121e+118

Iters

Range

Point

1.5706979261724853e+101

1.1623289505261668e+103

2.1921691367601414e+102

-8.710184335992647e-265

-1.439150348421662e-297

-6.989967742266468e-286

-4.8905778942266995e+118

-6.972514559688472e+117

-4.266218223523121e+118

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	124	70
1	124	70

end0.0ms

sample1.2s

Algorithm

intervals

Results

317.0ms	1063×	body	2560	valid
274.0ms	5126×	body	80	valid
212.0ms	869×	body	1280	valid
92.0ms	488×	body	640	valid
46.0ms	129×	body	5120	valid
33.0ms	235×	body	320	valid
32.0ms	646×	body	80	nan
20.0ms	387×	body	80	invalid
9.0ms	90×	body	160	valid

Details

analyze462.0ms

sample42.0ms

simplify245.0ms

prune7.0ms

localize11.0ms

rewrite30.0ms

series63.0ms

simplify41.0ms

prune123.0ms

localize12.0ms

rewrite30.0ms

series55.0ms

simplify70.0ms

prune116.0ms

localize16.0ms

rewrite86.0ms

series132.0ms

simplify159.0ms

prune1.2s

localize18.0ms

rewrite1.2s

series94.0ms

simplify1.4s

prune56.1s

regimes290.0ms

bsearch87.0ms

simplify3.0ms

end0.0ms

sample1.2s

Profiling