Details

analyze475.0ms

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

sample41.0ms

Algorithm

intervals

Results

10.0ms	181×	body	80	valid
7.0ms	28×	body	1280	valid
7.0ms	23×	body	2560	valid
3.0ms	16×	body	640	valid
1.0ms	25×	body	80	nan
1.0ms	3×	body	5120	valid
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 (243.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune10.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b) (.f64 a 2.0))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 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 4.0 (.f64 a c)))) b) (.f64 a 2.0))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b) (.f64 a 2.0))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
8.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4986	1298
1	4986	1298

prune316.0ms

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

rewrite34.0ms

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 4.0 (*.f64 a c)))) b) 2.0)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
7.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b) 2.0)
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
8.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5658	1622

prune114.0ms

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

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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:

9.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
26.0ms	(/.f64 a (/.f64 (/.f64 (neg.f64 (.f64 4.0 (.f64 a c))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))) 2.0))
10.0ms	(/.f64 (neg.f64 (.f64 4.0 (.f64 a c))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
31.0ms	(/.f64 a (/.f64 (/.f64 (neg.f64 (.f64 4.0 (.f64 a c))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))) 2.0))
78.0ms	(/.f64 (neg.f64 (.f64 4.0 (.f64 a c))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify111.0ms

Algorithm

egg-herbie

Counts

485 → 485

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5281	17163

prune1.2s

Filtered

369 candidates to 485 candidates (-31.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	483	2	485
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	483	11	494

Merged error: 6.4b

Counts

494 → 11

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(-.f64 (/.f64 c b) (/.f64 b a))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
6×	`times-frac_binary64`
4×	`difference-of-squares_binary64`
3×	`add-log-exp_binary64`
2×	`distribute-lft-out--_binary64`
1×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

1 → 18

Calls

1 calls:

13.0ms

(-.f64 (/.f64 c b) (/.f64 b a))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(-.f64 (/.f64 c b) (/.f64 b a))

simplify45.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4996	245
1	4996	245

prune21.0ms

Filtered

17 candidates to 21 candidates (-23.5%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	16	5	21
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	16	16	32

Merged error: 6.4b

Counts

32 → 16

regimes369.0ms

Accuracy

83.9% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 34.5b

bsearch50.0ms

Steps

Iters	Range		Point
9	1.1186246520695868e-45	3.3139379921630177e-38	8.399917751723213e-42
6	-4.8905778942266995e+118	-6.972514559688472e+117	-4.266218223523121e+118

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	113	41
1	113	41

end0.0ms

sample1.3s

Algorithm

intervals

Results

329.0ms	1063×	body	2560	valid
279.0ms	5126×	body	80	valid
223.0ms	869×	body	1280	valid
99.0ms	488×	body	640	valid
47.0ms	129×	body	5120	valid
35.0ms	235×	body	320	valid
33.0ms	646×	body	80	nan
21.0ms	387×	body	80	invalid
9.0ms	90×	body	160	valid

Details

analyze475.0ms

sample41.0ms

simplify245.0ms

prune10.0ms

localize10.0ms

rewrite31.0ms

series69.0ms

simplify44.0ms

prune316.0ms

localize12.0ms

rewrite34.0ms

series57.0ms

simplify59.0ms

prune114.0ms

localize14.0ms

rewrite85.0ms

series143.0ms

simplify111.0ms

prune1.2s

localize6.0ms

rewrite13.0ms

series7.0ms

simplify45.0ms

prune21.0ms

regimes369.0ms

bsearch50.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling