Details

analyze472.0ms

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

sample46.0ms

Algorithm

intervals

Results

11.0ms	36×	body	2560	valid
10.0ms	158×	body	80	valid
6.0ms	25×	body	1280	valid
4.0ms	22×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	15×	body	80	nan
1.0ms	7×	body	160	valid
1.0ms	11×	body	80	invalid

simplify218.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (215.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	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: 35.6b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 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 4 (.f64 a c)))) b) (.f64 a 2))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5261	1302

prune126.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

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: 5.7b

Counts

83 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
1.4b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
23.1b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

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`
3×	`distribute-lft-out--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_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` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
11.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
15.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
15.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify66.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4910	1289
1	4910	1289

prune95.0ms

Filtered

59 candidates to 82 candidates (-39.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	82	8	90

Merged error: 5.7b

Counts

90 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
3.6b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
10.9b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
23.1b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

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×	`flip3-+_binary64` `associate-/r*_binary64` `pow1_binary64` `flip-+_binary64`
4×	`distribute-lft-out_binary64` `div-inv_binary64`
3×	`sqrt-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 101

Calls

4 calls:

5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
48.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
63.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
17.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify40.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5289	2015

prune126.0ms

Filtered

75 candidates to 113 candidates (-50.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	112	9	121

Merged error: 5.6b

Counts

121 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
3.6b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4))))))) (/.f64 (.f64 c -4) (sqrt.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))))) (*.f64 a 2))
23.1b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
23.1b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`cbrt-undiv_binary64` `div-exp_binary64`
23×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`sqrt-div_binary64`
3×	`flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate-/r_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `+-commutative_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64`

Counts

4 → 85

Calls

4 calls:

5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
25.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4))))))) (/.f64 (.f64 c -4) (sqrt.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))))) (*.f64 a 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
5.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
50.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4))))))) (/.f64 (.f64 c -4) (sqrt.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))))) (*.f64 a 2))
15.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
17.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify51.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4984	2108
1	4984	2108

prune92.0ms

Filtered

59 candidates to 97 candidates (-64.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	97	9	106

Merged error: 5.6b

Counts

106 → 9

regimes290.0ms

Accuracy

90.4% (2.5b remaining)

Error of 8.2b against oracle of 5.7b and baseline of 32.1b

bsearch91.0ms

Steps

Iters	Range	Point
5	8.194603973169982e+33	3.0846633980758607e+34	1.1883717871229594e+34
11	-1.890663320861311e-283	4.3393826695715665e-302	-7.59554765878054e-309
10	-1.0998777673255094e+163	-5.456439854623745e+151	-1.3667361231028956e+152

Iters

Range

Point

8.194603973169982e+33

3.0846633980758607e+34

1.1883717871229594e+34

-1.890663320861311e-283

4.3393826695715665e-302

-7.59554765878054e-309

-1.0998777673255094e+163

-5.456439854623745e+151

-1.3667361231028956e+152

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	76
1	69	76

end0.0ms

sample1.2s

Algorithm

intervals

Results

311.0ms	1028×	body	2560	valid
275.0ms	5192×	body	80	valid
228.0ms	895×	body	1280	valid
88.0ms	449×	body	640	valid
38.0ms	104×	body	5120	valid
33.0ms	229×	body	320	valid
32.0ms	636×	body	80	nan
20.0ms	372×	body	80	invalid
10.0ms	103×	body	160	valid

Details

analyze472.0ms

sample46.0ms

simplify218.0ms

prune7.0ms

localize11.0ms

rewrite30.0ms

series70.0ms

simplify42.0ms

prune126.0ms

localize11.0ms

rewrite30.0ms

series68.0ms

simplify66.0ms

prune95.0ms

localize12.0ms

rewrite39.0ms

series137.0ms

simplify40.0ms

prune126.0ms

localize16.0ms

rewrite43.0ms

series92.0ms

simplify51.0ms

prune92.0ms

regimes290.0ms

bsearch91.0ms

simplify3.0ms

end0.0ms

sample1.2s

Profiling