Details

analyze501.0ms

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
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample35.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
2.0ms	25×	body	80	nan
1.0ms	9×	body	80	invalid

simplify259.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (256.0ms)

Iter	Nodes	Cost
0	2747	36
1	2747	36

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: 20.0b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
19.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4972	950
1	4972	950

prune107.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 9.1b

Counts

69 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

11.8b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

3.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify30.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5471	898

prune102.0ms

Filtered

57 candidates to 68 candidates (-19.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Merged error: 9.1b

Counts

75 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.4b	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)))
7.3b	(/.f64 (*.f64 a c) b)
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
5×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-/r*_binary64` `times-frac_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3--_binary64` `associate-r/_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
14.0ms	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)))
5.0ms	(/.f64 (*.f64 a c) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
14.0ms	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)))
5.0ms	(/.f64 (*.f64 a c) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5037	846

prune97.0ms

Filtered

58 candidates to 83 candidates (-43.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	81	9	90

Merged error: 8.5b

Counts

90 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.4b	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (/.f64 a (/.f64 b c)) b)))
4.2b	(/.f64 a (/.f64 b c))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
21.0ms	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (/.f64 a (/.f64 b c)) b)))
7.0ms	(/.f64 a (/.f64 b c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
14.0ms	(/.f64 (.f64 c 2) (.f64 2 (-.f64 (/.f64 a (/.f64 b c)) b)))
6.0ms	(/.f64 a (/.f64 b c))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4966	1468
1	4966	1468

prune121.0ms

Filtered

101 candidates to 132 candidates (-30.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	130	11	141

Merged error: 7.0b

Counts

141 → 11

regimes268.0ms

Accuracy

93.6% (0.9b remaining)

Error of 6.9b against oracle of 6.0b and baseline of 20.1b

bsearch36.0ms

Steps

Iters	Range		Point
4	1.8716690684573866e+105	2.6004788336923513e+105	2.1413501573873043e+105
6	-2.0226102132763034e+111	-4.2990669334119585e+110	-8.403599521210245e+110

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	127	90
1	127	90

end0.0ms

sample1.0s

Algorithm

intervals

Results

715.0ms	8000×	body	80	valid
55.0ms	639×	body	80	nan
33.0ms	395×	body	80	invalid

Details

analyze501.0ms

sample35.0ms

simplify259.0ms

prune9.0ms

localize20.0ms

rewrite27.0ms

series67.0ms

simplify52.0ms

prune107.0ms

localize25.0ms

rewrite20.0ms

series68.0ms

simplify30.0ms

prune102.0ms

localize23.0ms

rewrite33.0ms

series52.0ms

simplify45.0ms

prune97.0ms

localize23.0ms

rewrite45.0ms

series55.0ms

simplify45.0ms

prune121.0ms

regimes268.0ms

bsearch36.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling