Details

analyze553.0ms

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
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

sample61.0ms

Algorithm

intervals

Results

19.0ms	40×	body	1280	valid
11.0ms	37×	body	640	valid
8.0ms	152×	body	80	valid
4.0ms	19×	body	320	valid
3.0ms	7×	body	1280	invalid
2.0ms	6×	body	640	invalid
1.0ms	8×	body	160	valid
1.0ms	5×	body	320	invalid
1.0ms	5×	body	160	invalid
1.0ms	9×	body	80	invalid
0.0ms	5×	body	80	nan

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4776	9
1	4776	9

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: 12.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
7.5b	(pow (/ x (+ x y)) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 66

Calls

2 calls:

5.0ms	(/ x (+ x y))
9.0ms	(pow (/ x (+ x y)) x)

series23.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ x (+ x y))
17.0ms	(pow (/ x (+ x y)) x)

simplify46.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4978	850
1	4978	850

prune123.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	7	73

Merged error: 1.3b

Counts

73 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(* (cbrt (+ x y)) (cbrt (+ x y)))
7.1b	(pow (* (cbrt x) (/ (cbrt x) (* (cbrt (+ x y)) (cbrt (+ x y))))) x)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
29×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
16×	`add-exp-log`
15×	`add-cube-cbrt`
14×	`pow1`
12×	`cbrt-div`
9×	`swap-sqr`
8×	`pow1/3`
7×	`associate-r` `associate-l`
6×	`flip3-+` `flip-+` `distribute-lft-out`
5×	`prod-exp`
4×	`frac-times` `pow-exp` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `pow-prod-down`
2×	`pow-pow` `associate-r/` `div-exp` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-to-exp` `unpow-prod-down` `pow-plus` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
10.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
14.0ms	(pow (* (cbrt x) (/ (cbrt x) (* (cbrt (+ x y)) (cbrt (+ x y))))) x)

series118.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
22.0ms	(cbrt x)
40.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
35.0ms	(pow (* (cbrt x) (/ (cbrt x) (* (cbrt (+ x y)) (cbrt (+ x y))))) x)

simplify34.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5015	1298

prune173.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Merged error: 1.1b

Counts

113 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
4.4b	(pow (/ x (+ x y)) (sqrt x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
6×	`pow-unpow`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `sqrt-prod` `associate-/l*`
2×	`flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 69

Calls

2 calls:

5.0ms	(/ x (+ x y))
7.0ms	(pow (/ x (+ x y)) (sqrt x))

series46.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ x (+ x y))
41.0ms	(pow (/ x (+ x y)) (sqrt x))

simplify44.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4952	931
1	4952	931

prune119.0ms

Filtered

52 candidates to 75 candidates (-44.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	75	5	80

Merged error: 1.1b

Counts

80 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
24.4b	(pow (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
36×	`*-un-lft-identity`
33×	`unpow-prod-down`
24×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`cbrt-prod`
17×	`add-exp-log`
6×	`div-exp` `distribute-lft-out`
5×	`pow1` `pow-exp`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`prod-exp` `div-inv`
1×	`pow-to-exp` `pow-pow` `associate-/r/` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
13.0ms	(pow (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))) x)

series87.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
25.0ms	(cbrt x)
21.0ms	(cbrt x)
20.0ms	(pow (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))) x)

simplify94.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4915	1163
1	4915	1163

prune110.0ms

Filtered

66 candidates to 96 candidates (-45.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	96	5	101

Merged error: 1.1b

Counts

101 → 5

regimes131.0ms

Accuracy

42.7% (9.8b remaining)

Error of 11.0b against oracle of 1.2b and baseline of 18.3b

bsearch225.0ms

Steps

Iters	Range		Point
6	48.43614580902031	728.8349589326887	55.27842919862897
8	-7.72210177220418e-150	-1.51181328436254e-152	-4.887923752884152e-150
10	-5.2065265572835664e+73	-1.0986385542395783e+60	-1.1164790089715684e+60

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	232	145
1	232	145

end0.0ms

sample1.9s

Algorithm

intervals

Results

715.0ms	1462×	body	1280	valid
338.0ms	1162×	body	640	valid
244.0ms	4390×	body	80	valid
138.0ms	670×	body	320	valid
72.0ms	257×	body	640	invalid
43.0ms	99×	body	1280	invalid
41.0ms	316×	body	160	valid
35.0ms	190×	body	320	invalid
16.0ms	136×	body	160	invalid
8.0ms	140×	body	80	invalid
8.0ms	191×	body	80	nan

Details

analyze553.0ms

sample61.0ms

simplify44.0ms

prune7.0ms

localize6.0ms

rewrite16.0ms

series23.0ms

simplify46.0ms

prune123.0ms

localize18.0ms

rewrite30.0ms

series118.0ms

simplify34.0ms

prune173.0ms

localize10.0ms

rewrite14.0ms

series46.0ms

simplify44.0ms

prune119.0ms

localize14.0ms

rewrite20.0ms

series87.0ms

simplify94.0ms

prune110.0ms

regimes131.0ms

bsearch225.0ms

simplify4.0ms

end0.0ms

sample1.9s

Profiling