Details

analyze418.0ms

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
12.5%	68.6%	18.9%	6
18.7%	62.4%	18.9%	7
18.7%	59.3%	22%	8
28.1%	39%	32.9%	9
32.8%	34.3%	32.9%	10
32.8%	32%	35.3%	11
38.2%	20.7%	41.1%	12
41%	17.9%	41.1%	13
41%	16.6%	42.5%	14

sample65.0ms

Algorithm

intervals

Results

26.0ms	115×	body	320	valid
23.0ms	140×	body	160	valid
3.0ms	40×	body	80	nan
0.0ms	1×	body	80	valid

simplify109.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4881	36
1	4881	36

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.6b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

7.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
29.9b	(sqrt (- (* g g) (* h h)))
29.9b	(sqrt (- (* g g) (* h h)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

18.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
16.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
76.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

simplify41.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5360	1068

prune254.0ms

Filtered

65 candidates to 72 candidates (-10.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	56	16	72
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	57	17	74

Merged error: 31.5b

Counts

74 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
29.9b	(sqrt (- (* g g) (* h h)))
29.9b	(sqrt (- (* g g) (* h h)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 58

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
6.0ms	(sqrt (- (* g g) (* h h)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (* g g) (* h h))
61.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
6.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify38.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4922	834
1	4922	834

prune233.0ms

Filtered

60 candidates to 70 candidates (-16.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	68	19	87

Merged error: 30.5b

Counts

87 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
29.9b	(sqrt (- (* g g) (* h h)))
29.9b	(sqrt (- (* g g) (* h h)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 58

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (* g g) (* h h))
59.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4922	834
1	4922	834

prune217.0ms

Filtered

60 candidates to 70 candidates (-16.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	69	20	89

Merged error: 30.4b

Counts

89 → 20

localize22.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
7.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
29.9b	(sqrt (- (* g g) (* h h)))
29.9b	(sqrt (- (* g g) (* h h)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 58

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (* g g) (* h h))
64.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
6.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5217	847

prune173.0ms

Filtered

59 candidates to 70 candidates (-18.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	70	20	90

Merged error: 30.4b

Counts

90 → 20

regimes944.0ms

Accuracy

61.5% (1.4b remaining)

Error of 31.4b against oracle of 30.1b and baseline of 33.6b

bsearch92.0ms

Steps

Iters	Range		Point
12	-1.429954197556781e-125	-3.585032508441546e-175	-5.606360982697196e-160

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	76	75
1	76	75

end0.0ms

sample1.9s

Algorithm

intervals

Results

891.0ms	3805×	body	320	valid
631.0ms	4057×	body	160	valid
97.0ms	1247×	body	80	nan
11.0ms	138×	body	80	valid

Details

analyze418.0ms

sample65.0ms

simplify109.0ms

prune13.0ms

localize17.0ms

rewrite44.0ms

series157.0ms

simplify41.0ms

prune254.0ms

localize20.0ms

rewrite27.0ms

series79.0ms

simplify38.0ms

prune233.0ms

localize18.0ms

rewrite25.0ms

series79.0ms

simplify37.0ms

prune217.0ms

localize22.0ms

rewrite25.0ms

series82.0ms

simplify39.0ms

prune173.0ms

regimes944.0ms

bsearch92.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling