Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample24.0ms

Algorithm

intervals

Results

6.0ms	191×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	22×	body	1280	valid
3.0ms	23×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	6×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5002	13

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 15.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
17.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series219.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
211.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5370	1005

prune113.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 14.2b

Counts

72 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.4b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
31×	`times-frac`
28×	`add-sqr-sqrt`
24×	`distribute-lft-out`
23×	`add-cube-cbrt`
10×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 88

Calls

3 calls:

7.0ms	(/ alpha (+ beta (+ alpha 2.0)))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series24.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
11.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5316	1076

prune152.0ms

Filtered

69 candidates to 97 candidates (-40.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	91	6	97
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	101	6	107

Merged error: 3.3b

Counts

107 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ alpha (+ beta 2.0)))
0.7b	(cbrt (+ alpha (+ beta 2.0)))
0.7b	(cbrt (+ alpha (+ beta 2.0)))
1.4b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 59

Calls

4 calls:

5.0ms	(cbrt (+ alpha (+ beta 2.0)))
5.0ms	(cbrt (+ alpha (+ beta 2.0)))
5.0ms	(cbrt (+ alpha (+ beta 2.0)))
15.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series62.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (+ alpha (+ beta 2.0)))
17.0ms	(cbrt (+ alpha (+ beta 2.0)))
17.0ms	(cbrt (+ alpha (+ beta 2.0)))
11.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify28.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5240	838

prune173.0ms

Filtered

57 candidates to 71 candidates (-24.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	71	6	77

Merged error: 3.3b

Counts

77 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.2b	(/ (/ beta (sqrt (+ alpha (+ beta 2.0)))) (sqrt (+ (+ alpha beta) 2.0)))
0.4b	(/ beta (sqrt (+ alpha (+ beta 2.0))))
1.4b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

560×	`*-un-lft-identity`
496×	`times-frac`
310×	`sqrt-prod`
233×	`add-sqr-sqrt`
228×	`add-cube-cbrt`
198×	`distribute-lft-out`
36×	`associate-/l*`
24×	`associate-/r/`
22×	`sqrt-div`
21×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 395

Calls

4 calls:

7.0ms	(/ alpha (+ beta (+ alpha 2.0)))
24.0ms	(/ (/ beta (sqrt (+ alpha (+ beta 2.0)))) (sqrt (+ (+ alpha beta) 2.0)))
8.0ms	(/ beta (sqrt (+ alpha (+ beta 2.0))))
13.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
14.0ms	(/ (/ beta (sqrt (+ alpha (+ beta 2.0)))) (sqrt (+ (+ alpha beta) 2.0)))
17.0ms	(/ beta (sqrt (+ alpha (+ beta 2.0))))
20.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify120.0ms

Algorithm

egg-herbie

Counts

407 → 407

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4973	8105
1	4973	8105

prune441.0ms

Filtered

159 candidates to 407 candidates (-156.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	406	1	407
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	406	7	413

Merged error: 3.3b

Counts

413 → 7

regimes118.0ms

Accuracy

75.9% (3.0b remaining)

Error of 5.9b against oracle of 2.9b and baseline of 15.5b

bsearch19.0ms

Steps

Iters	Range		Point
10	0.08337926088485935	15251913486.636438	4461477303.925521

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	358	56
1	358	56

end0.0ms

sample689.0ms

Algorithm

intervals

Results

176.0ms	5877×	body	80	valid
133.0ms	837×	body	1280	valid
120.0ms	8000×	pre	80	true
86.0ms	738×	body	640	valid
35.0ms	377×	body	320	valid
10.0ms	171×	body	160	valid

Details

analyze3.0ms

sample24.0ms

simplify59.0ms

prune5.0ms

localize8.0ms

rewrite29.0ms

series219.0ms

simplify48.0ms

prune113.0ms

localize11.0ms

rewrite31.0ms

series24.0ms

simplify49.0ms

prune152.0ms

localize18.0ms

rewrite31.0ms

series62.0ms

simplify28.0ms

prune173.0ms

localize16.0ms

rewrite78.0ms

series57.0ms

simplify120.0ms

prune441.0ms

regimes118.0ms

bsearch19.0ms

simplify8.0ms

end0.0ms

sample689.0ms

Profiling