Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	187×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	26×	body	1280	valid
3.0ms	26×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	6×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	418	13
1	418	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: 16.2b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite34.0ms

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))
22.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series19.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
12.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5295	998

prune118.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 15.5b

Counts

72 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.1b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

25.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
7.0ms	(/ alpha (+ beta (+ alpha 2.0)))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series38.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
9.0ms	(/ beta (+ (+ alpha beta) 2.0))
12.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify31.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5211	1698

prune185.0ms

Filtered

88 candidates to 123 candidates (-39.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	126	8	134

Merged error: 2.5b

Counts

134 → 8

localize17.0ms

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)))
2.1b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite28.0ms

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 → 60

Calls

4 calls:

5.0ms	(cbrt (+ alpha (+ beta 2.0)))
5.0ms	(cbrt (+ alpha (+ beta 2.0)))
5.0ms	(cbrt (+ alpha (+ beta 2.0)))
12.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series63.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (+ alpha (+ beta 2.0)))
16.0ms	(cbrt (+ alpha (+ beta 2.0)))
18.0ms	(cbrt (+ alpha (+ beta 2.0)))
11.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4965	831
1	4965	831

prune161.0ms

Filtered

54 candidates to 72 candidates (-33.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	74	6	80

Merged error: 2.5b

Counts

80 → 6

localize19.0ms

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))))
2.1b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite79.0ms

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 → 396

Calls

4 calls:

6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
21.0ms	(/ (/ beta (sqrt (+ alpha (+ beta 2.0)))) (sqrt (+ (+ alpha beta) 2.0)))
8.0ms	(/ beta (sqrt (+ alpha (+ beta 2.0))))
12.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series49.0ms

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

simplify89.0ms

Algorithm

egg-herbie

Counts

408 → 408

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4997	8112
1	4997	8112

prune641.0ms

Filtered

159 candidates to 408 candidates (-156.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	408	0	408
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	408	6	414

Merged error: 2.5b

Counts

414 → 6

regimes122.0ms

Accuracy

75.3% (3.1b remaining)

Error of 6.1b against oracle of 2.9b and baseline of 15.7b

bsearch18.0ms

Steps

Iters	Range		Point
7	22921240710501256.0	2.7895973467809126e+18	3.122024746116209e+16

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	78
1	46	78

end0.0ms

sample799.0ms

Algorithm

intervals

Results

185.0ms	5845×	body	80	valid
130.0ms	820×	body	1280	valid
123.0ms	8000×	pre	80	true
93.0ms	756×	body	640	valid
34.0ms	357×	body	320	valid
14.0ms	222×	body	160	valid

Details

sample29.0ms

simplify14.0ms

prune5.0ms

localize7.0ms

rewrite34.0ms

series19.0ms

simplify46.0ms

prune118.0ms

localize13.0ms

rewrite54.0ms

series38.0ms

simplify31.0ms

prune185.0ms

localize17.0ms

rewrite28.0ms

series63.0ms

simplify40.0ms

prune161.0ms

localize19.0ms

rewrite79.0ms

series49.0ms

simplify89.0ms

prune641.0ms

regimes122.0ms

bsearch18.0ms

simplify1.0ms

end0.0ms

sample799.0ms

Profiling