Details

sample32.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.823218%

Space saved by search: 43.823218%

Guaranteed chance to sample good point: 0%

Results

8.0ms	23×	body	1280	valid
6.0ms	198×	body	80	valid
4.0ms	256×	pre	80	true
2.0ms	19×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	6×	body	160	valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	6

prune3.0ms

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: 13.8b

Counts

2 → 1

localize7.0ms

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)

rewrite28.0ms

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:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
16.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series18.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
11.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify33.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502

prune106.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

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: 13.2b

Counts

72 → 10

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

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 → 89

Calls

3 calls:

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

series23.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify149.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	328	582
1	1072	553
2	4874	544
3	5001	544

prune145.0ms

Filtered

66 candidates to 98 candidates (-48.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	101	7	108

Merged error: 2.6b

Counts

108 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) 2.0) alpha)
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.6b	(/ 1 (/ (+ (+ alpha beta) 2.0) alpha))
1.4b	(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

185×	`*-un-lft-identity`
153×	`times-frac`
94×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
60×	`distribute-lft-out`
27×	`associate-/r*`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
8×	`div-inv`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv` `difference-of-squares`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+` `associate-/l/` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `flip--` `inv-pow`

Counts

4 → 193

Calls

4 calls:

8.0ms	(/ (+ (+ alpha beta) 2.0) alpha)
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
10.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) alpha))
26.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)

series31.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ (+ (+ alpha beta) 2.0) alpha)
10.0ms	(/ beta (+ (+ alpha beta) 2.0))
6.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) alpha))
11.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	595	1520
1	2545	1281
2	5001	1268

prune182.0ms

Filtered

103 candidates to 205 candidates (-99.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	205	7	212

Merged error: 2.6b

Counts

212 → 7

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

rewrite30.0ms

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))
14.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series63.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	278	606
1	720	576
2	2734	500
3	5001	491

prune142.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	71	8	79

Merged error: 2.6b

Counts

79 → 8

regimes135.0ms

Accuracy

75.5% (3.1b remaining)

Error of 6.0b against oracle of 2.9b and baseline of 15.6b

bsearch35.0ms

Steps

Iters	Range		Point
9	4.680205097797723e+17	4.094392917574696e+22	6.555240909395125e+19

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	37
1	45	37

end0.0ms

sample737.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.823218%

Space saved by search: 43.823218%

Guaranteed chance to sample good point: 0%

Results

193.0ms	5854×	body	80	valid
144.0ms	883×	body	1280	valid
129.0ms	8000×	pre	80	true
89.0ms	717×	body	640	valid
32.0ms	347×	body	320	valid
12.0ms	199×	body	160	valid

Details

sample32.0ms

simplify65.0ms

prune3.0ms

localize7.0ms

rewrite28.0ms

series18.0ms

simplify33.0ms

prune106.0ms

localize9.0ms

rewrite28.0ms

series23.0ms

simplify149.0ms

prune145.0ms

localize10.0ms

rewrite58.0ms

series31.0ms

simplify65.0ms

prune182.0ms

localize17.0ms

rewrite30.0ms

series63.0ms

simplify66.0ms

prune142.0ms

regimes135.0ms

bsearch35.0ms

simplify1.0ms

end0.0ms

sample737.0ms

Profiling