Details

sample91.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 99.21875%

Results

10.0ms	184×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	28×	body	1280	valid
3.0ms	24×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	9×	body	160	valid

simplify69.0ms

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: 17.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite30.0ms

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)

series19.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
11.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (31.0ms)

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

prune112.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

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: 16.3b

Counts

72 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite57.0ms

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

series35.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify46.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	450	903
1	1596	871
2	5002	859

prune175.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Merged error: 2.8b

Counts

134 → 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))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite29.0ms

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

series62.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify67.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (60.0ms)

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

prune169.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Merged error: 2.8b

Counts

79 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.2b	(exp (log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)))
2.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
4.8b	(log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
25×	`times-frac`
21×	`distribute-lft-out`
19×	`add-cube-cbrt`
8×	`log-prod`
7×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`log-div` `exp-prod` `flip3-+` `exp-sum` `flip-+`
2×	`exp-diff` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `sum-log` `flip--` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
17.0ms	(exp (log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)))
18.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
19.0ms	(log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0))

series50.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
14.0ms	(exp (log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)))
11.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
17.0ms	(log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	384	905
1	1176	844
2	5002	822

prune132.0ms

Filtered

74 candidates to 110 candidates (-48.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	110	8	118

Merged error: 2.8b

Counts

118 → 8

regimes266.0ms

Accuracy

99.3% (0.1b remaining)

Error of 3.3b against oracle of 3.2b and baseline of 16.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	51
1	49	51
2	51	51
3	51	51

end0.0ms

sample864.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 99.21875%

Results

185.0ms	5820×	body	80	valid
130.0ms	8000×	pre	80	true
129.0ms	839×	body	1280	valid
93.0ms	735×	body	640	valid
36.0ms	395×	body	320	valid
13.0ms	211×	body	160	valid

Details

sample91.0ms

simplify69.0ms

prune3.0ms

localize8.0ms

rewrite30.0ms

series19.0ms

simplify39.0ms

prune112.0ms

localize9.0ms

rewrite57.0ms

series35.0ms

simplify46.0ms

prune175.0ms

localize17.0ms

rewrite29.0ms

series62.0ms

simplify67.0ms

prune169.0ms

localize11.0ms

rewrite67.0ms

series50.0ms

simplify41.0ms

prune132.0ms

regimes266.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample864.0ms

Profiling