Details

analyze3.0ms

Algorithm

sampling

Space saved by range analysis: 43.823218%

Space saved by search: 43.823218%

Guaranteed chance to sample good point: 100%

sample26.0ms

Algorithm

intervals

Results

6.0ms	182×	body	80	valid
5.0ms	29×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	25×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	7×	body	160	valid

simplify68.0ms

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: 17.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite33.0ms

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))
21.0ms	(+ (/ (- 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)

simplify34.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (27.0ms)

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

prune123.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 16.6b

Counts

72 → 13

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	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite58.0ms

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:

26.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
14.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series37.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
6.0ms	(/ alpha (+ (+ alpha beta) 2.0))
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (35.0ms)

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

prune181.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Merged error: 2.7b

Counts

136 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite32.0ms

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

series60.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify72.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (63.0ms)

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

prune176.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	73	7	80

Merged error: 2.7b

Counts

80 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.1b	(exp (log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)))
1.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
5.2b	(log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0))

rewrite65.0ms

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:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
19.0ms	(exp (log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)))
17.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
16.0ms	(log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0))

series46.0ms

Counts

4 → 12

Calls

4 calls:

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

prune135.0ms

Filtered

74 candidates to 110 candidates (-48.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	110	7	117

Merged error: 2.7b

Counts

117 → 7

regimes273.0ms

Accuracy

99.4% (0.1b remaining)

Error of 3.0b against oracle of 2.9b and baseline of 16.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	39
1	46	39

end0.0ms

analyze2.0ms

Algorithm

sampling

Space saved by range analysis: 43.823218%

Space saved by search: 43.823218%

Guaranteed chance to sample good point: 100%

sample733.0ms

Algorithm

intervals

Results

193.0ms	5825×	body	80	valid
140.0ms	847×	body	1280	valid
123.0ms	8000×	pre	80	true
91.0ms	704×	body	640	valid
42.0ms	410×	body	320	valid
14.0ms	214×	body	160	valid

Details

analyze3.0ms

sample26.0ms

simplify68.0ms

prune3.0ms

localize8.0ms

rewrite33.0ms

series18.0ms

simplify34.0ms

prune123.0ms

localize9.0ms

rewrite58.0ms

series37.0ms

simplify47.0ms

prune181.0ms

localize17.0ms

rewrite32.0ms

series60.0ms

simplify72.0ms

prune176.0ms

localize11.0ms

rewrite65.0ms

series46.0ms

simplify41.0ms

prune135.0ms

regimes273.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze2.0ms

sample733.0ms

Profiling