Details

sample33.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 100%

Results

6.0ms	185×	body	80	valid
5.0ms	33×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	25×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	7×	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: 16.3b

Counts

2 → 1

localize12.0ms

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)

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:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
18.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series19.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify35.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (27.0ms)

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

prune107.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	9	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 15.5b

Counts

72 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

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

series24.0ms

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)

simplify154.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (28.0ms)

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

prune151.0ms

Filtered

66 candidates to 98 candidates (-48.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	99	8	107

Merged error: 3.7b

Counts

107 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 105

Calls

4 calls:

13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
24.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
21.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
22.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify127.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	336	1065
1	979	1017
2	4616	980
3	5001	980

prune285.0ms

Filtered

86 candidates to 117 candidates (-36.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	115	10	125

Merged error: 3.7b

Counts

125 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
1.6b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

301×	`add-sqr-sqrt`
184×	`times-frac`
171×	`*-un-lft-identity`
120×	`difference-of-squares`
111×	`unpow-prod-down` `cube-prod`
71×	`add-cube-cbrt`
51×	`sqr-pow`
36×	`associate-/l*`
30×	`distribute-lft-out`
25×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*` `associate-/r/`
6×	`add-log-exp`
5×	`pow1` `difference-cubes`
4×	`flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`flip3--` `frac-2neg` `pow-exp` `clear-num` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `diff-log` `unpow3` `div-sub`

Counts

4 → 293

Calls

4 calls:

7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
67.0ms	(/ (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)))
10.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
40.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series80.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ alpha (+ (+ alpha beta) 2.0))
36.0ms	(/ (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)))
17.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
20.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify164.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	950	6215
1	4205	6043
2	5001	6039

prune647.0ms

Filtered

148 candidates to 305 candidates (-106.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	303	2	305
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	305	10	315

Merged error: 3.7b

Counts

315 → 10

regimes560.0ms

Accuracy

98.9% (0.1b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 16.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	39
1	39	39

end0.0ms

sample804.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 100%

Results

185.0ms	5805×	body	80	valid
138.0ms	874×	body	1280	valid
133.0ms	8000×	pre	80	true
93.0ms	730×	body	640	valid
36.0ms	396×	body	320	valid
12.0ms	195×	body	160	valid

Details

sample33.0ms

simplify65.0ms

prune3.0ms

localize12.0ms

rewrite30.0ms

series19.0ms

simplify35.0ms

prune107.0ms

localize9.0ms

rewrite32.0ms

series24.0ms

simplify154.0ms

prune151.0ms

localize13.0ms

rewrite41.0ms

series78.0ms

simplify127.0ms

prune285.0ms

localize18.0ms

rewrite142.0ms

series80.0ms

simplify164.0ms

prune647.0ms

regimes560.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample804.0ms

Profiling