Details

sample29.0ms

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	190×	body	80	valid
4.0ms	26×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	24×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	8×	body	160	valid

simplify71.0ms

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: 15.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite242.0ms

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))
229.0ms	(+ (/ (- 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)

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune122.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 15.0b

Counts

72 → 12

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))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite60.0ms

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:

27.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series38.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
6.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (36.0ms)

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

prune171.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	11	0	11
Picked	1	0	1
Done	0	0	0
Total	131	4	135

Merged error: 1.8b

Counts

135 → 4

localize18.0ms

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))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite33.0ms

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:

7.0ms	(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:

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

simplify71.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (64.0ms)

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

prune156.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	71	5	76

Merged error: 1.8b

Counts

76 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.8b	(pow (+ (+ alpha beta) 2.0) 1/3)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`cbrt-prod`
9×	`distribute-lft-out`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `unpow-prod-down`
4×	`cbrt-div` `add-cbrt-cube`
3×	`pow-unpow`
2×	`flip3-+` `pow1/3` `flip-+` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `times-frac` `unpow1/3` `diff-log` `pow-exp` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.0ms	(pow (+ (+ alpha beta) 2.0) 1/3)

series62.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
17.0ms	(pow (+ (+ alpha beta) 2.0) 1/3)

simplify107.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	326	588
1	992	543
2	4149	467
3	5002	467

prune150.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Merged error: 1.8b

Counts

82 → 5

regimes120.0ms

Accuracy

68.7% (4.4b remaining)

Error of 7.3b against oracle of 3.0b and baseline of 17.0b

bsearch19.0ms

Steps

Iters	Range		Point
8	6125.90808030222	6402678.889602042	1951636.631430457

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	55
1	52	55

end0.0ms

sample787.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 100%

Results

186.0ms	5887×	body	80	valid
132.0ms	835×	body	1280	valid
129.0ms	8000×	pre	80	true
90.0ms	724×	body	640	valid
32.0ms	351×	body	320	valid
12.0ms	203×	body	160	valid

Details

sample29.0ms

simplify71.0ms

prune3.0ms

localize8.0ms

rewrite242.0ms

series19.0ms

simplify37.0ms

prune122.0ms

localize9.0ms

rewrite60.0ms

series38.0ms

simplify48.0ms

prune171.0ms

localize18.0ms

rewrite33.0ms

series63.0ms

simplify71.0ms

prune156.0ms

localize25.0ms

rewrite31.0ms

series62.0ms

simplify107.0ms

prune150.0ms

regimes120.0ms

bsearch19.0ms

simplify2.0ms

end0.0ms

sample787.0ms

Profiling