Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	191×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	20×	body	1280	valid
3.0ms	24×	body	640	valid
2.0ms	17×	body	320	valid
0.0ms	4×	body	160	valid

simplify67.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 15.6b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.7b	(+ (/ (- 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)

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune122.0ms

Filtered

71 candidates to 46 candidates (35.2%)

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: 14.8b

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))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite55.0ms

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)

series38.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ 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

prune188.0ms

Filtered

123 candidates to 84 candidates (31.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Merged error: 3.0b

Counts

135 → 9

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))
1.7b	(- (/ 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))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series64.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (+ (+ alpha beta) 2.0))
17.0ms	(cbrt (+ (+ alpha beta) 2.0))
19.0ms	(cbrt (+ (+ alpha beta) 2.0))
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (62.0ms)

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

prune173.0ms

Filtered

72 candidates to 53 candidates (26.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	73	8	81

Merged error: 3.0b

Counts

81 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.0b	(/ (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)) (+ (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (+ (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (/ beta (+ (+ alpha beta) 2.0)))) (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0)))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

245×	`add-sqr-sqrt`
146×	`times-frac`
140×	`*-un-lft-identity`
102×	`difference-of-squares`
88×	`unpow-prod-down` `cube-prod`
60×	`frac-add`
55×	`distribute-lft-out--`
46×	`add-cube-cbrt`
44×	`associate-/r/`
40×	`sqr-pow`
38×	`frac-times`
37×	`associate-/l*`
29×	`flip3--` `flip--`
26×	`associate-*r/`
20×	`associate-*l/`
10×	`flip3-+` `flip-+` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `difference-cubes` `cube-div` `associate-/l/`
3×	`sub-neg` `diff-log` `associate-/r*`
2×	`frac-sub`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 257

Calls

4 calls:

12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
106.0ms	(/ (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)) (+ (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (+ (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (/ beta (+ (+ alpha beta) 2.0)))) (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0)))))

series158.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
125.0ms	(/ (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)) (+ (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (+ (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (/ beta (+ (+ alpha beta) 2.0)))) (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0)))))

simplify135.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1484	12643
1	5001	12513

prune962.0ms

Filtered

269 candidates to 154 candidates (42.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	264	5	269
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	266	11	277

Merged error: 3.0b

Counts

277 → 11

regimes191.0ms

Accuracy

80.2% (2.7b remaining)

Error of 5.8b against oracle of 3.1b and baseline of 16.8b

bsearch23.0ms

Steps

Iters	Range		Point
10	865.4952717311924	15868467154750.623	6398347157978.596

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	57
1	53	57
2	55	57
3	55	57

end0.0ms

sample789.0ms

Algorithm

intervals

Results

181.0ms	5828×	body	80	valid
137.0ms	838×	body	1280	valid
121.0ms	8000×	pre	80	true
89.0ms	739×	body	640	valid
37.0ms	402×	body	320	valid
12.0ms	193×	body	160	valid

Details

sample27.0ms

simplify67.0ms

prune3.0ms

localize12.0ms

rewrite30.0ms

series19.0ms

simplify36.0ms

prune122.0ms

localize9.0ms

rewrite55.0ms

series38.0ms

simplify48.0ms

prune188.0ms

localize17.0ms

rewrite30.0ms

series64.0ms

simplify69.0ms

prune173.0ms

localize22.0ms

rewrite166.0ms

series158.0ms

simplify135.0ms

prune962.0ms

regimes191.0ms

bsearch23.0ms

simplify2.0ms

end0.0ms

sample789.0ms

Profiling