Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	184×	body	80	valid
4.0ms	28×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	16×	body	640	valid
1.0ms	19×	body	320	valid
0.0ms	9×	body	160	valid

simplify72.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 16.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
3.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l-` `flip3--` `frac-2neg` `clear-num` `flip--` `div-inv`

Counts

2 → 12

Calls

2 calls:

5.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
7.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series109.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
64.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	176	123
1	509	118
2	2097	110
3	5002	110

prune53.0ms

Filtered

18 candidates to 16 candidates (88.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	12	6	18
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	6	19

Merged error: 16.0b

Counts

19 → 6

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))
3.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`frac-2neg` `clear-num` `associate-/r/`
3×	`sub-neg`
2×	`flip3-+` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 27

Calls

4 calls:

10.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
4.0ms	(/ alpha (+ (+ alpha beta) 2.0))
4.0ms	(/ beta (+ (+ alpha beta) 2.0))
5.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series226.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
75.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	365	428
1	1534	420
2	5001	420

prune117.0ms

Filtered

39 candidates to 32 candidates (82.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	34	5	39
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	40	5	45

Merged error: 4.2b

Counts

45 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
3.5b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

507×	`associate-*r/`
411×	`frac-times`
352×	`frac-add`
329×	`flip3-+` `flip-+`
274×	`associate-/l/`
272×	`frac-sub`
208×	`clear-num`
185×	`frac-2neg`
171×	`associate-*l/`
114×	`associate-/r/`
104×	`flip3--` `flip--`
23×	`un-div-inv`
6×	`div-inv`
5×	`div-sub`
4×	`associate--r+`
3×	`sub-neg` `unpow-prod-down` `swap-sqr` `associate-r` `associate-l` `sqr-pow`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/r` `-commutative`
1×	`difference-cubes` `pow2` `pow-to-exp` `unpow3` `difference-of-squares`

Counts

4 → 427

Calls

4 calls:

9.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
99.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
3.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
6.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series634.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
392.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
68.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
117.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify240.0ms

Algorithm

egg-herbie

Counts

439 → 439

Iterations

Useful iterations: 1 (67.0ms)

Iter	Nodes	Cost
0	4536	19038
1	5001	19037

prune4.2s

Filtered

439 candidates to 398 candidates (90.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	435	4	439
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	438	6	444

Merged error: 4.1b

Counts

444 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) 0) (+ (+ alpha beta) 2.0)))
3.5b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

393×	`associate-*r/`
293×	`frac-times`
274×	`associate-/l/`
272×	`frac-sub`
256×	`frac-add`
249×	`flip3-+` `flip-+`
154×	`clear-num`
137×	`frac-2neg`
121×	`associate-*l/`
104×	`flip3--` `flip--`
18×	`associate-/r/`
17×	`un-div-inv`
6×	`div-inv`
5×	`div-sub`
4×	`associate--r+`
3×	`sub-neg` `unpow-prod-down` `swap-sqr` `associate-r` `associate-l` `sqr-pow`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/r` `-commutative`
1×	`difference-cubes` `pow2` `pow-to-exp` `unpow3` `difference-of-squares`

Counts

4 → 331

Calls

4 calls:

9.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
3.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
77.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) 0) (+ (+ alpha beta) 2.0)))
6.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series524.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
67.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
275.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) 0) (+ (+ alpha beta) 2.0)))
119.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify156.0ms

Algorithm

egg-herbie

Counts

343 → 343

Iterations

Useful iterations: 1 (52.0ms)

Iter	Nodes	Cost
0	3128	11073
1	5002	11068

prune3.8s

Filtered

343 candidates to 326 candidates (95.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	334	9	343
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	336	13	349

Merged error: 4.1b

Counts

349 → 13

regimes302.0ms

Accuracy

80.4% (2.8b remaining)

Error of 5.8b against oracle of 3.0b and baseline of 17.1b

bsearch48.0ms

Steps

Iters	Range		Point
6	124901983.736051	1011980410.8264618	999297775.8503832

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	60
1	65	60

end0.0ms

sample633.0ms

Algorithm

intervals

Results

147.0ms	5764×	body	80	valid
118.0ms	880×	body	1280	valid
98.0ms	8000×	pre	80	true
75.0ms	742×	body	640	valid
34.0ms	411×	body	320	valid
10.0ms	203×	body	160	valid