Details

sample31.0ms

Algorithm

intervals

Results

6.0ms	25×	body	640	valid
6.0ms	188×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	22×	body	1280	valid
1.0ms	14×	body	320	valid
0.0ms	7×	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: 16.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- 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:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
18.0ms	(+ (/ (- 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)

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune149.0ms

Filtered

71 candidates to 46 candidates (64.8%)

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: 15.2b

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)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
56×	`times-frac`
36×	`add-cube-cbrt`
24×	`distribute-lft-out`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`add-log-exp`
4×	`pow1` `associate-/r/` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `frac-sub` `flip-+`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 137

Calls

4 calls:

33.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series243.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
52.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	544	1336
1	1910	1268
2	5001	1268

prune306.0ms

Filtered

149 candidates to 103 candidates (69.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	140	9	149
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	151	10	161

Merged error: 3.7b

Counts

161 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
2.1b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

234×	`*-un-lft-identity`
131×	`times-frac`
89×	`distribute-lft-out`
84×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
39×	`swap-sqr`
21×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
11×	`pow1`
9×	`associate-/r*`
7×	`associate-/l*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 200

Calls

4 calls:

37.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
17.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series351.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
53.0ms	(/ beta (+ (+ alpha beta) 2.0))
61.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
95.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify126.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	825	2427
1	4052	2191
2	5001	2151

prune382.0ms

Filtered

212 candidates to 124 candidates (58.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	211	11	222

Merged error: 3.7b

Counts

222 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
2.1b	(- (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* 1.0 1.0) (* 1.0 1.0)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
300×	`times-frac`
216×	`distribute-lft-out`
184×	`add-sqr-sqrt`
148×	`add-cube-cbrt`
117×	`swap-sqr`
63×	`associate-r` `associate-l`
40×	`add-exp-log` `add-cbrt-cube`
25×	`pow1`
24×	`associate-/r/`
12×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
6×	`add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 340

Calls

4 calls:

25.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
27.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
38.0ms	(- (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* 1.0 1.0) (* 1.0 1.0)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
66.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
61.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
101.0ms	(- (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* 1.0 1.0) (* 1.0 1.0)))

simplify109.0ms

Algorithm

egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	565	3905
1	2727	3370
2	5001	3168

prune647.0ms

Filtered

352 candidates to 172 candidates (48.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	351	1	352
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	352	11	363

Merged error: 3.7b

Counts

363 → 11

regimes122.0ms

Accuracy

73.7% (3.2b remaining)

Error of 6.4b against oracle of 3.1b and baseline of 15.4b

bsearch52.0ms

Steps

Iters	Range		Point
7	20637641668174496.0	1.196592586218352e+18	9.267807070620555e+16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	36
1	46	36

end0.0ms

sample710.0ms

Algorithm

intervals

Results

177.0ms	5872×	body	80	valid
128.0ms	8000×	pre	80	true
125.0ms	839×	body	1280	valid
85.0ms	714×	body	640	valid
34.0ms	367×	body	320	valid
14.0ms	208×	body	160	valid