Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	194×	body	80	valid
4.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	20×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	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: 14.7b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite33.0ms

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))
20.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series119.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
66.0ms	(+ (/ (- 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	314	535
1	1004	510
2	5001	502

prune111.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	8	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Merged error: 14.1b

Counts

72 → 8

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))
1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

85×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
32×	`times-frac`
30×	`distribute-lft-out`
28×	`add-cube-cbrt`
22×	`frac-sub`
20×	`associate-/r*`
13×	`flip3--` `flip--`
12×	`associate-/l*`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `frac-2neg` `diff-log` `clear-num` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg`
2×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 131

Calls

4 calls:

31.0ms	(- (/ 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))
18.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series252.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
53.0ms	(/ beta (+ (+ alpha beta) 2.0))
83.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify90.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	741	1634
1	3452	1592
2	5001	1592

prune259.0ms

Filtered

143 candidates to 96 candidates (67.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	145	6	151

Merged error: 3.1b

Counts

151 → 6

localize16.0ms

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))
1.3b	(- (/ 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:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series401.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (+ (+ alpha beta) 2.0))
105.0ms	(cbrt (+ (+ alpha beta) 2.0))
110.0ms	(cbrt (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	271	567
1	668	537
2	2423	521
3	5002	521

prune241.0ms

Filtered

72 candidates to 59 candidates (81.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Merged error: 3.1b

Counts

78 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
5.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
5.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
5.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
42×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
36×	`distribute-lft-out`
33×	`cbrt-div`
15×	`associate-/r*`
9×	`associate-/l*`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`frac-2neg` `flip3-+` `pow1/3` `clear-num` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 135

Calls

4 calls:

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

series556.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
159.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
156.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
156.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify141.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	347	1257
1	945	1209
2	4307	1172
3	5001	1154

prune341.0ms

Filtered

147 candidates to 104 candidates (70.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	146	7	153

Merged error: 3.1b

Counts

153 → 7

regimes78.0ms

Accuracy

75.4% (3.2b remaining)

Error of 6.2b against oracle of 3.1b and baseline of 16.0b

bsearch54.0ms

Steps

Iters	Range		Point
8	1.153430813483477e+25	1.1596729939708742e+29	1.2287740376387863e+26

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

sample817.0ms

Algorithm

intervals

Results

312.0ms	885×	body	1280	valid
150.0ms	5823×	body	80	valid
103.0ms	8000×	pre	80	true
70.0ms	718×	body	640	valid
27.0ms	369×	body	320	valid
10.0ms	205×	body	160	valid