Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	192×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	23×	body	1280	valid
2.0ms	22×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	8×	body	160	valid

simplify74.0ms

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: 15.0b

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)

rewrite34.0ms

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))
22.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series110.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune142.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 14.2b

Counts

72 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

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:

26.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
51.0ms	(/ alpha (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (38.0ms)

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

prune244.0ms

Filtered

123 candidates to 84 candidates (68.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	114	9	123
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Merged error: 2.9b

Counts

133 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.1b	(- (log (exp (/ alpha (+ (+ alpha beta) 2.0)))) 1.0)
3.5b	(log (exp (/ alpha (+ (+ alpha beta) 2.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

93×	`*-un-lft-identity`
45×	`times-frac`
37×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
33×	`distribute-lft-out`
23×	`log-pow`
21×	`exp-prod`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `log-prod` `associate-/r/` `associate-/l*`
5×	`add-log-exp`
3×	`flip3-+` `associate--l+` `flip-+` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

4 → 125

Calls

4 calls:

7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
17.0ms	(- (log (exp (/ alpha (+ (+ alpha beta) 2.0)))) 1.0)
9.0ms	(log (exp (/ alpha (+ (+ alpha beta) 2.0))))

series231.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ beta (+ (+ alpha beta) 2.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
80.0ms	(- (log (exp (/ alpha (+ (+ alpha beta) 2.0)))) 1.0)
53.0ms	(log (exp (/ alpha (+ (+ alpha beta) 2.0))))

simplify158.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	377	783
1	1141	725
2	4953	715
3	5002	715

prune272.0ms

Filtered

137 candidates to 95 candidates (69.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	137	10	147

Merged error: 2.9b

Counts

147 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 105

Calls

4 calls:

17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
153.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
152.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
146.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify125.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	333	1077
1	892	1029
2	4058	992
3	5001	980

prune295.0ms

Filtered

117 candidates to 86 candidates (73.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	119	8	127

Merged error: 2.9b

Counts

127 → 8

regimes88.0ms

Accuracy

77.4% (2.8b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 15.6b

bsearch46.0ms

Steps

Iters	Range		Point
7	12753422947354472.0	5.168889984207901e+17	8.716404371789643e+16

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	25
1	38	25

end0.0ms

sample603.0ms

Algorithm

intervals

Results

148.0ms	5866×	body	80	valid
106.0ms	811×	body	1280	valid
100.0ms	8000×	pre	80	true
76.0ms	780×	body	640	valid
26.0ms	360×	body	320	valid
9.0ms	183×	body	160	valid