Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	184×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	25×	body	1280	valid
2.0ms	23×	body	640	valid
1.0ms	17×	body	320	valid
0.0ms	7×	body	160	valid

simplify75.0ms

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))
2.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite36.0ms

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))
23.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series108.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (31.0ms)

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

prune162.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 16.2b

Counts

72 → 13

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))
2.9b	(- (/ 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	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series237.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
49.0ms	(/ beta (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (39.0ms)

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

prune245.0ms

Filtered

123 candidates to 84 candidates (68.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	129	7	136

Merged error: 2.7b

Counts

136 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite39.0ms

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:

13.0ms	(- (/ 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)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
148.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
147.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
150.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify123.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (110.0ms)

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

prune341.0ms

Filtered

117 candidates to 86 candidates (73.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	115	9	124

Merged error: 2.7b

Counts

124 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.9b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt`
24×	`distribute-lft-out`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `clear-num` `flip-+` `div-inv` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 110

Calls

4 calls:

8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
14.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
76.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	368	741
1	1180	696
2	5001	683

prune255.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	122	9	131

Merged error: 2.7b

Counts

131 → 9

regimes158.0ms

Accuracy

99.4% (0.1b remaining)

Error of 3.0b against oracle of 2.9b and baseline of 15.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	39
1	39	39

end0.0ms

sample593.0ms

Algorithm

intervals

Results

143.0ms	5867×	body	80	valid
99.0ms	823×	body	1280	valid
96.0ms	8000×	pre	80	true
73.0ms	754×	body	640	valid
26.0ms	364×	body	320	valid
9.0ms	192×	body	160	valid

Details

sample24.0ms

simplify75.0ms

prune2.0ms

localize8.0ms

rewrite36.0ms

series108.0ms

simplify39.0ms

prune162.0ms

localize9.0ms

rewrite58.0ms

series237.0ms

simplify51.0ms

prune245.0ms

localize13.0ms

rewrite39.0ms

series527.0ms

simplify123.0ms

prune341.0ms

localize14.0ms

rewrite49.0ms

series254.0ms

simplify46.0ms

prune255.0ms

regimes158.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample593.0ms

Profiling