Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	196×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	24×	body	1280	valid
2.0ms	25×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify70.0ms

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
done	1035	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite188.0ms

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:

43.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
142.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series108.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify34.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

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

prune140.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite605.0ms

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:

33.0ms	(/ alpha (+ (+ alpha beta) 2.0))
32.0ms	(/ beta (+ (+ alpha beta) 2.0))
371.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
165.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
61.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify49.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (36.0ms)

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

prune263.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.0b	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.6b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
0.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite676.0ms

Algorithm

rewrite-expression-head

Rules

162×	`*-un-lft-identity`
139×	`times-frac`
89×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
48×	`distribute-lft-out`
22×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
8×	`div-exp` `div-inv` `associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`cbrt-undiv` `diff-log`
3×	`sub-neg` `flip3--` `flip--`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `frac-sub` `associate-/l/` `associate--r+`
1×	`pow-flip` `flip3-+` `associate-/r/` `flip-+` `inv-pow` `associate--r-`

Counts

4 → 179

Calls

4 calls:

65.0ms	(/ (+ (+ alpha beta) 2.0) beta)
402.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
37.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
164.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series259.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (+ alpha beta) 2.0) beta)
99.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
58.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify68.0ms

Counts

191 → 191

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	643	1681
1	2882	1442
2	5002	1436
done	5002	1436

prune278.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (/ 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)))

rewrite216.0ms

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:

162.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
16.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
17.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
17.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
142.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
137.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
142.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify117.0ms

Counts

117 → 117

Iterations

Useful iterations: 3 (107.0ms)

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

prune333.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

regimes81.0ms

Accuracy

76.7% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 15.9b

bsearch61.0ms

Steps

Iters	Range		Point
10	1918684245868153.5	3.072219510867474e+30	6.769387663364106e+18

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	36
1	44	36
done	44	36

end0.0ms

sample639.0ms

Algorithm

intervals

Results

149.0ms	5822×	body	80	valid
98.0ms	848×	body	1280	valid
97.0ms	8000×	pre	80	true
66.0ms	716×	body	640	valid
28.0ms	411×	body	320	valid
9.0ms	203×	body	160	valid