Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	190×	body	80	valid
3.0ms	28×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	24×	body	640	valid
0.0ms	7×	body	320	valid
0.0ms	7×	body	160	valid

simplify401.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	52	13
4	73	13
5	118	13
6	149	13
7	177	13
8	208	13
9	246	13
10	274	13
11	285	13
12	297	13
13	301	13
done	301	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite190.0ms

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))
144.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series120.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
67.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: 3 (533.0ms)

Iter	Nodes	Cost
0	124	1134
1	320	1074
2	886	1014
3	2832	1006
done	5000	1006

prune149.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.7b

localize10.0ms

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))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite615.0ms

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:

379.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
33.0ms	(/ alpha (+ (+ alpha beta) 2.0))
166.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series250.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.9s

Counts

123 → 123

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	193	1936
1	448	1814
2	1242	1730
3	4330	1698
done	5000	1686

prune287.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) 2.0) alpha)
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.3b	(/ 1 (/ (+ (+ alpha beta) 2.0) alpha))
1.9b	(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

185×	`*-un-lft-identity`
153×	`times-frac`
94×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
60×	`distribute-lft-out`
27×	`associate-/r*`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
8×	`div-inv`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv` `difference-of-squares`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+` `associate-/l/` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `flip--` `inv-pow`

Counts

4 → 193

Calls

4 calls:

68.0ms	(/ (+ (+ alpha beta) 2.0) alpha)
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
40.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) alpha))
200.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)

series212.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (+ alpha beta) 2.0) alpha)
53.0ms	(/ beta (+ (+ alpha beta) 2.0))
48.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) alpha))
85.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)

simplify1.8s

Counts

205 → 205

Iterations

Useful iterations: 3 (934.0ms)

Iter	Nodes	Cost
0	263	3152
1	582	2736
2	1328	2439
3	3605	2399
done	5000	2399

prune334.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.9b	(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
15×	`cbrt-prod`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `times-frac` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `div-inv`

Counts

4 → 64

Calls

4 calls:

15.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
15.0ms	(cbrt (+ (+ alpha beta) 2.0))
199.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)

series404.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (+ (+ alpha beta) 2.0))
107.0ms	(cbrt (+ (+ alpha beta) 2.0))
106.0ms	(cbrt (+ (+ alpha beta) 2.0))
83.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)

simplify1.3s

Counts

76 → 76

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	133	1217
1	308	1180
2	724	1106
3	1873	973
done	5000	948

prune275.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.4b

regimes78.0ms

Accuracy

76.7% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 15.8b

bsearch69.0ms

Steps

Iters	Range		Point
11	0.0002838148613743618	1.2869252738965294e+18	538664.5023162543

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	81
1	42	81
done	42	81

end0.0ms

sample611.0ms

Algorithm

intervals

Results

140.0ms	5846×	body	80	valid
100.0ms	859×	body	1280	valid
90.0ms	8000×	pre	80	true
65.0ms	710×	body	640	valid
27.0ms	396×	body	320	valid
9.0ms	189×	body	160	valid