Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	189×	body	80	valid
5.0ms	29×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	24×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify552.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite342.0ms

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:

53.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
285.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series135.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
71.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.8s

Counts

71 → 71

Iterations

Useful iterations: 3 (875.0ms)

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

prune175.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
31×	`times-frac`
28×	`add-sqr-sqrt`
24×	`distribute-lft-out`
23×	`add-cube-cbrt`
10×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 89

Calls

3 calls:

40.0ms	(/ beta (+ (+ alpha beta) 2.0))
66.0ms	(/ alpha (+ (+ alpha beta) 2.0))
212.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series240.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(/ beta (+ (+ alpha beta) 2.0))
73.0ms	(/ alpha (+ (+ alpha beta) 2.0))
100.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

98 → 98

Iterations

Useful iterations: 3 (595.0ms)

Iter	Nodes	Cost
0	153	1237
1	326	1164
2	776	1090
3	2065	1082
done	5001	1082

prune336.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.7b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite582.0ms

Algorithm

rewrite-expression-head

Rules

182×	`*-un-lft-identity`
148×	`times-frac`
85×	`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`
7×	`div-inv`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+` `associate-/l/` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 189

Calls

4 calls:

95.0ms	(/ (+ (+ alpha beta) 2.0) beta)
57.0ms	(/ alpha (+ (+ alpha beta) 2.0))
85.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
325.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series293.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (+ alpha beta) 2.0) beta)
80.0ms	(/ alpha (+ (+ alpha beta) 2.0))
83.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
101.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.8s

Counts

201 → 201

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	259	3011
1	573	2605
2	1318	2354
3	3548	2314
done	5001	2314

prune524.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.2b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.4b	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
9.4b	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
9.4b	(cbrt (/ (+ (+ alpha beta) 2.0) beta))

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

298.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
31.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
25.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
28.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))

series842.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
209.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
237.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
251.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))

simplify1.5s

Counts

111 → 111

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	159	2042
1	309	1979
2	681	1892
3	1661	1701
done	5000	1647

prune544.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.2b

regimes149.0ms

Accuracy

70.8% (3.8b remaining)

Error of 6.9b against oracle of 3.1b and baseline of 16.2b

bsearch62.0ms

Steps

Iters	Range		Point
5	3.726174372304574e+36	1.2219886942032108e+37	4.960190917426964e+36

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	90
1	36	90
done	36	90

end0.0ms

sample1.9s

Algorithm

intervals

Results

747.0ms	864×	body	1280	valid
362.0ms	5789×	body	80	valid
211.0ms	8000×	pre	80	true
141.0ms	731×	body	640	valid
104.0ms	406×	body	320	valid
21.0ms	210×	body	160	valid