Details

sample33.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
4.0ms	33×	body	640	valid
4.0ms	256×	pre	80	true
3.0ms	20×	body	1280	valid
2.0ms	14×	body	320	valid
0.0ms	6×	body	160	valid

simplify583.0ms

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: 17.2b

localize18.0ms

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)

rewrite289.0ms

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:

65.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
219.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series156.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
94.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.8s

Counts

71 → 71

Iterations

Useful iterations: 3 (776.0ms)

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

prune280.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.3b

localize12.0ms

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

rewrite1.1s

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:

634.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
62.0ms	(/ alpha (+ (+ alpha beta) 2.0))
51.0ms	(/ beta (+ (+ alpha beta) 2.0))
299.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series344.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
79.0ms	(/ beta (+ (+ alpha beta) 2.0))
119.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.0s

Counts

123 → 123

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	193	1936
1	448	1814
2	1239	1730
3	4328	1698
done	5000	1686

prune808.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite932.0ms

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:

52.0ms	(/ alpha (+ (+ alpha beta) 2.0))
39.0ms	(/ beta (+ (+ alpha beta) 2.0))
548.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
289.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series388.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ alpha (+ (+ alpha beta) 2.0))
85.0ms	(/ beta (+ (+ alpha beta) 2.0))
130.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

122 → 122

Iterations

Useful iterations: 3 (695.0ms)

Iter	Nodes	Cost
0	182	1600
1	365	1478
2	822	1364
3	2142	1354
done	5000	1354

prune460.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize45.0ms

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

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

33.0ms	(cbrt (+ (+ alpha beta) 2.0))
31.0ms	(cbrt (+ (+ alpha beta) 2.0))
30.0ms	(cbrt (+ (+ alpha beta) 2.0))
190.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series600.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (+ (+ alpha beta) 2.0))
168.0ms	(cbrt (+ (+ alpha beta) 2.0))
142.0ms	(cbrt (+ (+ alpha beta) 2.0))
132.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

72 → 72

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	120	1076
1	282	1043
2	675	977
3	1727	888
done	5001	863

prune374.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

regimes186.0ms

Accuracy

76.8% (2.9b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 15.6b

bsearch88.0ms

Steps

Iters	Range		Point
8	976503.8483825806	50707504882.44517	45468567748.04238

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	72
1	39	72
done	39	72

end0.0ms

sample1.4s

Algorithm

intervals

Results

413.0ms	5869×	body	80	valid
227.0ms	836×	body	1280	valid
181.0ms	8000×	pre	80	true
132.0ms	691×	body	640	valid
130.0ms	405×	body	320	valid
66.0ms	199×	body	160	valid