Details

sample58.0ms

Algorithm

intervals

Results

13.0ms	178×	body	80	valid
10.0ms	31×	body	1280	valid
9.0ms	29×	body	640	valid
8.0ms	256×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	7×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
18	2002
17	1763
16	1558
15	1364
14	1138
13	931
12	742
11	607
10	526
9	431
8	318
7	267
6	197
5	124
4	69
3	50
2	33
1	20
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite154.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `insert-posit16` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Counts

2 → 67

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
105.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series148.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
95.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	2000
3	2000
2	1126
1	328
0	126

prune280.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
56×	`times-frac`
36×	`add-cube-cbrt`
24×	`distribute-lft-out`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
6×	`add-log-exp`
4×	`pow1` `associate-/r/` `insert-posit16` `associate-/l/`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--`
2×	`flip3-+` `frac-sub` `flip-+`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 141

Calls

4 calls:

44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
961.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
24.0ms	(/ beta (+ (+ alpha beta) 2.0))
126.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series357.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ alpha (+ (+ alpha beta) 2.0))
95.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
81.0ms	(/ beta (+ (+ alpha beta) 2.0))
118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

153 → 153

Iterations

Iter	Nodes
done	2037
3	2037
2	1880
1	567
0	242

prune780.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize85.0ms

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))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite206.0ms

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-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `times-frac` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

12.0ms	(cbrt (+ (+ alpha beta) 2.0))
21.0ms	(cbrt (+ (+ alpha beta) 2.0))
11.0ms	(cbrt (+ (+ alpha beta) 2.0))
161.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series530.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (+ (+ alpha beta) 2.0))
146.0ms	(cbrt (+ (+ alpha beta) 2.0))
127.0ms	(cbrt (+ (+ alpha beta) 2.0))
109.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify964.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2016
3	2016
2	751
1	284
0	122

prune596.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.9b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.8b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite747.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
64×	`times-frac`
50×	`log-prod`
37×	`add-cube-cbrt`
25×	`exp-sum`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
12×	`distribute-lft-out`
9×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`exp-prod` `insert-posit16`
3×	`div-inv` `associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `associate-/r/` `log-pow`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `exp-diff` `diff-log` `flip-+` `flip--` `rem-exp-log`

Counts

4 → 130

Calls

4 calls:

32.0ms	(/ beta (+ (+ alpha beta) 2.0))
229.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
176.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
305.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series473.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ beta (+ (+ alpha beta) 2.0))
95.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
113.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
211.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify1.3s

Counts

142 → 142

Iterations

Iter	Nodes
done	2001
3	2001
2	1466
1	568
0	273

prune641.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

regimes227.0ms

Accuracy

76.3% (3.0b remaining)

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

bsearch118.0ms

Steps

Iters	Range		Point
9	2224838044.2478166	1531887432751931.0	139510554198006.0

simplify10.0ms

Iterations

Iter	Nodes
done	44
2	44
1	42
0	36

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	5866×	body	80	valid
428.0ms	816×	body	1280	valid
308.0ms	8000×	pre	80	true
296.0ms	734×	body	640	valid
120.0ms	385×	body	320	valid
37.0ms	199×	body	160	valid