Details

sample31.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
5.0ms	32×	body	1280	valid
4.0ms	13×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	16×	body	640	valid
0.0ms	3×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
32	4930
31	4722
30	4510
29	4301
28	4120
27	3916
26	3715
25	3502
24	3325
23	3117
22	2909
21	2698
20	2516
19	2291
18	2012
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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite199.0ms

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-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Counts

2 → 65

Calls

2 calls:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
146.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series193.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
108.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5003
2	1119
1	326
0	124

prune400.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.5b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite288.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 89

Calls

3 calls:

33.0ms	(/ beta (+ (+ alpha beta) 2.0))
50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
201.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series256.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ beta (+ (+ alpha beta) 2.0))
69.0ms	(/ alpha (+ (+ alpha beta) 2.0))
110.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5022
3	4942
2	1047
1	341
0	153

prune527.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
1.0b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite342.0ms

Algorithm

rewrite-expression-head

Rules

244×	`*-un-lft-identity`
130×	`times-frac`
96×	`distribute-lft-out`
84×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
39×	`swap-sqr`
21×	`associate-r` `associate-l`
20×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r/`
11×	`pow1`
10×	`associate-/r*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `difference-of-squares`

Counts

4 → 196

Calls

4 calls:

41.0ms	(/ alpha (+ (+ alpha beta) 2.0))
27.0ms	(/ alpha (+ (+ alpha beta) 2.0))
203.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
61.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series345.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ alpha (+ (+ alpha beta) 2.0))
61.0ms	(/ alpha (+ (+ alpha beta) 2.0))
105.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
99.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify1.9s

Counts

208 → 208

Iterations

Iter	Nodes
done	5016
2	2309
1	629
0	191

prune1000.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize120.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
1.0b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
1.0b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
1.0b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

184×	`*-un-lft-identity`
100×	`times-frac`
72×	`distribute-lft-out`
64×	`add-sqr-sqrt`
52×	`add-cube-cbrt`
39×	`swap-sqr`
21×	`associate-r` `associate-l`
16×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
10×	`add-log-exp`
8×	`associate-/r/`
4×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 148

Calls

4 calls:

189.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
37.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
72.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
39.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series474.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
133.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
110.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
144.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify2.0s

Counts

160 → 160

Iterations

Iter	Nodes
done	5004
2	2094
1	585
0	177

prune988.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.2b

regimes176.0ms

Accuracy

74.9% (3.2b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 15.6b

bsearch73.0ms

Steps

Iters	Range		Point
8	1541639454070.677	19367525498197844.0	7715362331151764.0

simplify16.0ms

Iterations

Iter	Nodes
done	36
1	36
0	32

end0.0ms

sample1.6s

Algorithm

intervals

Results

684.0ms	5862×	body	80	valid
247.0ms	841×	body	1280	valid
233.0ms	694×	body	640	valid
192.0ms	8000×	pre	80	true
52.0ms	410×	body	320	valid
17.0ms	193×	body	160	valid