Details

sample37.0ms

Algorithm

intervals

Results

10.0ms	32×	body	1280	valid
6.0ms	192×	body	80	valid
4.0ms	256×	pre	80	true
2.0ms	16×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	3×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	4613
8	1507
7	644
6	306
5	164
4	74
3	53
2	34
1	20
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize25.0ms

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)

rewrite262.0ms

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:

60.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
197.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series163.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
89.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.0s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1359
1	326
0	124

prune315.0ms

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)

rewrite256.0ms

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:

37.0ms	(/ beta (+ (+ alpha beta) 2.0))
28.0ms	(/ alpha (+ (+ alpha beta) 2.0))
187.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series222.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ beta (+ (+ alpha beta) 2.0))
61.0ms	(/ alpha (+ (+ alpha beta) 2.0))
87.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1315
1	341
0	153

prune517.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize32.0ms

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))

rewrite393.0ms

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:

55.0ms	(/ alpha (+ (+ alpha beta) 2.0))
54.0ms	(/ alpha (+ (+ alpha beta) 2.0))
212.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
63.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series360.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ alpha (+ (+ alpha beta) 2.0))
61.0ms	(/ alpha (+ (+ alpha beta) 2.0))
91.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
137.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify2.6s

Counts

208 → 208

Iterations

Iter	Nodes
done	5001
2	4027
1	640
0	191

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize126.0ms

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))

rewrite374.0ms

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:

170.0ms	(* (/ 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))
73.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
53.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series476.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
132.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
122.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
140.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify2.7s

Counts

160 → 160

Iterations

Iter	Nodes
done	5002
2	3512
1	601
0	177

prune966.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.2b

regimes245.0ms

Accuracy

74.9% (3.2b remaining)

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

bsearch102.0ms

Steps

Iters	Range		Point
8	1541639454070.677	19367525498197844.0	7715362331151764.0

simplify16.0ms

Iterations

Iter	Nodes
done	36
1	36
0	32

end0.0ms

sample1.7s

Algorithm

intervals

Results

667.0ms	841×	body	1280	valid
362.0ms	5862×	body	80	valid
228.0ms	8000×	pre	80	true
141.0ms	694×	body	640	valid
89.0ms	410×	body	320	valid
18.0ms	193×	body	160	valid