Details

sample75.0ms

Algorithm

intervals

Results

20.0ms	187×	body	80	valid
13.0ms	24×	body	1280	valid
11.0ms	256×	pre	80	true
9.0ms	21×	body	640	valid
5.0ms	15×	body	320	valid
2.0ms	9×	body	160	valid

simplify1.8s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.0b	(+ (/ (- 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-+` `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:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
145.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series140.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
83.0ms	(+ (/ (- 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

prune264.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.5b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite695.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 115

Calls

4 calls:

417.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
22.0ms	(/ beta (+ (+ alpha beta) 2.0))
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
208.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series386.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
75.0ms	(/ beta (+ (+ alpha beta) 2.0))
74.0ms	(/ alpha (+ (+ alpha beta) 2.0))
134.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	2008
3	2008
2	1554
1	467
0	197

prune684.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.4b

localize76.0ms

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

rewrite316.0ms

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` `insert-posit16` `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 → 200

Calls

4 calls:

45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
178.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
39.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series434.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ alpha (+ (+ alpha beta) 2.0))
81.0ms	(/ alpha (+ (+ alpha beta) 2.0))
107.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
161.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify1.2s

Counts

212 → 212

Iterations

Iter	Nodes
done	2001
2	2001
1	634
0	194

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize54.0ms

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

rewrite289.0ms

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` `insert-posit16` `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 → 200

Calls

4 calls:

44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
43.0ms	(/ alpha (+ (+ alpha beta) 2.0))
155.0ms	(* (/ 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))

series355.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ alpha (+ (+ alpha beta) 2.0))
67.0ms	(/ alpha (+ (+ alpha beta) 2.0))
76.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
131.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify1.1s

Counts

212 → 212

Iterations

Iter	Nodes
done	2001
2	2001
1	634
0	194

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

regimes240.0ms

Accuracy

62.1% (5.7b remaining)

Error of 6.2b against oracle of 0.5b and baseline of 15.5b

bsearch71.0ms

Steps

Iters	Range		Point
5	5322986266.083726	16482023217.760546	12650120878.39988

simplify19.0ms

Iterations

Iter	Nodes
done	43
1	43
0	36

end0.0ms

sample2.2s

Algorithm

intervals

Results

611.0ms	5869×	body	80	valid
428.0ms	8000×	pre	80	true
424.0ms	831×	body	1280	valid
307.0ms	670×	body	640	valid
175.0ms	400×	body	320	valid
43.0ms	230×	body	160	valid