Details

sample26.0ms

Algorithm

intervals

Results

4.0ms	178×	body	80	valid
4.0ms	34×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify286.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	33	13
3	51	13
4	70	13
5	119	13
6	144	13
7	180	13
8	213	13
9	264	13
10	304	13
11	316	13
12	328	13
13	340	13
done	340	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite109.0ms

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:

23.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
82.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series108.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	124	1134
1	319	1074
2	811	1014
3	2431	1006
done	5001	1005

prune154.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.3b

localize9.0ms

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))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite353.0ms

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-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:

17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
218.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
50.0ms	(/ beta (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

123 → 123

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	193	1936
1	448	1814
2	1224	1730
3	4057	1698
done	5000	1696

prune291.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize17.0ms

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))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite121.0ms

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:

10.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
93.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series377.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(cbrt (+ (+ alpha beta) 2.0))
102.0ms	(cbrt (+ (+ alpha beta) 2.0))
75.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify767.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (270.0ms)

Iter	Nodes	Cost
0	120	1076
1	282	1043
2	660	977
3	1690	888
done	5001	888

prune270.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.6b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.6b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite448.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
14×	`log-prod`
12×	`distribute-lft-out`
8×	`log-div`
7×	`add-exp-log` `exp-sum` `distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`flip3--` `associate-/r*` `flip--`
4×	`exp-prod` `exp-diff` `frac-sub`
3×	`associate-/l*`
2×	`associate-/r/` `log-pow`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 95

Calls

4 calls:

18.0ms	(/ beta (+ (+ alpha beta) 2.0))
166.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
92.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
168.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ beta (+ (+ alpha beta) 2.0))
67.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
129.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.4s

Counts

107 → 107

Iterations

Useful iterations: 3 (646.0ms)

Iter	Nodes	Cost
0	211	2358
1	467	2197
2	1212	2032
3	3798	1980
done	5000	1980

prune265.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

regimes126.0ms

Accuracy

78.1% (2.8b remaining)

Error of 6.0b against oracle of 3.3b and baseline of 15.9b

bsearch35.0ms

Steps

Iters	Range		Point
5	391248603.19673574	1027443772.3458656	1015227874.2528594

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	99
1	41	99
done	41	99

end0.0ms

sample599.0ms

Algorithm

intervals

Results

141.0ms	5870×	body	80	valid
109.0ms	828×	body	1280	valid
97.0ms	8000×	pre	80	true
67.0ms	692×	body	640	valid
29.0ms	409×	body	320	valid
10.0ms	201×	body	160	valid