Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	192×	body	80	valid
4.0ms	30×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	23×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	6×	body	160	valid

simplify314.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.9b	(+ (/ (- 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:

22.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
83.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series111.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
64.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

71 → 71

Iterations

Useful iterations: done (1.5s)

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

prune156.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite356.0ms

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:

221.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
17.0ms	(/ beta (+ (+ alpha beta) 2.0))
95.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series237.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.6s

Counts

123 → 123

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	193	1936
1	448	1814
2	1224	1730
3	4061	1698
done	5000	1696

prune286.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

localize18.0ms

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))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite122.0ms

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:

8.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series376.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(cbrt (+ (+ alpha beta) 2.0))
102.0ms	(cbrt (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify854.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (286.0ms)

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

prune276.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.4b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.7b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite452.0ms

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:

17.0ms	(/ beta (+ (+ alpha beta) 2.0))
166.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
95.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
169.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ beta (+ (+ alpha beta) 2.0))
63.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
124.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.6s

Counts

107 → 107

Iterations

Useful iterations: 3 (699.0ms)

Iter	Nodes	Cost
0	211	2358
1	467	2197
2	1212	2032
3	3798	1980
done	5001	1980

prune270.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.1b

regimes96.0ms

Accuracy

76.1% (3.1b remaining)

Error of 6.2b against oracle of 3.1b and baseline of 16.1b

bsearch33.0ms

Steps

Iters	Range		Point
5	6.313757509671862e+29	2.4877244354034998e+30	6.48438097382689e+29

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	53
1	32	53
done	32	53

end0.0ms

sample597.0ms

Algorithm

intervals

Results

144.0ms	5812×	body	80	valid
98.0ms	807×	body	1280	valid
95.0ms	8000×	pre	80	true
75.0ms	765×	body	640	valid
32.0ms	395×	body	320	valid
11.0ms	221×	body	160	valid