Details

sample48.0ms

Algorithm

intervals

Results

10.0ms	180×	body	80	valid
7.0ms	28×	body	1280	valid
6.0ms	25×	body	640	valid
5.0ms	256×	pre	80	true
2.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid

simplify566.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	52	13
4	73	13
5	118	13
6	149	13
7	177	13
8	208	13
9	246	13
10	274	13
11	285	13
12	297	13
13	301	13
done	301	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite313.0ms

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:

98.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
210.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series163.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
99.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.8s

Counts

71 → 71

Iterations

Useful iterations: 3 (826.0ms)

Iter	Nodes	Cost
0	124	1134
1	320	1074
2	886	1014
3	2832	1006
done	5000	1006

prune236.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.1b

localize11.0ms

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))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.0s

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:

611.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
70.0ms	(/ beta (+ (+ alpha beta) 2.0))
70.0ms	(/ alpha (+ (+ alpha beta) 2.0))
251.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series362.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
75.0ms	(/ beta (+ (+ alpha beta) 2.0))
56.0ms	(/ alpha (+ (+ alpha beta) 2.0))
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.7s

Counts

123 → 123

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	193	1936
1	448	1814
2	1242	1730
3	4330	1698
done	5000	1686

prune414.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.2b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite970.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

49.0ms	(/ beta (+ (+ alpha beta) 2.0))
54.0ms	(/ alpha (+ (+ alpha beta) 2.0))
606.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
256.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series352.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ beta (+ (+ alpha beta) 2.0))
70.0ms	(/ alpha (+ (+ alpha beta) 2.0))
107.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
111.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.6s

Counts

122 → 122

Iterations

Useful iterations: 3 (653.0ms)

Iter	Nodes	Cost
0	182	1600
1	365	1478
2	826	1364
3	2144	1354
done	5000	1354

prune474.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.2b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite960.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
10×	`cbrt-prod`
8×	`add-cube-cbrt`
7×	`log-pow`
6×	`exp-prod` `distribute-lft-out` `add-log-exp`
5×	`pow1` `log-prod`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `flip3-+` `times-frac` `pow1/3` `exp-sum` `flip-+` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 66

Calls

4 calls:

31.0ms	(cbrt (+ (+ alpha beta) 2.0))
32.0ms	(cbrt (+ (+ alpha beta) 2.0))
610.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
282.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series488.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (+ (+ alpha beta) 2.0))
147.0ms	(cbrt (+ (+ alpha beta) 2.0))
92.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
126.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

78 → 78

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	149	1178
1	321	1106
2	726	1012
3	1806	948
done	5001	931

prune528.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.0b

regimes126.0ms

Accuracy

77.4% (3.0b remaining)

Error of 5.9b against oracle of 2.9b and baseline of 16.0b

bsearch71.0ms

Steps

Iters	Range		Point
7	9579072.400219804	506205769.9975147	307451316.1096792

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	72
1	39	72
done	39	72

end0.0ms

sample2.0s

Algorithm

intervals

Results

729.0ms	8000×	pre	80	true
346.0ms	5834×	body	80	valid
320.0ms	860×	body	1280	valid
229.0ms	697×	body	640	valid
61.0ms	385×	body	320	valid
25.0ms	224×	body	160	valid