Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	189×	body	80	valid
3.0ms	28×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	20×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	6×	body	160	valid

simplify364.0ms

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: 15.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite190.0ms

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:

43.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
144.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series113.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
66.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: 3 (501.0ms)

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

prune155.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite237.0ms

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

Counts

3 → 89

Calls

3 calls:

33.0ms	(/ alpha (+ (+ alpha beta) 2.0))
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
168.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series180.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify965.0ms

Counts

98 → 98

Iterations

Useful iterations: 3 (400.0ms)

Iter	Nodes	Cost
0	153	1237
1	326	1164
2	775	1090
3	2063	1082
done	5000	1082

prune237.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize13.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite440.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 105

Calls

4 calls:

167.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
234.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
17.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
17.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
141.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
146.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
141.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify989.0ms

Counts

117 → 117

Iterations

Useful iterations: done (985.0ms)

Iter	Nodes	Cost
0	161	1985
1	334	1895
2	784	1760
3	2065	1731
done	5001	1695

prune327.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.9b

localize17.0ms

Local error

Found 4 expressions with local error:

7.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.6b	(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
84×	`cbrt-prod`
60×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`distribute-lft-out`
25×	`log-pow`
24×	`exp-prod`
8×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`
3×	`cbrt-div` `log-prod` `pow1/3`
1×	`rem-log-exp`

Counts

4 → 126

Calls

4 calls:

19.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
17.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
17.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
74.0ms	(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
142.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
145.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
143.0ms	(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

simplify952.0ms

Counts

138 → 138

Iterations

Useful iterations: done (947.0ms)

Iter	Nodes	Cost
0	163	2228
1	277	2041
2	592	1892
3	1517	1866
done	5000	1818

prune435.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.9b

regimes81.0ms

Accuracy

74.6% (3.3b remaining)

Error of 6.4b against oracle of 3.1b and baseline of 16.1b

bsearch33.0ms

Steps

Iters	Range		Point
6	9.393778871846807e+23	5.890861695143504e+24	2.494813499756589e+24

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	71
1	35	71
done	35	71

end0.0ms

sample608.0ms

Algorithm

intervals

Results

141.0ms	5829×	body	80	valid
99.0ms	868×	body	1280	valid
88.0ms	8000×	pre	80	true
62.0ms	707×	body	640	valid
25.0ms	378×	body	320	valid
12.0ms	218×	body	160	valid