Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	205×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	21×	body	1280	valid
1.0ms	13×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	5×	body	160	valid

simplify560.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite265.0ms

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:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
217.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series152.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
82.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.9s

Counts

71 → 71

Iterations

Useful iterations: 3 (902.0ms)

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

prune292.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.5b

localize15.0ms

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite955.0ms

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:

591.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
41.0ms	(/ beta (+ (+ alpha beta) 2.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
271.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series385.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
86.0ms	(/ beta (+ (+ alpha beta) 2.0))
75.0ms	(/ alpha (+ (+ alpha beta) 2.0))
116.0ms	(- (/ 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

prune399.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.1b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

528.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
43.0ms	(/ alpha (+ (+ alpha beta) 2.0))
446.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
224.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series355.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
64.0ms	(/ alpha (+ (+ alpha beta) 2.0))
96.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
89.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

103 → 103

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	154	1383
1	323	1283
2	794	1168
3	2201	1156
done	5000	1155

prune359.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.1b

localize22.0ms

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite314.0ms

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:

17.0ms	(cbrt (+ (+ alpha beta) 2.0))
22.0ms	(cbrt (+ (+ alpha beta) 2.0))
19.0ms	(cbrt (+ (+ alpha beta) 2.0))
253.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series500.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (+ (+ alpha beta) 2.0))
145.0ms	(cbrt (+ (+ alpha beta) 2.0))
129.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	120	1076
1	282	1043
2	675	977
3	1727	888
done	5001	863

prune702.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.1b

regimes246.0ms

Accuracy

98.5% (0.2b remaining)

Error of 3.1b against oracle of 2.9b and baseline of 15.7b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	52
1	31	52
done	31	52

end0.0ms

sample1.1s

Algorithm

intervals

Results

259.0ms	5855×	body	80	valid
189.0ms	901×	body	1280	valid
149.0ms	8000×	pre	80	true
114.0ms	685×	body	640	valid
52.0ms	375×	body	320	valid
20.0ms	184×	body	160	valid