Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	188×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	26×	body	1280	valid
3.0ms	28×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	2×	body	160	valid

simplify306.0ms

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: 16.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.9b	(+ (/ (- 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))
84.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series110.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
64.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify976.0ms

Counts

71 → 71

Iterations

Useful iterations: done (974.0ms)

Iter	Nodes	Cost
0	124	1134
1	319	1074
2	811	1014
3	2431	1006
done	5000	1005

prune140.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite352.0ms

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	(/ beta (+ (+ alpha beta) 2.0))
220.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
94.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ beta (+ (+ alpha beta) 2.0))
64.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

123 → 123

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	193	1936
1	448	1814
2	1225	1730
3	4065	1698
done	5001	1696

prune276.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize12.0ms

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))
0.9b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite512.0ms

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:

184.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
209.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
97.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series281.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
81.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify925.0ms

Counts

103 → 103

Iterations

Useful iterations: 3 (397.0ms)

Iter	Nodes	Cost
0	154	1383
1	324	1283
2	786	1168
3	2188	1156
done	5000	1156

prune257.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

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))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite123.0ms

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))
94.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series380.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ (+ alpha beta) 2.0))
105.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
75.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify633.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (264.0ms)

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

prune250.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.8b

regimes135.0ms

Accuracy

98% (0.3b remaining)

Error of 3.2b against oracle of 3.0b and baseline of 16.3b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	58
1	32	58
done	32	58

end0.0ms

sample610.0ms

Algorithm

intervals

Results

152.0ms	5765×	body	80	valid
108.0ms	855×	body	1280	valid
90.0ms	8000×	pre	80	true
71.0ms	733×	body	640	valid
35.0ms	436×	body	320	valid
13.0ms	211×	body	160	valid