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

simplify896.0ms

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	173	13
8	208	13
9	259	13
10	298	13
11	331	13
12	378	13
13	415	13
14	463	13
15	525	13
16	551	13
17	578	13
18	610	13
19	618	13
done	618	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize8.0ms

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)

rewrite113.0ms

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:

23.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
87.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series112.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
66.0ms	(+ (/ (- 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	867	1014
3	3700	1006
done	5000	1005

prune150.0ms

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)

rewrite358.0ms

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:

20.0ms	(/ beta (+ (+ alpha beta) 2.0))
221.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
95.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series236.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 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))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify501.0ms

Counts

123 → 123

Iterations

Useful iterations: done (497.0ms)

Iter	Nodes	Cost
0	193	1936
1	448	1814
2	1350	1730
done	5000	1700

prune479.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize13.0ms

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)

rewrite508.0ms

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:

181.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
206.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series264.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
75.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

103 → 103

Iterations

Useful iterations: 3 (420.0ms)

Iter	Nodes	Cost
0	154	1383
1	324	1283
2	874	1168
3	3642	1160
done	5001	1160

prune252.0ms

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)

rewrite124.0ms

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))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
97.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series372.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(cbrt (+ (+ alpha beta) 2.0))
97.0ms	(cbrt (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify795.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (270.0ms)

Iter	Nodes	Cost
0	120	1076
1	282	1043
2	674	977
3	2050	888
done	5000	888

prune247.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.8b

regimes130.0ms

Accuracy

98% (0.3b remaining)

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

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample605.0ms

Algorithm

intervals

Results

143.0ms	5765×	body	80	valid
105.0ms	855×	body	1280	valid
94.0ms	8000×	pre	80	true
76.0ms	733×	body	640	valid
30.0ms	436×	body	320	valid
10.0ms	211×	body	160	valid