Details

sample65.0ms

Algorithm

intervals

Results

13.0ms	256×	pre	80	true
13.0ms	190×	body	80	valid
9.0ms	28×	body	1280	valid
6.0ms	22×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	4×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
32	4930
31	4722
30	4510
29	4301
28	4120
27	3916
26	3715
25	3502
24	3325
23	3117
22	2909
21	2698
20	2516
19	2291
18	2012
17	1763
16	1558
15	1364
14	1138
13	931
12	742
11	607
10	526
9	431
8	318
7	267
6	197
5	124
4	69
3	50
2	33
1	20
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite266.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Counts

2 → 65

Calls

2 calls:

71.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
190.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series167.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
103.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5003
2	1119
1	326
0	124

prune398.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.7b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
56×	`times-frac`
36×	`add-cube-cbrt`
24×	`distribute-lft-out`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
6×	`add-log-exp`
4×	`pow1` `associate-/r/` `associate-/l/`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--`
2×	`flip3-+` `frac-sub` `flip-+`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 137

Calls

4 calls:

1.3s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
55.0ms	(/ alpha (+ (+ alpha beta) 2.0))
39.0ms	(/ beta (+ (+ alpha beta) 2.0))
210.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series316.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
67.0ms	(/ alpha (+ (+ alpha beta) 2.0))
53.0ms	(/ beta (+ (+ alpha beta) 2.0))
101.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.6s

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
2	1872
1	563
0	238

prune760.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.1b	(log (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
48×	`times-frac`
39×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`distribute-lft-out`
13×	`log-prod` `associate-/r*`
10×	`add-cbrt-cube`
9×	`add-exp-log` `associate-/l*`
5×	`pow1`
4×	`exp-prod` `div-exp` `associate-/r/` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg`
2×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `pow-div`
1×	`log-div`

Counts

4 → 127

Calls

4 calls:

33.0ms	(/ alpha (+ (+ alpha beta) 2.0))
139.0ms	(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
36.0ms	(/ beta (+ (+ alpha beta) 2.0))
105.0ms	(log (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ alpha (+ (+ alpha beta) 2.0))
200.0ms	(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
78.0ms	(/ beta (+ (+ alpha beta) 2.0))
176.0ms	(log (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0)))

simplify1.4s

Counts

139 → 139

Iterations

Iter	Nodes
done	5002
2	1369
1	478
0	219

prune873.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.1b	(log (sqrt (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))))
1.1b	(log (sqrt (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))))

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
42×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`log-prod`
26×	`sqrt-prod`
12×	`distribute-lft-out`
8×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log` `log-pow`
6×	`exp-prod` `associate-/l*`
4×	`sqrt-pow1` `div-inv` `add-log-exp`
3×	`pow-div`
2×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp` `associate-/r/`
1×	`flip3-+` `flip-+`

Counts

4 → 123

Calls

4 calls:

150.0ms	(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
37.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(log (sqrt (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))))
82.0ms	(log (sqrt (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))))

series889.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
67.0ms	(/ beta (+ (+ alpha beta) 2.0))
329.0ms	(log (sqrt (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))))
308.0ms	(log (sqrt (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))))

simplify2.9s

Counts

135 → 135

Iterations

Iter	Nodes
done	5006
3	4522
2	1072
1	399
0	209

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

regimes202.0ms

Accuracy

77.5% (2.9b remaining)

Error of 5.9b against oracle of 3.0b and baseline of 15.9b

bsearch33.0ms

Steps

Iters	Range		Point
5	805227075.7906344	1807605485.6585176	1470024490.544248

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	29

end0.0ms

sample1.7s

Algorithm

intervals

Results

785.0ms	5818×	body	80	valid
268.0ms	857×	body	1280	valid
174.0ms	8000×	pre	80	true
135.0ms	719×	body	640	valid
54.0ms	372×	body	320	valid
21.0ms	234×	body	160	valid