Details

sample42.0ms

Algorithm

intervals

Results

12.0ms	190×	body	80	valid
5.0ms	28×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	22×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	4×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	4613
8	1507
7	644
6	306
5	164
4	74
3	53
2	34
1	20
0	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize13.0ms

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)

rewrite257.0ms

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:

55.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
200.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series156.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
101.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1359
1	326
0	124

prune343.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.7b

localize38.0ms

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)

rewrite1.5s

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:

1.2s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
42.0ms	(/ alpha (+ (+ alpha beta) 2.0))
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
200.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series360.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
64.0ms	(/ alpha (+ (+ alpha beta) 2.0))
78.0ms	(/ beta (+ (+ alpha beta) 2.0))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.8s

Counts

149 → 149

Iterations

Iter	Nodes
done	5002
2	2417
1	563
0	238

prune851.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize38.0ms

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)))

rewrite309.0ms

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:

48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
134.0ms	(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
38.0ms	(/ beta (+ (+ alpha beta) 2.0))
82.0ms	(log (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0)))

series540.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ alpha (+ (+ alpha beta) 2.0))
211.0ms	(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
58.0ms	(/ beta (+ (+ alpha beta) 2.0))
187.0ms	(log (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0)))

simplify1.3s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
2	1791
1	478
0	219

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize70.0ms

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))))

rewrite397.0ms

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:

139.0ms	(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
54.0ms	(/ beta (+ (+ alpha beta) 2.0))
97.0ms	(log (sqrt (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))))
97.0ms	(log (sqrt (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))))

series896.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))
65.0ms	(/ beta (+ (+ alpha beta) 2.0))
286.0ms	(log (sqrt (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))))
330.0ms	(log (sqrt (/ (exp (/ alpha (+ (+ alpha beta) 2.0))) (exp 1.0))))

simplify1.1s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1319
1	399
0	209

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

regimes256.0ms

Accuracy

77.5% (2.9b remaining)

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

bsearch57.0ms

Steps

Iters	Range		Point
5	805227075.7906344	1807605485.6585176	1470024490.544248

simplify11.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample1.3s

Algorithm

intervals

Results

313.0ms	5818×	body	80	valid
254.0ms	857×	body	1280	valid
196.0ms	719×	body	640	valid
176.0ms	8000×	pre	80	true
79.0ms	372×	body	320	valid
19.0ms	234×	body	160	valid