Details

sample459.0ms

Algorithm

intervals

Results

403.0ms	48×	body	640	valid
20.0ms	52×	body	1280	valid
13.0ms	271×	body	80	nan
9.0ms	132×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize13.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (log (+ N 1)) (log N))
3.9b	(log (+ N 1))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`add-sqr-sqrt` `pow1`
5×	`log-pow` `add-cube-cbrt`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

8.0ms	(- (log (+ N 1)) (log N))
4.0ms	(log (+ N 1))

series85.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(- (log (+ N 1)) (log N))
25.0ms	(log (+ N 1))

simplify1.4s

Counts

49 → 49

Iterations

Iter	Nodes
4	2935
3	1181
2	416
1	194
0	97

prune443.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1) N)
2.5b	(log (/ (+ N 1) N))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`div-exp` `rem-log-exp` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 62

Calls

2 calls:

13.0ms	(/ (+ N 1) N)
4.0ms	(log (/ (+ N 1) N))

series109.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (+ N 1) N)
48.0ms	(log (/ (+ N 1) N))

simplify3.2s

Counts

68 → 68

Iterations

Iter	Nodes
4	5391
3	1555
2	508
1	225
0	102

prune461.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (/ (+ N 1) (sqrt N)) (sqrt N))
0.4b	(/ (+ N 1) (sqrt N))
15.6b	(log (/ (/ (+ N 1) (sqrt N)) (sqrt N)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

672×	`times-frac`
500×	`*-un-lft-identity`
342×	`sqrt-prod`
330×	`add-sqr-sqrt` `add-cube-cbrt`
172×	`log-prod`
85×	`distribute-lft-out`
32×	`associate-/l*`
16×	`add-exp-log` `div-inv`
12×	`associate-/r*`
10×	`add-cbrt-cube`
7×	`div-exp`
4×	`pow1` `cbrt-undiv`
3×	`rem-log-exp` `insert-posit16` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`log-div` `flip3-+` `log-pow` `flip-+`

Counts

3 → 452

Calls

3 calls:

32.0ms	(/ (/ (+ N 1) (sqrt N)) (sqrt N))
14.0ms	(/ (+ N 1) (sqrt N))
6.0ms	(log (/ (/ (+ N 1) (sqrt N)) (sqrt N)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (/ (+ N 1) (sqrt N)) (sqrt N))
78.0ms	(/ (+ N 1) (sqrt N))
75.0ms	(log (/ (/ (+ N 1) (sqrt N)) (sqrt N)))

simplify1.0s

Counts

461 → 461

Iterations

Iter	Nodes
2	2208
1	1034
0	458

prune4.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (/ (+ N 1) (sqrt N))) (sqrt N))
0.4b	(/ (+ N 1) (sqrt N))
0.4b	(/ (+ N 1) (sqrt N))
3.0b	(+ (log (/ (sqrt (/ (+ N 1) (sqrt N))) 1)) (log (/ (sqrt (/ (+ N 1) (sqrt N))) (sqrt N))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
859×	`sqrt-prod`
677×	`*-un-lft-identity`
453×	`add-sqr-sqrt` `add-cube-cbrt`
287×	`log-prod`
190×	`associate-+r+`
114×	`distribute-lft-out`
97×	`associate-+l+`
39×	`associate-/l*`
21×	`div-inv`
18×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
5×	`associate-/l/`
4×	`log-pow` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+`
2×	`log-div`
1×	`+-commutative` `sqrt-undiv` `associate-+r-` `sum-log` `sqrt-div` `associate-+l-`

Counts

4 → 641

Calls

4 calls:

28.0ms	(/ (sqrt (/ (+ N 1) (sqrt N))) (sqrt N))
22.0ms	(/ (+ N 1) (sqrt N))
14.0ms	(/ (+ N 1) (sqrt N))
32.0ms	(+ (log (/ (sqrt (/ (+ N 1) (sqrt N))) 1)) (log (/ (sqrt (/ (+ N 1) (sqrt N))) (sqrt N))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (sqrt (/ (+ N 1) (sqrt N))) (sqrt N))
79.0ms	(/ (+ N 1) (sqrt N))
67.0ms	(/ (+ N 1) (sqrt N))
272.0ms	(+ (log (/ (sqrt (/ (+ N 1) (sqrt N))) 1)) (log (/ (sqrt (/ (+ N 1) (sqrt N))) (sqrt N))))

simplify1.6s

Counts

653 → 653

Iterations

Iter	Nodes
2	2649
1	1412
0	750

prune8.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes42.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch47.0ms

Steps

Iters	Range		Point
8	41.60074012902226	43862.50504651285	7250.408229147694

simplify6.0ms

Iterations

Iter	Nodes
2	23
1	23
0	19

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	1752×	body	1280	valid
517.0ms	8041×	body	80	nan
496.0ms	1281×	body	640	valid
407.0ms	4105×	body	80	valid
135.0ms	591×	body	320	valid
64.0ms	271×	body	160	valid