Details

sample85.0ms

Algorithm

intervals

Results

25.0ms	57×	body	1280	valid
13.0ms	275×	body	80	nan
12.0ms	39×	body	640	valid
11.0ms	136×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (log (+ N 1.0)) (log N))
2.8b	(log (+ N 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

13.0ms	(- (log (+ N 1.0)) (log N))
5.0ms	(log (+ N 1.0))

series216.0ms

Counts

2 → 6

Calls

2 calls:

140.0ms	(- (log (+ N 1.0)) (log N))
76.0ms	(log (+ N 1.0))

simplify1.6s

Counts

47 → 47

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	101	510
1	213	488
2	643	445
3	2849	443
done	5001	438

prune149.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.3b	(log (/ (+ N 1.0) N))

rewrite53.0ms

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` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

37.0ms	(/ (+ N 1.0) N)
12.0ms	(log (/ (+ N 1.0) N))

series592.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(/ (+ N 1.0) N)
515.0ms	(log (/ (+ N 1.0) N))

simplify633.0ms

Counts

66 → 66

Iterations

Useful iterations: done (630.0ms)

Iter	Nodes	Cost
0	108	723
1	243	690
2	1010	637
done	5000	624

prune141.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
2.1b	(log (sqrt (/ (+ N 1.0) N)))
2.1b	(log (sqrt (/ (+ N 1.0) N)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `log-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 118

Calls

4 calls:

11.0ms	(sqrt (/ (+ N 1.0) N))
15.0ms	(sqrt (/ (+ N 1.0) N))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (/ (+ N 1.0) N))
52.0ms	(sqrt (/ (+ N 1.0) N))
201.0ms	(log (sqrt (/ (+ N 1.0) N)))
148.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify1.0s

Counts

130 → 130

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	123	1684
1	202	1574
2	469	1426
3	1649	1426
done	5001	1424

prune406.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
1.9b	(log (sqrt (sqrt (/ (+ N 1.0) N))))
1.9b	(log (sqrt (sqrt (/ (+ N 1.0) N))))
2.1b	(log (sqrt (/ (+ N 1.0) N)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

102×	`sqrt-prod`
65×	`*-un-lft-identity`
63×	`log-prod`
49×	`times-frac`
44×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
13×	`pow1` `log-pow`
12×	`distribute-lft-out`
10×	`sqrt-pow1`
7×	`add-exp-log`
6×	`pow1/2` `sqrt-div`
4×	`add-cbrt-cube` `div-inv` `add-log-exp`
3×	`log-div` `rem-log-exp`
2×	`rem-sqrt-square`

Counts

4 → 131

Calls

4 calls:

13.0ms	(sqrt (/ (+ N 1.0) N))
9.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
15.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
14.0ms	(log (sqrt (/ (+ N 1.0) N)))

series777.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (/ (+ N 1.0) N))
264.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
286.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
155.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify1.5s

Counts

143 → 143

Iterations

Useful iterations: 3 (601.0ms)

Iter	Nodes	Cost
0	202	2064
1	309	1935
2	685	1765
3	2435	1761
done	5001	1761

prune532.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.2b

bsearch32.0ms

Steps

Iters	Range		Point
7	309.51167567074003	13587.758917488305	7140.532646773333

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	47
1	34	45
2	36	45
3	38	45
done	38	45

end0.0ms

sample2.9s

Algorithm

intervals

Results

913.0ms	1776×	body	1280	valid
537.0ms	8189×	body	80	nan
363.0ms	1219×	body	640	valid
348.0ms	4111×	body	80	valid
156.0ms	595×	body	320	valid
90.0ms	299×	body	160	valid