Details

sample74.0ms

Algorithm

intervals

Results

23.0ms	60×	body	1280	valid
10.0ms	260×	body	80	nan
10.0ms	43×	body	640	valid
8.0ms	126×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize16.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (log (+ 1.0 N)) (log N))
4.8b	(log (+ 1.0 N))

rewrite30.0ms

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-+` `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:

24.0ms	(- (log (+ 1.0 N)) (log N))
4.0ms	(log (+ 1.0 N))

series208.0ms

Counts

2 → 6

Calls

2 calls:

133.0ms	(- (log (+ 1.0 N)) (log N))
75.0ms	(log (+ 1.0 N))

simplify1.2s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	2683
2	637
1	213
0	100

prune235.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

1.6b	(log (/ (+ N 1.0) N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
15×	`*-un-lft-identity`
12×	`times-frac`
9×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log`
3×	`distribute-lft-out`
2×	`pow1` `rem-log-exp`
1×	`log-div` `add-cbrt-cube` `div-exp` `log-pow` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

5.0ms

(log (/ (+ N 1.0) N))

series142.0ms

Counts

1 → 3

Calls

1 calls:

142.0ms

(log (/ (+ N 1.0) N))

simplify809.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1837
2	446
1	169
0	84

prune96.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (+ 1.0 N) N))
0.0b	(sqrt (/ (+ 1.0 N) N))
1.6b	(log (sqrt (/ (+ 1.0 N) N)))
1.6b	(log (sqrt (/ (+ 1.0 N) N)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

17.0ms	(sqrt (/ (+ 1.0 N) N))
9.0ms	(sqrt (/ (+ 1.0 N) N))
6.0ms	(log (sqrt (/ (+ 1.0 N) N)))
6.0ms	(log (sqrt (/ (+ 1.0 N) N)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (/ (+ 1.0 N) N))
65.0ms	(sqrt (/ (+ 1.0 N) N))
181.0ms	(log (sqrt (/ (+ 1.0 N) N)))
198.0ms	(log (sqrt (/ (+ 1.0 N) N)))

simplify945.0ms

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
3	1644
2	474
1	202
0	123

prune555.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

1.6b	(log (sqrt (/ (+ 1.0 N) N)))
1.6b	(log (sqrt (/ (+ 1.0 N) N)))
1.6b	(log (sqrt (/ (+ 1.0 N) N)))
1.6b	(log (sqrt (/ (+ 1.0 N) N)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

76×	`log-prod`
64×	`*-un-lft-identity` `sqrt-prod`
48×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`pow1` `log-pow` `distribute-lft-out`
8×	`add-exp-log`
4×	`log-div` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `rem-log-exp` `div-inv` `add-log-exp`

Counts

4 → 124

Calls

4 calls:

11.0ms	(log (sqrt (/ (+ 1.0 N) N)))
11.0ms	(log (sqrt (/ (+ 1.0 N) N)))
11.0ms	(log (sqrt (/ (+ 1.0 N) N)))
10.0ms	(log (sqrt (/ (+ 1.0 N) N)))

series755.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(log (sqrt (/ (+ 1.0 N) N)))
192.0ms	(log (sqrt (/ (+ 1.0 N) N)))
141.0ms	(log (sqrt (/ (+ 1.0 N) N)))
204.0ms	(log (sqrt (/ (+ 1.0 N) N)))

simplify750.0ms

Counts

136 → 136

Iterations

Iter	Nodes
done	5001
3	1292
2	364
1	168
0	110

prune777.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

100% (0.0b remaining)

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

bsearch42.0ms

Steps

Iters	Range		Point
8	6968.3439428623215	47495130.80298876	7883.767016394318

simplify2.0ms

Iterations

Iter	Nodes
done	22
1	22
0	20

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	1750×	body	1280	valid
409.0ms	1220×	body	640	valid
378.0ms	4104×	body	80	valid
365.0ms	8020×	body	80	nan
151.0ms	613×	body	320	valid
36.0ms	313×	body	160	valid