Details

sample55.0ms

Algorithm

intervals

Results

17.0ms	60×	body	1280	valid
8.0ms	260×	body	80	nan
8.0ms	43×	body	640	valid
6.0ms	126×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `pow1` `prod-diff`
14×	`log-pow` `add-cube-cbrt`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

11.0ms	(- (log (+ 1.0 N)) (log N))
4.0ms	(log (+ 1.0 N))

series220.0ms

Counts

2 → 6

Calls

2 calls:

174.0ms	(- (log (+ 1.0 N)) (log N))
46.0ms	(log (+ 1.0 N))

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1091
1	287
0	126

prune265.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `div-exp` `log-pow` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

5.0ms

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

series115.0ms

Counts

1 → 3

Calls

1 calls:

115.0ms

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

simplify1.0s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
3	1934
2	467
1	173
0	86

prune151.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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)))

rewrite53.0ms

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×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 126

Calls

4 calls:

16.0ms	(sqrt (/ (+ 1.0 N) N))
16.0ms	(sqrt (/ (+ 1.0 N) N))
9.0ms	(log (sqrt (/ (+ 1.0 N) N)))
6.0ms	(log (sqrt (/ (+ 1.0 N) N)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (/ (+ 1.0 N) N))
87.0ms	(sqrt (/ (+ 1.0 N) N))
195.0ms	(log (sqrt (/ (+ 1.0 N) N)))
170.0ms	(log (sqrt (/ (+ 1.0 N) N)))

simplify2.3s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
3	1865
2	500
1	211
0	127

prune763.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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×	`expm1-log1p-u` `log-div` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `rem-log-exp` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 132

Calls

4 calls:

7.0ms	(log (sqrt (/ (+ N 1.0) N)))
10.0ms	(log (sqrt (/ (+ N 1.0) N)))
8.0ms	(log (sqrt (/ (+ N 1.0) N)))
6.0ms	(log (sqrt (/ (+ 1.0 N) N)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(log (sqrt (/ (+ N 1.0) N)))
201.0ms	(log (sqrt (/ (+ N 1.0) N)))
144.0ms	(log (sqrt (/ (+ N 1.0) N)))
171.0ms	(log (sqrt (/ (+ 1.0 N) N)))

simplify741.0ms

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
3	1352
2	459
1	262
0	181

prune986.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

100% (0.0b remaining)

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

bsearch29.0ms

Steps

Iters	Range		Point
8	6968.3439428623215	47495130.80298876	7883.767016394318

simplify10.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample2.9s

Algorithm

intervals

Results

891.0ms	8020×	body	80	nan
765.0ms	1750×	body	1280	valid
357.0ms	4104×	body	80	valid
322.0ms	1220×	body	640	valid
107.0ms	613×	body	320	valid
66.0ms	313×	body	160	valid