Details

sample87.0ms

Algorithm

intervals

Results

27.0ms	60×	body	1280	valid
22.0ms	131×	body	80	valid
10.0ms	243×	body	80	nan
10.0ms	37×	body	640	valid
3.0ms	20×	body	320	valid
1.0ms	8×	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: 29.5b

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b	(log (+ N 1.0))
2.1b	(- (log (+ N 1.0)) (log N))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
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:

6.0ms	(log (+ N 1.0))
16.0ms	(- (log (+ N 1.0)) (log N))

series242.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(log (+ N 1.0))
166.0ms	(- (log (+ N 1.0)) (log N))

simplify3.8s

Counts

71 → 71

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	127	1052
1	277	855
2	666	705
3	2050	614
done	5000	592

prune197.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite55.0ms

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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

38.0ms	(/ (+ N 1.0) N)
13.0ms	(log (/ (+ N 1.0) N))

series209.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(/ (+ N 1.0) N)
131.0ms	(log (/ (+ N 1.0) N))

simplify4.0s

Counts

70 → 70

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	112	749
1	242	708
2	620	660
3	1531	647
4	4287	643
done	5000	612

prune198.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(log1p (expm1 (log1p (/ 1.0 N))))
0.0b	(log1p (/ 1.0 N))
2.9b	(expm1 (log1p (/ 1.0 N)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`expm1-log1p-u`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log1p-udef` `log1p-expm1`
1×	`expm1-log1p` `expm1-udef`

Counts

3 → 33

Calls

3 calls:

0.0ms	(log1p (expm1 (log1p (/ 1.0 N))))
1.0ms	(log1p (/ 1.0 N))
1.0ms	(expm1 (log1p (/ 1.0 N)))

series723.0ms

Counts

3 → 9

Calls

3 calls:

288.0ms	(log1p (expm1 (log1p (/ 1.0 N))))
133.0ms	(log1p (/ 1.0 N))
302.0ms	(expm1 (log1p (/ 1.0 N)))

simplify7.9s

Counts

42 → 42

Iterations

Useful iterations: 4 (5.8s)

Iter	Nodes	Cost
0	83	446
1	183	380
2	471	313
3	1418	310
4	4972	292
done	5000	292

prune104.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
done	6	6

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	1720×	body	1280	valid
412.0ms	7865×	body	80	nan
380.0ms	1262×	body	640	valid
298.0ms	4152×	body	80	valid
141.0ms	592×	body	320	valid
30.0ms	274×	body	160	valid