Details

sample105.0ms

Algorithm

intervals

Results

33.0ms	56×	body	1280	valid
20.0ms	278×	body	80	nan
16.0ms	38×	body	640	valid
14.0ms	134×	body	80	valid
5.0ms	20×	body	320	valid
1.0ms	8×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize12.0ms

Local error

Found 2 expressions with local error:

2.8b	(- (log (+ N 1)) (log N))
3.0b	(log (+ N 1))

rewrite48.0ms

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:

38.0ms	(- (log (+ N 1)) (log N))
7.0ms	(log (+ N 1))

series118.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(- (log (+ N 1)) (log N))
52.0ms	(log (+ N 1))

simplify1.6s

Counts

49 → 49

Iterations

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

prune343.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* (log (+ N 1)) (log (+ N 1))) (* (log N) (log N)))
3.0b	(log (+ N 1))
3.0b	(log (+ N 1))
3.0b	(log (+ N 1))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

21.0ms	(- (* (log (+ N 1)) (log (+ N 1))) (* (log N) (log N)))
6.0ms	(log (+ N 1))
6.0ms	(log (+ N 1))
6.0ms	(log (+ N 1))

series249.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(- (* (log (+ N 1)) (log (+ N 1))) (* (log N) (log N)))
38.0ms	(log (+ N 1))
32.0ms	(log (+ N 1))
23.0ms	(log (+ N 1))

simplify990.0ms

Counts

88 → 88

Iterations

Iter	Nodes
3	2667
2	821
1	315
0	138

prune867.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1) N)
3.0b	(log (/ (+ N 1) N))

rewrite41.0ms

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:

31.0ms	(/ (+ N 1) N)
8.0ms	(log (/ (+ N 1) N))

series118.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (+ N 1) N)
57.0ms	(log (/ (+ N 1) N))

simplify3.2s

Counts

68 → 68

Iterations

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

prune492.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize87.0ms

Local error

Found 4 expressions with local error:

3.0b	(log (+ N 1))
3.0b	(log (+ N 1))
3.0b	(log (+ N 1))
3.0b	(log (+ N 1))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod` `*-un-lft-identity`
8×	`add-sqr-sqrt` `pow1` `log-div` `add-exp-log` `add-cube-cbrt`
4×	`flip3-+` `add-cbrt-cube` `rem-log-exp` `log-pow` `flip-+` `insert-posit16` `distribute-lft-out` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

4.0ms	(log (+ N 1))
6.0ms	(log (+ N 1))
6.0ms	(log (+ N 1))
7.0ms	(log (+ N 1))

series98.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(log (+ N 1))
28.0ms	(log (+ N 1))
24.0ms	(log (+ N 1))
23.0ms	(log (+ N 1))

simplify1.9s

Counts

76 → 76

Iterations

Iter	Nodes
5	3338
4	1134
3	442
2	212
1	105
0	55

prune1.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes55.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.5b

bsearch56.0ms

Steps

Iters	Range		Point
7	186.95626557948964	5877.37978213442	4683.545058486523

simplify4.0ms

Iterations

Iter	Nodes
2	27
1	27
0	22

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	1733×	body	1280	valid
622.0ms	8086×	body	80	nan
536.0ms	1258×	body	640	valid
439.0ms	4077×	body	80	valid
244.0ms	641×	body	320	valid
49.0ms	291×	body	160	valid