Details

sample46.0ms

Algorithm

intervals

Results

13.0ms	55×	body	1280	valid
8.0ms	237×	body	80	nan
6.0ms	45×	body	640	valid
5.0ms	133×	body	80	valid
1.0ms	11×	body	320	valid
1.0ms	12×	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: 28.4b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (log (+ N 1.0)) (log N))
3.9b	(log (+ N 1.0))

rewrite23.0ms

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:

15.0ms	(- (log (+ N 1.0)) (log N))
5.0ms	(log (+ N 1.0))

series136.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(- (log (+ N 1.0)) (log N))
45.0ms	(log (+ N 1.0))

simplify2.6s

Counts

71 → 71

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	127	1052
1	277	855
2	668	705
3	2055	614
done	5000	592

prune126.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.4b	(log (/ (+ N 1.0) N))

rewrite31.0ms

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:

22.0ms	(/ (+ N 1.0) N)
7.0ms	(log (/ (+ N 1.0) N))

series128.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (+ N 1.0) N)
82.0ms	(log (/ (+ N 1.0) N))

simplify2.7s

Counts

70 → 70

Iterations

Useful iterations: done (2.7s)

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

prune132.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(log1p (expm1 (log1p (/ 1.0 N))))
0.0b	(log1p (/ 1.0 N))
2.8b	(expm1 (log1p (/ 1.0 N)))

rewrite2.0ms

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

series440.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(log1p (expm1 (log1p (/ 1.0 N))))
68.0ms	(log1p (/ 1.0 N))
190.0ms	(expm1 (log1p (/ 1.0 N)))

simplify5.4s

Counts

42 → 42

Iterations

Useful iterations: 4 (4.0s)

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

prune84.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (* (sqrt (/ 1.0 N)) (sqrt (/ 1.0 N))))
0.1b	(sqrt (/ 1.0 N))
0.1b	(sqrt (/ 1.0 N))
0.5b	(* (sqrt (/ 1.0 N)) (sqrt (/ 1.0 N)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

92×	`sqrt-prod`
84×	`add-sqr-sqrt`
62×	`times-frac`
50×	`add-cube-cbrt` `*-un-lft-identity`
21×	`pow1`
18×	`swap-sqr`
16×	`associate-r` `associate-l`
10×	`sqrt-pow1` `pow1/2`
9×	`unswap-sqr`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `div-inv`
5×	`expm1-log1p-u` `pow-prod-up`
4×	`rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
1×	`pow2` `frac-times` `log1p-udef` `pow-plus` `sqrt-unprod` `log1p-expm1` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 154

Calls

4 calls:

0.0ms	(log1p (* (sqrt (/ 1.0 N)) (sqrt (/ 1.0 N))))
4.0ms	(sqrt (/ 1.0 N))
4.0ms	(sqrt (/ 1.0 N))
36.0ms	(* (sqrt (/ 1.0 N)) (sqrt (/ 1.0 N)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(log1p (* (sqrt (/ 1.0 N)) (sqrt (/ 1.0 N))))
58.0ms	(sqrt (/ 1.0 N))
54.0ms	(sqrt (/ 1.0 N))
61.0ms	(* (sqrt (/ 1.0 N)) (sqrt (/ 1.0 N)))

simplify2.0s

Counts

166 → 166

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	210	2088
1	400	1425
2	1231	1319
3	3845	1272
done	5000	1272

prune330.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes13.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
done	6	6

end0.0ms

sample1.3s

Algorithm

intervals

Results

406.0ms	1719×	body	1280	valid
186.0ms	7989×	body	80	nan
176.0ms	1188×	body	640	valid
166.0ms	4135×	body	80	valid
63.0ms	647×	body	320	valid
18.0ms	311×	body	160	valid