Details

sample78.0ms

Algorithm

intervals

Results

26.0ms	63×	body	1280	valid
11.0ms	245×	body	80	nan
9.0ms	134×	body	80	valid
9.0ms	35×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	11×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize16.0ms

Local error

Found 2 expressions with local error:

2.8b	(log (+ N 1.0))
2.9b	(- (log (+ N 1.0)) (log N))

rewrite44.0ms

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:

9.0ms	(log (+ N 1.0))
29.0ms	(- (log (+ N 1.0)) (log N))

series288.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(log (+ N 1.0))
205.0ms	(- (log (+ N 1.0)) (log N))

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	127	1052
1	288	863
2	1098	705
done	5001	614

prune271.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.8b	(log (/ (+ N 1.0) N))

rewrite33.0ms

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:

21.0ms	(/ (+ N 1.0) N)
9.0ms	(log (/ (+ N 1.0) N))

series172.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ (+ N 1.0) N)
101.0ms	(log (/ (+ N 1.0) N))

simplify1.1s

Counts

70 → 70

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	112	749
1	253	708
2	1053	660
done	5000	647

prune254.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (/ (+ N 1.0) N))
0.0b	(/ (+ N 1.0) N)
2.9b	(expm1 (log1p (/ (+ N 1.0) N)))
29.2b	(log (expm1 (log1p (/ (+ N 1.0) N))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow1` `expm1-log1p-u`
4×	`log1p-expm1-u` `distribute-lft-out` `associate-/l*` `add-log-exp`
3×	`log-prod` `associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `frac-2neg` `flip3-+` `log1p-expm1` `div-exp` `rem-log-exp` `clear-num` `log-pow` `flip-+` `div-inv` `expm1-udef`

Counts

4 → 71

Calls

4 calls:

0.0ms	(log1p (/ (+ N 1.0) N))
26.0ms	(/ (+ N 1.0) N)
0.0ms	(expm1 (log1p (/ (+ N 1.0) N)))
3.0ms	(log (expm1 (log1p (/ (+ N 1.0) N))))

series592.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(log1p (/ (+ N 1.0) N))
88.0ms	(/ (+ N 1.0) N)
183.0ms	(expm1 (log1p (/ (+ N 1.0) N)))
240.0ms	(log (expm1 (log1p (/ (+ N 1.0) N))))

simplify1.1s

Counts

83 → 83

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	154	994
1	370	885
2	1600	773
done	5002	764

prune339.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 0.3333333333333333 (pow N 3))
0.3b	(/ 0.5 (* N N))
12.4b	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

rewrite580.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
71×	`times-frac`
52×	`add-sqr-sqrt`
48×	`add-cube-cbrt`
35×	`prod-diff`
17×	`distribute-lft-out`
13×	`add-exp-log` `associate-/r*`
12×	`unpow-prod-down` `cube-prod`
10×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-inv`
6×	`associate-/l*`
5×	`fma-neg` `div-exp`
4×	`cube-mult` `unpow3` `sqr-pow`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-sub` `log1p-expm1-u`
2×	`frac-2neg` `diff-log` `clear-num` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `flip3--` `flip3-+` `frac-add` `pow-exp` `prod-exp` `associate--l+` `sum-log` `flip--` `cbrt-unprod` `flip-+`

Counts

3 → 153

Calls

3 calls:

8.0ms	(/ 0.3333333333333333 (pow N 3))
12.0ms	(/ 0.5 (* N N))
553.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

series122.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ 0.3333333333333333 (pow N 3))
30.0ms	(/ 0.5 (* N N))
42.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

simplify4.1s

Counts

162 → 162

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	260	3457
1	684	2935
2	4788	2473
done	5000	2473

prune447.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 28.9b

bsearch47.0ms

Steps

Iters	Range		Point
9	1.2963151977280056	865094.0527290168	8323.846677005948

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	20	25
done	20	25

end0.0ms

sample2.6s

Algorithm

intervals

Results

734.0ms	1691×	body	1280	valid
485.0ms	1262×	body	640	valid
414.0ms	7921×	body	80	nan
327.0ms	4130×	body	80	valid
150.0ms	616×	body	320	valid
33.0ms	301×	body	160	valid