Details

sample74.0ms

Algorithm

intervals

Results

24.0ms	63×	body	1280	valid
10.0ms	245×	body	80	nan
9.0ms	134×	body	80	valid
8.0ms	35×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize42.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

9.0ms	(log (+ N 1.0))
26.0ms	(- (log (+ N 1.0)) (log N))

series213.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(log (+ N 1.0))
152.0ms	(- (log (+ N 1.0)) (log N))

simplify1.6s

Counts

47 → 47

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	101	510
1	213	488
2	644	445
3	2755	443
done	5001	438

prune225.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

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

Counts

2 → 60

Calls

2 calls:

22.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series223.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(/ (+ N 1.0) N)
128.0ms	(log (/ (+ N 1.0) N))

simplify680.0ms

Counts

66 → 66

Iterations

Useful iterations: done (677.0ms)

Iter	Nodes	Cost
0	108	723
1	243	690
2	1010	637
done	5000	624

prune220.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (+ N 1.0) (sqrt N)) (sqrt N))
0.4b	(/ (+ N 1.0) (sqrt N))
16.6b	(log (/ (/ (+ N 1.0) (sqrt N)) (sqrt N)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

672×	`times-frac`
500×	`*-un-lft-identity`
342×	`sqrt-prod`
330×	`add-sqr-sqrt` `add-cube-cbrt`
172×	`log-prod`
85×	`distribute-lft-out`
32×	`associate-/l*`
16×	`add-exp-log` `div-inv`
12×	`associate-/r*`
10×	`add-cbrt-cube`
7×	`div-exp`
4×	`pow1` `cbrt-undiv`
3×	`rem-log-exp` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`log-div` `flip3-+` `log-pow` `flip-+`

Counts

3 → 449

Calls

3 calls:

54.0ms	(/ (/ (+ N 1.0) (sqrt N)) (sqrt N))
20.0ms	(/ (+ N 1.0) (sqrt N))
24.0ms	(log (/ (/ (+ N 1.0) (sqrt N)) (sqrt N)))

series226.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (/ (+ N 1.0) (sqrt N)) (sqrt N))
63.0ms	(/ (+ N 1.0) (sqrt N))
111.0ms	(log (/ (/ (+ N 1.0) (sqrt N)) (sqrt N)))

simplify1.8s

Counts

458 → 458

Iterations

Useful iterations: 2 (738.0ms)

Iter	Nodes	Cost
0	461	9702
1	1070	8458
2	4183	7957
done	5000	7957

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite678.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
35×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
13×	`add-exp-log` `associate-/r*`
12×	`unpow-prod-down` `cube-prod`
10×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`div-exp`
4×	`cube-mult` `unpow3` `sqr-pow`
3×	`pow1` `cbrt-undiv` `frac-sub`
2×	`frac-2neg` `diff-log` `clear-num` `div-inv` `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-+` `distribute-lft-out`

Counts

3 → 107

Calls

3 calls:

17.0ms	(/ 0.3333333333333333 (pow N 3))
20.0ms	(/ 0.5 (* N N))
633.0ms	(- (+ (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)) (/ 0.5 (* N N)))

series141.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ 0.3333333333333333 (pow N 3))
39.0ms	(/ 0.5 (* N N))
34.0ms	(- (+ (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)) (/ 0.5 (* N N)))

simplify3.4s

Counts

116 → 116

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	197	1558
1	526	1372
2	3929	1292
done	5002	1292

prune393.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes76.0ms

Accuracy

100% (0.0b remaining)

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

bsearch48.0ms

Steps

Iters	Range		Point
9	1.2963151977280056	865094.0527290168	8323.846677005948

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	29
1	22	29
done	22	29

end0.0ms

sample3.0s

Algorithm

intervals

Results

874.0ms	1691×	body	1280	valid
870.0ms	7921×	body	80	nan
349.0ms	1262×	body	640	valid
303.0ms	4130×	body	80	valid
111.0ms	616×	body	320	valid
34.0ms	301×	body	160	valid