Details

sample43.0ms

Algorithm

intervals

Results

13.0ms	55×	body	1280	valid
7.0ms	45×	body	640	valid
6.0ms	237×	body	80	nan
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

prune5.0ms

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))

rewrite17.0ms

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:

12.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

series135.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (log (+ N 1.0)) (log N))
42.0ms	(log (+ N 1.0))

simplify1.9s

Counts

47 → 47

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	101	510
1	213	488
2	462	445
3	1063	443
4	2574	438
done	5001	426

prune103.0ms

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))

rewrite28.0ms

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:

20.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series133.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (+ N 1.0) N)
86.0ms	(log (/ (+ N 1.0) N))

simplify2.3s

Counts

66 → 66

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	108	723
1	232	690
2	583	637
3	1417	624
4	3874	622
done	5001	622

prune114.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
3.9b	(log (+ N 1.0))
3.9b	(log (+ N 1.0))
3.9b	(log (+ N 1.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod`
23×	`pow1`
19×	`log-pow`
17×	`distribute-lft-out--`
16×	`difference-of-squares`
12×	`log-prod`
8×	`sqr-pow`
7×	`add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`add-cbrt-cube`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 91

Calls

4 calls:

30.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
4.0ms	(log (+ N 1.0))
4.0ms	(log (+ N 1.0))
5.0ms	(log (+ N 1.0))

series320.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
44.0ms	(log (+ N 1.0))
42.0ms	(log (+ N 1.0))
46.0ms	(log (+ N 1.0))

simplify739.0ms

Counts

103 → 103

Iterations

Useful iterations: done (735.0ms)

Iter	Nodes	Cost
0	193	1673
1	481	1563
2	1521	1497
done	5000	1481

prune280.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (/ (+ N 1.0) (sqrt N)) (sqrt N))
0.4b	(/ (+ N 1.0) (sqrt N))
15.7b	(log (/ (/ (+ N 1.0) (sqrt N)) (sqrt N)))

rewrite108.0ms

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:

34.0ms	(/ (/ (+ N 1.0) (sqrt N)) (sqrt N))
18.0ms	(/ (+ N 1.0) (sqrt N))
19.0ms	(log (/ (/ (+ N 1.0) (sqrt N)) (sqrt N)))

series179.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (/ (+ N 1.0) (sqrt N)) (sqrt N))
53.0ms	(/ (+ N 1.0) (sqrt N))
79.0ms	(log (/ (/ (+ N 1.0) (sqrt N)) (sqrt N)))

simplify1.1s

Counts

458 → 458

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	461	9702
1	1034	8458
2	2286	7901
done	5000	7559

prune491.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.2b

bsearch26.0ms

Steps

Iters	Range		Point
8	8.870965552829853	36111.40013315285	6535.778532396666

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	27
1	21	27
done	21	27

end0.0ms

sample1.3s

Algorithm

intervals

Results

415.0ms	1719×	body	1280	valid
191.0ms	7989×	body	80	nan
175.0ms	1188×	body	640	valid
169.0ms	4135×	body	80	valid
62.0ms	647×	body	320	valid
19.0ms	311×	body	160	valid