Details

sample139.0ms

Algorithm

intervals

Results

46.0ms	68×	body	1280	valid
37.0ms	258×	body	80	nan
20.0ms	45×	body	640	valid
13.0ms	117×	body	80	valid
4.0ms	13×	body	320	valid
2.0ms	13×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize26.0ms

Local error

Found 2 expressions with local error:

3.1b	(log (+ N 1))
3.4b	(- (log (+ N 1)) (log N))

rewrite23.0ms

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:

6.0ms	(log (+ N 1))
16.0ms	(- (log (+ N 1)) (log N))

series131.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(log (+ N 1))
97.0ms	(- (log (+ N 1)) (log N))

simplify1.1s

Counts

49 → 49

Iterations

Iter	Nodes
done	2006
4	2006
3	1350
2	463
1	199
0	97

prune338.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/3 N) (* N N))
0.4b	(/ 1/3 N)
0.8b	(/ -1/2 (* N N))
13.4b	(+ (+ (/ -1/2 (* N N)) (/ 1 N)) (/ (/ 1/3 N) (* N N)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
35×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/l*`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
6×	`div-inv`
5×	`associate-/r*` `distribute-lft-out`
4×	`pow1` `frac-add` `insert-posit16`
3×	`clear-num` `sum-log` `frac-2neg` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `associate-+l+` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

10.0ms	(/ (/ 1/3 N) (* N N))
4.0ms	(/ 1/3 N)
6.0ms	(/ -1/2 (* N N))
135.0ms	(+ (+ (/ -1/2 (* N N)) (/ 1 N)) (/ (/ 1/3 N) (* N N)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (/ 1/3 N) (* N N))
18.0ms	(/ 1/3 N)
27.0ms	(/ -1/2 (* N N))
28.0ms	(+ (+ (/ -1/2 (* N N)) (/ 1 N)) (/ (/ 1/3 N) (* N N)))

simplify1.5s

Counts

129 → 129

Iterations

Iter	Nodes
done	2002
3	2002
2	1848
1	535
0	200

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1) N)
3.2b	(log (/ (+ N 1) 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` `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:

19.0ms	(/ (+ N 1) N)
8.0ms	(log (/ (+ N 1) N))

series129.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(/ (+ N 1) N)
57.0ms	(log (/ (+ N 1) N))

simplify956.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	2000
3	2000
2	620
1	233
0	102

prune529.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (+ N 1) (sqrt N)))
0.2b	(/ 1 (sqrt N))
0.3b	(/ (+ N 1) (sqrt N))
3.4b	(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1) (sqrt N))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

121×	`*-un-lft-identity`
108×	`times-frac`
79×	`add-sqr-sqrt` `add-cube-cbrt`
78×	`log-prod`
60×	`sqrt-prod`
28×	`associate-+r+`
23×	`distribute-lft-out`
22×	`associate-+l+`
13×	`add-exp-log`
12×	`associate-/r*`
11×	`pow1`
8×	`add-cbrt-cube`
7×	`associate-/l*`
5×	`log-pow` `div-inv`
4×	`div-exp` `insert-posit16` `add-log-exp`
3×	`log-div` `pow-flip`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `rem-log-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `rec-exp` `associate-+r-` `sum-log` `sqrt-pow1` `pow1/2` `1-exp` `associate-+l-` `inv-pow`

Counts

4 → 203

Calls

4 calls:

8.0ms	(log (/ (+ N 1) (sqrt N)))
11.0ms	(/ 1 (sqrt N))
29.0ms	(/ (+ N 1) (sqrt N))
38.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1) (sqrt N))))

series532.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(log (/ (+ N 1) (sqrt N)))
49.0ms	(/ 1 (sqrt N))
93.0ms	(/ (+ N 1) (sqrt N))
240.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1) (sqrt N))))

simplify1.3s

Counts

215 → 215

Iterations

Iter	Nodes
done	2002
3	2002
2	1519
1	606
0	271

prune2.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes129.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.4b

bsearch16.0ms

Steps

Iters	Range		Point
4	5124.349206015988	8718.24681470488	7726.51655081009

simplify2.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.0s	1718×	body	1280	valid
759.0ms	4146×	body	80	valid
649.0ms	8102×	body	80	nan
493.0ms	1248×	body	640	valid
177.0ms	605×	body	320	valid
45.0ms	283×	body	160	valid