Details

sample55.0ms

Algorithm

intervals

Results

16.0ms	58×	body	1280	valid
8.0ms	252×	body	80	nan
7.0ms	41×	body	640	valid
6.0ms	122×	body	80	valid
3.0ms	22×	body	320	valid
1.0ms	13×	body	160	valid

simplify8.0ms

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: 31.2b

localize15.0ms

Local error

Found 2 expressions with local error:

3.2b	(- (log (+ N 1.0)) (log N))
3.4b	(log (+ N 1.0))

rewrite55.0ms

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:

43.0ms	(- (log (+ N 1.0)) (log N))
9.0ms	(log (+ N 1.0))

series250.0ms

Counts

2 → 6

Calls

2 calls:

164.0ms	(- (log (+ N 1.0)) (log N))
86.0ms	(log (+ N 1.0))

simplify1.7s

Counts

47 → 47

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	101	510
1	213	488
2	643	445
3	2849	443
done	5001	438

prune158.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 N) (/ 0.5 (* N N)))
0.2b	(/ 0.3333333333333333 (pow N 3))
0.5b	(/ 0.5 (* N N))
10.8b	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
41×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
31×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `cube-mult` `unpow3` `difference-of-squares` `sqr-pow`
3×	`cbrt-undiv` `frac-add`
2×	`sub-neg` `associate-+l+` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `associate-+l-` `flip3-+` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 124

Calls

4 calls:

27.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
9.0ms	(/ 0.3333333333333333 (pow N 3))
8.0ms	(/ 0.5 (* N N))
212.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
74.0ms	(/ 0.3333333333333333 (pow N 3))
35.0ms	(/ 0.5 (* N N))
37.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

simplify3.4s

Counts

136 → 136

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	210	1847
1	534	1627
2	3960	1528
done	5000	1528

prune423.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

10.8b	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))
17.4b	(cbrt (+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3))))
17.4b	(cbrt (+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3))))
17.4b	(cbrt (+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3))))

rewrite635.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
15×	`cbrt-prod` `cbrt-div`
12×	`frac-add`
9×	`add-log-exp`
8×	`distribute-lft-out`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `flip3-+` `frac-sub` `add-cbrt-cube` `flip--` `flip-+` `distribute-lft-out--`
3×	`pow1/3`
2×	`associate-+l+` `sum-log`
1×	`+-commutative` `associate-+l-` `sub-neg` `diff-log`

Counts

4 → 74

Calls

4 calls:

256.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))
139.0ms	(cbrt (+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3))))
112.0ms	(cbrt (+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3))))
124.0ms	(cbrt (+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3))))

series725.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))
186.0ms	(cbrt (+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3))))
265.0ms	(cbrt (+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3))))
223.0ms	(cbrt (+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3))))

simplify1.2s

Counts

86 → 86

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	151	2971
1	398	2859
2	1753	2661
done	5000	2616

prune457.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 1 expressions with local error:

3.5b	(log (/ (+ N 1.0) N))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
15×	`*-un-lft-identity`
12×	`times-frac`
9×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log`
3×	`distribute-lft-out`
2×	`pow1` `rem-log-exp`
1×	`log-div` `div-exp` `log-pow` `add-cbrt-cube` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

6.0ms

(log (/ (+ N 1.0) N))

series122.0ms

Counts

1 → 3

Calls

1 calls:

122.0ms

(log (/ (+ N 1.0) N))

simplify1.1s

Counts

30 → 30

Iterations

Useful iterations: 3 (423.0ms)

Iter	Nodes	Cost
0	84	381
1	169	363
2	452	334
3	1875	321
done	5001	321

prune60.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes52.0ms

Accuracy

100% (0.0b remaining)

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

bsearch29.0ms

Steps

Iters	Range		Point
6	3569.546420151095	44039.89650146889	7998.135430633448

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.9s

Algorithm

intervals

Results

767.0ms	1782×	body	1280	valid
757.0ms	1228×	body	640	valid
391.0ms	8028×	body	80	nan
314.0ms	4057×	body	80	valid
198.0ms	606×	body	320	valid
32.0ms	327×	body	160	valid