Details

sample48.0ms

Algorithm

intervals

Results

16.0ms	66×	body	1280	valid
7.0ms	46×	body	640	valid
6.0ms	278×	body	80	nan
5.0ms	114×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize7.0ms

Local error

Found 2 expressions with local error:

2.4b	(- (log (+ N 1.0)) (log N))
2.5b	(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))

series143.0ms

Counts

2 → 6

Calls

2 calls:

100.0ms	(- (log (+ N 1.0)) (log N))
44.0ms	(log (+ N 1.0))

simplify52.0ms

Counts

47 → 47

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1874	250
3	5001	247
done	5001	247

prune103.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.5b	(/ 1 (pow N 2))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
57×	`times-frac`
42×	`*-un-lft-identity`
36×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
12×	`div-exp`
10×	`prod-exp` `add-cbrt-cube`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*`
6×	`pow-to-exp` `rec-exp` `1-exp` `associate-r` `pow-exp`
5×	`pow1` `frac-add` `add-log-exp`
4×	`distribute-rgt-in` `frac-times` `sub-neg` `associate-+l+` `flip3--` `distribute-lft-in` `associate-*r/` `flip--`
3×	`associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `div-inv` `difference-of-squares`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--` `inv-pow`

Counts

3 → 150

Calls

3 calls:

30.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
64.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
8.0ms	(/ 1 (pow N 2))

series124.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
76.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
17.0ms	(/ 1 (pow N 2))

simplify72.0ms

Counts

159 → 159

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	583	1087
1	2726	904
2	5001	841
done	5001	841

prune254.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

2.5b	(log (/ (+ N 1.0) N))

rewrite6.0ms

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:

5.0ms

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

series81.0ms

Counts

1 → 3

Calls

1 calls:

81.0ms

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

simplify59.0ms

Counts

30 → 30

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	167	209
1	455	196
2	1964	184
3	5002	184
done	5002	184

prune57.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
3.1b	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

57×	`log-prod`
55×	`*-un-lft-identity`
49×	`times-frac`
46×	`associate-+r+`
37×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`cbrt-prod`
28×	`sqrt-prod`
11×	`associate-+l+` `distribute-lft-out`
8×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`log-div` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+r-` `flip3-+` `sum-log` `flip-+`

Counts

4 → 107

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)
52.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

series791.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt N)
182.0ms	(cbrt N)
178.0ms	(cbrt N)
240.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

simplify45.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	507	1315
1	1618	1245
2	5001	1128
done	5001	1128

prune331.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.3b

bsearch20.0ms

Steps

Iters	Range		Point
6	5364.146891578128	78679.13042368767	9757.882283737008

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10
done	24	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

422.0ms	1721×	body	1280	valid
204.0ms	1332×	body	640	valid
183.0ms	8018×	body	80	nan
169.0ms	4039×	body	80	valid
59.0ms	606×	body	320	valid
18.0ms	302×	body	160	valid