Details

sample69.0ms

Algorithm

intervals

Results

23.0ms	60×	body	1280	valid
10.0ms	43×	body	640	valid
9.0ms	238×	body	80	nan
8.0ms	123×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize11.0ms

Local error

Found 2 expressions with local error:

2.8b	(- (log (+ N 1.0)) (log N))
3.2b	(log (+ N 1.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `pow1` `prod-diff`
14×	`log-pow` `add-cube-cbrt`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

28.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

series196.0ms

Counts

2 → 6

Calls

2 calls:

145.0ms	(- (log (+ N 1.0)) (log N))
51.0ms	(log (+ N 1.0))

simplify2.5s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	2048
2	709
1	286
0	127

prune275.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 0.3333333333333333 N) (/ (/ 1 N) N))
0.1b	(/ (/ 1 N) N)
0.1b	(/ (/ 1 N) N)
10.8b	(- (* (/ 0.3333333333333333 N) (/ (/ 1 N) N)) (* 0.5 (/ (/ 1 N) N)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
161×	`add-sqr-sqrt`
132×	`*-un-lft-identity`
130×	`add-cube-cbrt`
57×	`add-exp-log`
43×	`associate-r`
35×	`add-cbrt-cube`
29×	`div-exp`
26×	`associate-/l*`
17×	`div-inv`
15×	`cbrt-undiv`
13×	`associate-l`
12×	`pow1`
10×	`prod-exp` `unswap-sqr`
8×	`associate-*r/`
6×	`associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `pow-div`
3×	`associate-*l/` `frac-sub`
2×	`frac-times` `clear-num` `frac-2neg` `pow-flip` `inv-pow` `sub-div` `associate-/l/`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 270

Calls

4 calls:

68.0ms	(* (/ 0.3333333333333333 N) (/ (/ 1 N) N))
18.0ms	(/ (/ 1 N) N)
25.0ms	(/ (/ 1 N) N)
19.0ms	(- (* (/ 0.3333333333333333 N) (/ (/ 1 N) N)) (* 0.5 (/ (/ 1 N) N)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (/ 0.3333333333333333 N) (/ (/ 1 N) N))
33.0ms	(/ (/ 1 N) N)
28.0ms	(/ (/ 1 N) N)
121.0ms	(- (* (/ 0.3333333333333333 N) (/ (/ 1 N) N)) (* 0.5 (/ (/ 1 N) N)))

simplify1.9s

Counts

282 → 282

Iterations

Iter	Nodes
done	5041
2	3117
1	894
0	300

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 N) N)
0.1b	(/ (/ 1 N) N)
0.8b	(log (exp (- (* (/ 0.3333333333333333 N) (/ (/ 1 N) N)) (* 0.5 (/ (/ 1 N) N)))))
10.8b	(- (* (/ 0.3333333333333333 N) (/ (/ 1 N) N)) (* 0.5 (/ (/ 1 N) N)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
90×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
26×	`associate-/l*`
22×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`div-exp`
11×	`pow1`
10×	`div-inv`
7×	`associate-*r/`
6×	`cbrt-undiv` `log-prod` `associate-/r*` `add-log-exp`
5×	`log-pow`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `pow-div`
3×	`exp-sum` `frac-sub`
2×	`rec-exp` `clear-num` `sub-neg` `frac-2neg` `distribute-rgt-out--` `1-exp` `prod-diff` `associate-*l/` `pow-flip` `inv-pow` `sub-div` `associate-/l/`
1×	`frac-times` `log-div` `flip3--` `exp-diff` `fma-neg` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 196

Calls

4 calls:

11.0ms	(/ (/ 1 N) N)
10.0ms	(/ (/ 1 N) N)
64.0ms	(log (exp (- (* (/ 0.3333333333333333 N) (/ (/ 1 N) N)) (* 0.5 (/ (/ 1 N) N)))))
29.0ms	(- (* (/ 0.3333333333333333 N) (/ (/ 1 N) N)) (* 0.5 (/ (/ 1 N) N)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (/ 1 N) N)
31.0ms	(/ (/ 1 N) N)
144.0ms	(log (exp (- (* (/ 0.3333333333333333 N) (/ (/ 1 N) N)) (* 0.5 (/ (/ 1 N) N)))))
142.0ms	(- (* (/ 0.3333333333333333 N) (/ (/ 1 N) N)) (* 0.5 (/ (/ 1 N) N)))

simplify1.7s

Counts

208 → 208

Iterations

Iter	Nodes
done	5000
2	1759
1	554
0	227

prune919.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

2.7b	(log (/ (+ 1.0 N) 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×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `div-exp` `log-pow` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

5.0ms

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

series130.0ms

Counts

1 → 3

Calls

1 calls:

130.0ms

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

simplify2.8s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
4	3729
3	1118
2	376
1	173
0	86

prune112.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.2b

bsearch34.0ms

Steps

Iters	Range		Point
7	1875.4132169206714	53640.016154094046	10264.431052191152

simplify6.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample2.5s

Algorithm

intervals

Results

925.0ms	1807×	body	1280	valid
424.0ms	1282×	body	640	valid
374.0ms	8087×	body	80	nan
315.0ms	4016×	body	80	valid
102.0ms	603×	body	320	valid
31.0ms	292×	body	160	valid