Details

sample70.0ms

Algorithm

intervals

Results

27.0ms	56×	body	1280	valid
11.0ms	246×	body	80	nan
9.0ms	39×	body	640	valid
8.0ms	128×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	13×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	11
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize14.0ms

Local error

Found 2 expressions with local error:

2.6b	(log (+ N 1))
3.8b	(- (log (+ N 1)) (log N))

rewrite25.0ms

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))
17.0ms	(- (log (+ N 1)) (log N))

series151.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(log (+ N 1))
115.0ms	(- (log (+ N 1)) (log N))

simplify1.4s

Counts

49 → 49

Iterations

Iter	Nodes
4	2935
3	1186
2	414
1	195
0	97

prune493.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
3.9b	(log (/ (+ 1 N) N))

rewrite17.0ms

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:

13.0ms	(/ (+ 1 N) N)
3.0ms	(log (/ (+ 1 N) N))

series144.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(/ (+ 1 N) N)
80.0ms	(log (/ (+ 1 N) N))

simplify2.1s

Counts

68 → 68

Iterations

Iter	Nodes
4	5195
3	1441
2	492
1	223
0	102

prune447.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ 1 (sqrt N)))
0.3b	(/ 1 (sqrt N))
0.4b	(/ (+ 1 N) (sqrt N))
4.0b	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

107×	`*-un-lft-identity`
102×	`times-frac`
77×	`add-sqr-sqrt` `add-cube-cbrt`
72×	`log-prod`
57×	`sqrt-prod`
28×	`associate-+r+`
22×	`associate-+l+`
17×	`distribute-lft-out`
15×	`add-exp-log`
13×	`pow1`
12×	`associate-/r*`
9×	`log-pow`
8×	`add-cbrt-cube`
7×	`associate-/l*`
6×	`pow-flip`
5×	`div-exp` `div-inv`
4×	`rem-log-exp` `insert-posit16` `add-log-exp`
3×	`log-div`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `1-exp` `flip-+` `inv-pow` `associate-/l/`
1×	`+-commutative` `associate-+r-` `sum-log` `log-rec` `associate-+l-`

Counts

4 → 204

Calls

4 calls:

4.0ms	(log (/ 1 (sqrt N)))
9.0ms	(/ 1 (sqrt N))
22.0ms	(/ (+ 1 N) (sqrt N))
16.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(log (/ 1 (sqrt N)))
37.0ms	(/ 1 (sqrt N))
64.0ms	(/ (+ 1 N) (sqrt N))
249.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))

simplify2.8s

Counts

216 → 216

Iterations

Iter	Nodes
3	4427
2	1466
1	601
0	272

prune2.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/3 N) (* N N))
0.4b	(/ 1/3 N)
0.5b	(/ 1/2 (* N N))
11.2b	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

rewrite114.0ms

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*`
4×	`pow1` `insert-posit16`
3×	`clear-num` `frac-2neg` `frac-add` `prod-exp` `cbrt-unprod` `distribute-lft-out`
2×	`associate-+r+` `sum-log` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `flip3--` `diff-log` `frac-sub` `flip-+` `flip--` `associate-/l/`

Counts

4 → 119

Calls

4 calls:

19.0ms	(/ (/ 1/3 N) (* N N))
7.0ms	(/ 1/3 N)
12.0ms	(/ 1/2 (* N N))
72.0ms	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (/ 1/3 N) (* N N))
18.0ms	(/ 1/3 N)
41.0ms	(/ 1/2 (* N N))
45.0ms	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

simplify10.9s

Counts

131 → 131

Iterations

Iter	Nodes
3	9615
2	1919
1	541
0	200

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.8b

bsearch54.0ms

Steps

Iters	Range		Point
10	19.9847175368848	4649870806659.843	8114.657537075721

simplify5.0ms

Iterations

Iter	Nodes
2	21
1	21
0	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

930.0ms	1694×	body	1280	valid
630.0ms	8213×	body	80	nan
492.0ms	1215×	body	640	valid
396.0ms	4159×	body	80	valid
146.0ms	614×	body	320	valid
45.0ms	318×	body	160	valid