Details

sample47.0ms

Algorithm

intervals

Results

14.0ms	53×	body	1280	valid
6.0ms	217×	body	80	nan
6.0ms	139×	body	80	valid
6.0ms	33×	body	640	valid
2.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify17.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize14.0ms

Local error

Found 2 expressions with local error:

2.4b	(- (log (+ N 1.0)) (log N))
3.5b	(log (+ N 1.0))

rewrite34.0ms

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:

23.0ms	(- (log (+ N 1.0)) (log N))
9.0ms	(log (+ N 1.0))

series230.0ms

Counts

2 → 6

Calls

2 calls:

166.0ms	(- (log (+ N 1.0)) (log N))
63.0ms	(log (+ N 1.0))

simplify922.0ms

Counts: 47 → 47

prune199.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.5b	(log (/ (+ N 1.0) N))

rewrite33.0ms

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` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

18.0ms	(/ (+ N 1.0) N)
13.0ms	(log (/ (+ N 1.0) N))

series199.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (+ N 1.0) N)
126.0ms	(log (/ (+ N 1.0) N))

simplify1.2s

Counts: 66 → 66

prune181.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))
0.3b	(/ (cbrt (+ N 1.0)) (sqrt N))
3.3b	(+ (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (log (/ (cbrt (+ N 1.0)) (sqrt N))))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
96×	`times-frac`
69×	`add-sqr-sqrt` `add-cube-cbrt`
56×	`cbrt-prod` `log-prod`
54×	`sqrt-prod`
46×	`associate-+r+`
18×	`distribute-lft-out`
16×	`cbrt-div`
12×	`associate-/r*`
11×	`add-exp-log`
10×	`associate-+l+` `associate-/l/`
9×	`flip3-+` `flip-+`
8×	`pow1` `add-cbrt-cube` `associate-/l*`
4×	`frac-times` `log-pow` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`log-div` `frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`+-commutative` `associate-+l-` `associate-+r-` `pow1/3` `prod-exp` `sum-log` `cbrt-unprod`

Counts

4 → 191

Calls

4 calls:

8.0ms	(cbrt (+ N 1.0))
26.0ms	(/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))
18.0ms	(/ (cbrt (+ N 1.0)) (sqrt N))
120.0ms	(+ (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (log (/ (cbrt (+ N 1.0)) (sqrt N))))

series1.6s

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (+ N 1.0))
332.0ms	(/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))
273.0ms	(/ (cbrt (+ N 1.0)) (sqrt N))
826.0ms	(+ (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (log (/ (cbrt (+ N 1.0)) (sqrt N))))

simplify1.4s

Counts: 203 → 203

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ 1 (sqrt N)))
0.2b	(/ 1 (sqrt N))
0.4b	(/ (+ N 1.0) (sqrt N))
2.6b	(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

rewrite114.0ms

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` `add-log-exp`
3×	`log-div`
2×	`cbrt-undiv` `rec-exp` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `1-exp` `clear-num` `flip-+` `associate-/l/` `inv-pow`
1×	`+-commutative` `associate-+l-` `associate-+r-` `log-rec` `sum-log`

Counts

4 → 200

Calls

4 calls:

8.0ms	(log (/ 1 (sqrt N)))
12.0ms	(/ 1 (sqrt N))
41.0ms	(/ (+ N 1.0) (sqrt N))
33.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(log (/ 1 (sqrt N)))
40.0ms	(/ 1 (sqrt N))
80.0ms	(/ (+ N 1.0) (sqrt N))
242.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

simplify1.1s

Counts: 212 → 212

prune695.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.8b

bsearch35.0ms

Steps

Iters	Range		Point
7	108.32890937213158	24341.35050109186	12631.98063969317

simplify570.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

858.0ms	7899×	body	80	nan
835.0ms	1771×	body	1280	valid
421.0ms	1256×	body	640	valid
290.0ms	4022×	body	80	valid
115.0ms	648×	body	320	valid
33.0ms	303×	body	160	valid