Details

sample42.0ms

Algorithm

intervals

Results

13.0ms	54×	body	1280	valid
6.0ms	269×	body	80	nan
6.0ms	39×	body	640	valid
6.0ms	143×	body	80	valid
1.0ms	11×	body	320	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (log (+ N 1.0)) (log N))
3.1b	(log (+ N 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
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:

7.0ms	(- (log (+ N 1.0)) (log N))
2.0ms	(log (+ N 1.0))

series148.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(- (log (+ N 1.0)) (log N))
50.0ms	(log (+ N 1.0))

simplify3.0s

Counts

71 → 71

Iterations

Useful iterations: 3 (441.0ms)

Iter	Nodes	Cost
0	127	1052
1	279	855
2	868	705
3	3734	614
done	5001	614

prune199.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.0b	(log (/ (+ N 1.0) N))

rewrite21.0ms

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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

12.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series173.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
122.0ms	(log (/ (+ N 1.0) N))

simplify1.8s

Counts

70 → 70

Iterations

Useful iterations: 3 (317.0ms)

Iter	Nodes	Cost
0	112	749
1	240	708
2	747	660
3	3443	647
done	5000	647

prune147.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (+ N 1.0) (sqrt N))
1.9b	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
48×	`times-frac`
39×	`add-sqr-sqrt` `add-cube-cbrt`
34×	`log-prod`
30×	`sqrt-prod`
28×	`associate-+r+`
19×	`distribute-lft-out`
16×	`fma-def`
11×	`pow1` `log-pow`
10×	`distribute-rgt-neg-in`
6×	`distribute-lft-neg-in` `associate-+l+` `distribute-neg-in` `associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
3×	`add-log-exp`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip-+` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `associate-+r-` `neg-mul-1` `log-div` `frac-2neg` `div-exp` `neg-log` `clear-num`

Counts

2 → 122

Calls

2 calls:

9.0ms	(/ (+ N 1.0) (sqrt N))
24.0ms	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

series260.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (+ N 1.0) (sqrt N))
207.0ms	(+ (- (log (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

simplify566.0ms

Counts

128 → 128

Iterations

Useful iterations: done (560.0ms)

Iter	Nodes	Cost
0	185	1533
1	433	1433
2	1426	1289
done	5000	1176

prune320.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (log (/ (+ N 1.0) N)))
2.0b	(log (/ (+ N 1.0) N))
2.0b	(log (/ (+ N 1.0) N))
2.0b	(log (/ (+ N 1.0) N))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
47×	`*-un-lft-identity`
36×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`add-exp-log`
9×	`distribute-lft-out`
8×	`pow1`
6×	`rem-log-exp`
4×	`cbrt-prod` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `div-exp` `div-inv`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

1.0ms	(cbrt (log (/ (+ N 1.0) N)))
3.0ms	(log (/ (+ N 1.0) N))
4.0ms	(log (/ (+ N 1.0) N))
4.0ms	(log (/ (+ N 1.0) N))

series485.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(cbrt (log (/ (+ N 1.0) N)))
85.0ms	(log (/ (+ N 1.0) N))
87.0ms	(log (/ (+ N 1.0) N))
90.0ms	(log (/ (+ N 1.0) N))

simplify497.0ms

Counts

113 → 113

Iterations

Useful iterations: done (492.0ms)

Iter	Nodes	Cost
0	153	1528
1	344	1445
2	1049	1347
done	5000	1263

prune326.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.5b

bsearch28.0ms

Steps

Iters	Range		Point
6	2942.2625356967415	22276.40736340321	4688.133507746426

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	31
1	25	31
done	25	31

end0.0ms

sample1.4s

Algorithm

intervals

Results

458.0ms	1743×	body	1280	valid
223.0ms	8101×	body	80	nan
205.0ms	1250×	body	640	valid
188.0ms	4055×	body	80	valid
65.0ms	608×	body	320	valid
23.0ms	344×	body	160	valid