Details

sample113.0ms

Algorithm

intervals

Results

35.0ms	52×	body	1280	valid
21.0ms	48×	body	640	valid
20.0ms	271×	body	80	nan
15.0ms	132×	body	80	valid
4.0ms	15×	body	320	valid
2.0ms	9×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	9
0	6

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize44.0ms

Local error

Found 1 expressions with local error:

2.6b	(- (log1p N) (log N))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-diff`
10×	`add-cube-cbrt`
5×	`pow1`
4×	`log-pow`
3×	`log-prod` `fma-neg` `associate--r+`
2×	`diff-log` `distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `log1p-udef` `sub-neg` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`

Counts

1 → 37

Calls

1 calls:

10.0ms

(- (log1p N) (log N))

series60.0ms

Counts

1 → 3

Calls

1 calls:

60.0ms

(- (log1p N) (log N))

simplify1.5s

Counts

40 → 40

Iterations

Iter	Nodes
4	2678
3	962
2	372
1	184
0	83

prune330.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
2.5b	(log (/ (+ 1 N) N))

rewrite20.0ms

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` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 66

Calls

2 calls:

14.0ms	(/ (+ 1 N) N)
4.0ms	(log (/ (+ 1 N) N))

series118.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (+ 1 N) N)
69.0ms	(log (/ (+ 1 N) N))

simplify4.2s

Counts

72 → 72

Iterations

Iter	Nodes
4	5667
3	1564
2	510
1	231
0	106

prune555.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (/ (+ 1 N) (sqrt N)) (sqrt N))
0.4b	(/ (+ 1 N) (sqrt N))
15.6b	(log (/ (/ (+ 1 N) (sqrt N)) (sqrt N)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

672×	`times-frac`
500×	`*-un-lft-identity`
342×	`sqrt-prod`
330×	`add-sqr-sqrt` `add-cube-cbrt`
172×	`log-prod`
85×	`distribute-lft-out`
32×	`associate-/l*`
16×	`add-exp-log` `div-inv`
12×	`associate-/r*`
10×	`add-cbrt-cube`
7×	`div-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `rem-log-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`log-div` `flip3-+` `log-pow` `flip-+`

Counts

3 → 458

Calls

3 calls:

38.0ms	(/ (/ (+ 1 N) (sqrt N)) (sqrt N))
26.0ms	(/ (+ 1 N) (sqrt N))
7.0ms	(log (/ (/ (+ 1 N) (sqrt N)) (sqrt N)))

series273.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (/ (+ 1 N) (sqrt N)) (sqrt N))
91.0ms	(/ (+ 1 N) (sqrt N))
105.0ms	(log (/ (/ (+ 1 N) (sqrt N)) (sqrt N)))

simplify1.1s

Counts

467 → 467

Iterations

Iter	Nodes
2	2255
1	1044
0	464

prune4.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (/ (+ 1 N) (sqrt N))) (sqrt N))
0.4b	(/ (+ 1 N) (sqrt N))
0.4b	(/ (+ 1 N) (sqrt N))
3.0b	(+ (log (/ (sqrt (/ (+ 1 N) (sqrt N))) 1)) (log (/ (sqrt (/ (+ 1 N) (sqrt N))) (sqrt N))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
859×	`sqrt-prod`
678×	`*-un-lft-identity`
454×	`add-sqr-sqrt` `add-cube-cbrt`
287×	`log-prod`
190×	`associate-+r+`
114×	`distribute-lft-out`
97×	`associate-+l+`
39×	`associate-/l*`
21×	`div-inv`
18×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
5×	`log-pow` `associate-/l/`
4×	`expm1-log1p-u` `fma-def` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+`
2×	`log-div`
1×	`+-commutative` `sqrt-undiv` `associate-+r-` `sum-log` `sqrt-div` `associate-+l-`

Counts

4 → 653

Calls

4 calls:

17.0ms	(/ (sqrt (/ (+ 1 N) (sqrt N))) (sqrt N))
23.0ms	(/ (+ 1 N) (sqrt N))
27.0ms	(/ (+ 1 N) (sqrt N))
27.0ms	(+ (log (/ (sqrt (/ (+ 1 N) (sqrt N))) 1)) (log (/ (sqrt (/ (+ 1 N) (sqrt N))) (sqrt N))))

series490.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (sqrt (/ (+ 1 N) (sqrt N))) (sqrt N))
66.0ms	(/ (+ 1 N) (sqrt N))
63.0ms	(/ (+ 1 N) (sqrt N))
240.0ms	(+ (log (/ (sqrt (/ (+ 1 N) (sqrt N))) 1)) (log (/ (sqrt (/ (+ 1 N) (sqrt N))) (sqrt N))))

simplify1.7s

Counts

665 → 665

Iterations

Iter	Nodes
2	2794
1	1436
0	756

prune9.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch61.0ms

Steps

Iters	Range		Point
8	41.60074012902226	43862.50504651285	7250.408229147694

simplify5.0ms

Iterations

Iter	Nodes
2	20
1	20
0	18

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.6s	1752×	body	1280	valid
693.0ms	8041×	body	80	nan
499.0ms	1281×	body	640	valid
402.0ms	4105×	body	80	valid
159.0ms	591×	body	320	valid
49.0ms	271×	body	160	valid