Details

sample67.0ms

Algorithm

intervals

Results

25.0ms	66×	body	1280	valid
10.0ms	235×	body	80	nan
9.0ms	131×	body	80	valid
7.0ms	30×	body	640	valid
4.0ms	26×	body	320	valid
0.0ms	3×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	11
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize9.0ms

Local error

Found 1 expressions with local error:

0.8b	(- (log1p N) (log N))

rewrite19.0ms

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:

19.0ms

(- (log1p N) (log N))

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

(- (log1p N) (log N))

simplify1.2s

Counts

40 → 40

Iterations

Iter	Nodes
done	2047
4	2047
3	1137
2	403
1	185
0	83

prune136.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b	(sqrt (log1p N))
0.1b	(sqrt (log1p N))
29.9b	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`sqrt-prod`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

3 → 43

Calls

3 calls:

2.0ms	(sqrt (log1p N))
2.0ms	(sqrt (log1p N))
1.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

series347.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(sqrt (log1p N))
61.0ms	(sqrt (log1p N))
215.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

simplify1.4s

Counts

52 → 52

Iterations

Iter	Nodes
done	2003
3	2003
2	737
1	229
0	100

prune322.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N))
0.1b	(/ (/ 1 N) (* N N))
0.2b	(/ -1/2 (* N N))
14.8b	(+ (/ -1/2 (* N N)) (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

37×	`times-frac`
31×	`add-exp-log`
24×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`add-cbrt-cube`
18×	`pow1`
16×	`associate-/l*`
14×	`div-exp`
8×	`cbrt-undiv` `pow-div`
7×	`fma-def`
6×	`add-log-exp`
5×	`prod-exp` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `pow-flip` `inv-pow`
3×	`cbrt-unprod`
2×	`pow2` `rec-exp` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `fma-udef`
1×	`+-commutative` `associate-+r+` `sum-log` `flip3-+` `flip-+` `distribute-lft-out` `associate-/l/`

Counts

4 → 119

Calls

4 calls:

0.0ms	(fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N))
27.0ms	(/ (/ 1 N) (* N N))
13.0ms	(/ -1/2 (* N N))
36.0ms	(+ (/ -1/2 (* N N)) (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N))
75.0ms	(/ (/ 1 N) (* N N))
48.0ms	(/ -1/2 (* N N))
47.0ms	(+ (/ -1/2 (* N N)) (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))

simplify1.1s

Counts

131 → 131

Iterations

Iter	Nodes
done	2085
3	2085
2	1082
1	445
0	190

prune435.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.6b

bsearch58.0ms

Steps

Iters	Range		Point
9	0.1386194397507998	32640636.358721357	3829.6646277712093

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.6s	1763×	body	1280	valid
630.0ms	8092×	body	80	nan
554.0ms	1226×	body	640	valid
487.0ms	4120×	body	80	valid
166.0ms	606×	body	320	valid
48.0ms	285×	body	160	valid