Details

sample91.0ms

Algorithm

intervals

Results

32.0ms	65×	body	1280	valid
16.0ms	213×	body	80	nan
12.0ms	134×	body	80	valid
11.0ms	30×	body	640	valid
6.0ms	24×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	11
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize9.0ms

Local error

Found 1 expressions with local error:

1.6b	(- (log1p N) (log N))

rewrite6.0ms

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:

6.0ms

(- (log1p N) (log N))

series76.0ms

Counts

1 → 3

Calls

1 calls:

76.0ms

(- (log1p N) (log N))

simplify707.0ms

Counts

40 → 40

Iterations

Iter	Nodes
done	2016
3	1137
2	403
1	185
0	83

prune108.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (log1p N))
0.0b	(sqrt (log1p N))
29.3b	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

rewrite3.0ms

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:

1.0ms	(sqrt (log1p N))
1.0ms	(sqrt (log1p N))
0.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

series299.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(sqrt (log1p N))
67.0ms	(sqrt (log1p N))
186.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

simplify635.0ms

Counts

52 → 52

Iterations

Iter	Nodes
done	2001
2	737
1	229
0	100

prune238.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1/3 N) 1/2)
0.1b	(fma (/ (/ 1 N) N) (- (/ 1/3 N) 1/2) (/ 1 N))
0.1b	(/ (/ 1 N) N)
0.4b	(/ 1/3 N)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

121×	`times-frac`
100×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
95×	`add-cube-cbrt`
39×	`prod-diff`
16×	`associate-/l*`
15×	`add-exp-log`
13×	`fma-neg`
11×	`add-cbrt-cube`
10×	`div-inv`
7×	`pow1` `div-exp`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg` `difference-of-squares` `pow-div`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `fma-udef` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow` `associate-/l/`

Counts

4 → 188

Calls

4 calls:

12.0ms	(- (/ 1/3 N) 1/2)
0.0ms	(fma (/ (/ 1 N) N) (- (/ 1/3 N) 1/2) (/ 1 N))
15.0ms	(/ (/ 1 N) N)
7.0ms	(/ 1/3 N)

series136.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (/ 1/3 N) 1/2)
34.0ms	(fma (/ (/ 1 N) N) (- (/ 1/3 N) 1/2) (/ 1 N))
40.0ms	(/ (/ 1 N) N)
18.0ms	(/ 1/3 N)

simplify832.0ms

Counts

200 → 200

Iterations

Iter	Nodes
done	2006
2	1400
1	613
0	285

prune649.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1/3 N) 1/2)
0.1b	(/ (/ 1 N) N)
0.4b	(/ 1/3 N)
1.1b	(log (exp (/ (/ 1 N) N)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

187×	`times-frac`
136×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
131×	`add-cube-cbrt`
44×	`log-pow`
43×	`exp-prod`
39×	`prod-diff`
16×	`associate-/l*`
15×	`add-exp-log`
14×	`div-inv`
13×	`fma-neg`
11×	`add-cbrt-cube`
8×	`pow1`
7×	`div-exp`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
3×	`log-prod`
2×	`clear-num` `frac-2neg` `difference-of-squares` `pow-div`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `rem-log-exp` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow` `associate-/l/`

Counts

4 → 235

Calls

4 calls:

32.0ms	(- (/ 1/3 N) 1/2)
15.0ms	(/ (/ 1 N) N)
8.0ms	(/ 1/3 N)
16.0ms	(log (exp (/ (/ 1 N) N)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (/ 1/3 N) 1/2)
19.0ms	(/ (/ 1 N) N)
19.0ms	(/ 1/3 N)
21.0ms	(log (exp (/ (/ 1 N) N)))

simplify779.0ms

Counts

247 → 247

Iterations

Iter	Nodes
done	2002
2	1339
1	645
0	362

prune1.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.7b

bsearch51.0ms

Steps

Iters	Range		Point
8	0.5242927222148749	9969.609054971397	5567.039381079165

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	17

end1.0ms

sample2.9s

Algorithm

intervals

Results

948.0ms	1780×	body	1280	valid
639.0ms	7964×	body	80	nan
423.0ms	1187×	body	640	valid
413.0ms	4113×	body	80	valid
170.0ms	628×	body	320	valid
42.0ms	292×	body	160	valid