Details

sample44.0ms

Algorithm

intervals

Results

15.0ms	65×	body	1280	valid
6.0ms	40×	body	640	valid
6.0ms	252×	body	80	nan
6.0ms	132×	body	80	valid
1.0ms	13×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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:

7.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series136.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (log (+ N 1.0)) (log N))
45.0ms	(log (+ N 1.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1874	250
3	5001	247

prune99.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
1.2b	(log (/ (+ N 1.0) N))

rewrite11.0ms

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:

5.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

series132.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (+ N 1.0) N)
84.0ms	(log (/ (+ N 1.0) N))

simplify100.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	233	373
1	773	351
2	3489	339
3	5002	339

prune110.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
1.2b	(log (sqrt (/ (+ N 1.0) N)))
1.2b	(log (sqrt (/ (+ N 1.0) N)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `log-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 118

Calls

4 calls:

5.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (/ (+ N 1.0) N))
50.0ms	(sqrt (/ (+ N 1.0) N))
122.0ms	(log (sqrt (/ (+ N 1.0) N)))
128.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify61.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	196	964
1	456	908
2	1761	868
3	5002	860

prune315.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ (+ N 1.0) N))
1.0b	(log (sqrt (cbrt (/ (+ N 1.0) N))))
1.2b	(log (sqrt (/ (+ N 1.0) N)))
1.2b	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
45×	`log-prod`
36×	`times-frac` `sqrt-prod`
32×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
18×	`log-pow`
17×	`pow1`
12×	`sqrt-pow1`
9×	`distribute-lft-out`
8×	`pow1/3`
7×	`add-exp-log`
6×	`cbrt-div`
5×	`log-div` `sqrt-div`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1/2` `rem-log-exp` `div-inv`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/`

Counts

4 → 117

Calls

4 calls:

4.0ms	(cbrt (/ (+ N 1.0) N))
6.0ms	(log (sqrt (cbrt (/ (+ N 1.0) N))))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))
12.0ms	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))

series689.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (/ (+ N 1.0) N))
218.0ms	(log (sqrt (cbrt (/ (+ N 1.0) N))))
128.0ms	(log (sqrt (/ (+ N 1.0) N)))
210.0ms	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))

simplify150.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	487	1204
1	1200	1116
2	4896	1081
3	5002	1081

prune466.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch29.0ms

Steps

Iters	Range		Point
8	1078.5849367128544	2068602.189562926	8090.075772612433

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	16
1	26	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

420.0ms	1742×	body	1280	valid
194.0ms	1264×	body	640	valid
184.0ms	7850×	body	80	nan
165.0ms	4111×	body	80	valid
56.0ms	584×	body	320	valid
18.0ms	299×	body	160	valid