Details

sample50.0ms

Algorithm

intervals

Results

20.0ms	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

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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

series139.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(- (log (+ N 1.0)) (log N))
41.0ms	(log (+ N 1.0))

simplify126.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	345

prune131.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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:

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

series132.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
82.0ms	(log (/ (+ N 1.0) N))

simplify103.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	243	383
1	808	358
2	3663	347
3	5001	344

prune123.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

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)))

rewrite29.0ms

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×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 126

Calls

4 calls:

5.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(sqrt (/ (+ N 1.0) N))
9.0ms	(log (sqrt (/ (+ N 1.0) N)))
6.0ms	(log (sqrt (/ (+ N 1.0) N)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt (/ (+ N 1.0) N))
42.0ms	(sqrt (/ (+ N 1.0) N))
126.0ms	(log (sqrt (/ (+ N 1.0) N)))
120.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify65.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	205	1000
1	482	936
2	1903	904
3	5001	886

prune336.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

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)))))

rewrite38.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 125

Calls

4 calls:

4.0ms	(cbrt (/ (+ N 1.0) N))
6.0ms	(log (sqrt (cbrt (/ (+ N 1.0) N))))
6.0ms	(log (sqrt (/ (+ N 1.0) N)))
13.0ms	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (/ (+ N 1.0) N))
216.0ms	(log (sqrt (cbrt (/ (+ N 1.0) N))))
125.0ms	(log (sqrt (/ (+ N 1.0) N)))
208.0ms	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	508	1251
1	1290	1156
2	5001	1137

prune514.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

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

bsearch28.0ms

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	23	15
1	23	15

end0.0ms

sample1.3s

Algorithm

intervals

Results

438.0ms	1742×	body	1280	valid
205.0ms	7850×	body	80	nan
200.0ms	1264×	body	640	valid
181.0ms	4111×	body	80	valid
61.0ms	584×	body	320	valid
19.0ms	299×	body	160	valid