Details

sample43.0ms

Algorithm

intervals

Results

14.0ms	57×	body	1280	valid
7.0ms	288×	body	80	nan
5.0ms	132×	body	80	valid
5.0ms	31×	body	640	valid
2.0ms	22×	body	320	valid
1.0ms	14×	body	160	valid

simplify8.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize6.0ms

Local error

Found 2 expressions with local error:

1.7b	(log (+ N 1.0))
3.3b	(- (log (+ N 1.0)) (log N))

rewrite10.0ms

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:

2.0ms	(log (+ N 1.0))
7.0ms	(- (log (+ N 1.0)) (log N))

series140.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(log (+ N 1.0))
98.0ms	(- (log (+ N 1.0)) (log N))

simplify52.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1875	250
3	5001	247

prune103.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.0b	(log (/ (+ N 1.0) N))

rewrite16.0ms

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:

10.0ms	(/ (+ N 1.0) N)
3.0ms	(log (/ (+ N 1.0) N))

series138.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (+ N 1.0) N)
89.0ms	(log (/ (+ N 1.0) N))

simplify98.0ms

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

prune113.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ N 1.0)) (sqrt N))
0.1b	(/ (sqrt (+ N 1.0)) (sqrt N))
3.1b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
3.1b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

194×	`sqrt-prod`
170×	`*-un-lft-identity`
168×	`times-frac`
118×	`add-sqr-sqrt` `add-cube-cbrt`
92×	`log-prod`
26×	`distribute-lft-out`
14×	`add-exp-log` `associate-/l*`
12×	`associate-/r*`
8×	`add-cbrt-cube`
6×	`pow1`
4×	`sqrt-div` `div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `log-div` `sqrt-undiv` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

4 → 254

Calls

4 calls:

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

series405.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
68.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
132.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
138.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))

simplify52.0ms

Algorithm

egg-herbie

Counts

266 → 266

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	375	2668
1	1134	2550
2	5001	2396

prune495.0ms

Filtered

266 candidates to 134 candidates (50.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

3.1b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
3.1b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
3.1b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
3.1b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

184×	`log-prod`
180×	`sqrt-prod`
168×	`times-frac`
160×	`*-un-lft-identity`
112×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`distribute-lft-out`
16×	`add-exp-log`
8×	`pow1` `rem-log-exp`
4×	`log-div` `div-exp` `log-pow` `add-cbrt-cube` `div-inv` `add-log-exp`

Counts

4 → 228

Calls

4 calls:

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

series550.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
140.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
133.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
139.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))

simplify90.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	281	2776
1	755	2676
2	3772	2480
3	5001	2472

prune521.0ms

Filtered

240 candidates to 116 candidates (48.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

regimes29.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.9b

bsearch19.0ms

Steps

Iters	Range		Point
5	4717.815806685034	11257.791762216355	5578.40769447651

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

end0.0ms

sample1.2s

Algorithm

intervals

Results

431.0ms	1800×	body	1280	valid
183.0ms	8031×	body	80	nan
182.0ms	1213×	body	640	valid
164.0ms	4078×	body	80	valid
60.0ms	613×	body	320	valid
18.0ms	296×	body	160	valid