Details

sample51.0ms

Algorithm

intervals

Results

14.0ms	49×	body	1280	valid
8.0ms	255×	body	80	nan
7.0ms	38×	body	640	valid
6.0ms	133×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	15×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.3b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.1b	(- (log (+ N 1.0)) (log N))
4.3b	(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:

6.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series10.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	232	285
1	628	264
2	2171	244
3	5001	244

prune134.0ms

Filtered

47 candidates to 34 candidates (27.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	42	5	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	5	48

Merged error: 0.0b

Counts

48 → 5

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.0b	(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×	`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))

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify94.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	221	370
1	736	343
2	3220	333
3	5002	333

prune167.0ms

Filtered

66 candidates to 45 candidates (31.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	66	5	71

Merged error: 0.0b

Counts

71 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
3.0b	(log (sqrt (/ (+ N 1.0) N)))
3.0b	(log (sqrt (/ (+ N 1.0) N)))

rewrite27.0ms

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:

4.0ms	(sqrt (/ (+ N 1.0) N))
4.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))
8.0ms	(log (sqrt (/ (+ N 1.0) N)))

series19.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify120.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	242	986
1	753	932
2	3218	884
3	5002	876

prune465.0ms

Filtered

130 candidates to 94 candidates (27.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	131	4	135

Merged error: 0.0b

Counts

135 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.2b	(/ (sqrt (+ N 1.0)) (sqrt N))
3.0b	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
3.0b	(log (sqrt (/ (+ N 1.0) N)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

129×	`sqrt-prod`
116×	`*-un-lft-identity`
109×	`times-frac`
81×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
65×	`log-prod`
19×	`distribute-lft-out`
10×	`add-exp-log`
8×	`pow1`
7×	`associate-/l*`
6×	`associate-/r*` `add-cbrt-cube`
4×	`sqrt-div` `log-pow` `div-inv` `add-log-exp`
3×	`rem-log-exp`
2×	`rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `div-exp` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `flip3-+` `clear-num` `flip-+`

Counts

4 → 186

Calls

4 calls:

4.0ms	(sqrt (/ (+ N 1.0) N))
7.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
7.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(/ (sqrt (+ N 1.0)) (sqrt N))
8.0ms	(log (/ (sqrt (+ N 1.0)) (sqrt N)))
8.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify60.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	541	1850
1	1840	1768
2	5001	1674

prune1.1s

Filtered

198 candidates to 114 candidates (42.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	197	5	202

Merged error: 0.0b

Counts

202 → 5

regimes47.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.0b

bsearch51.0ms

Steps

Iters	Range		Point
9	142.62154401734003	53342933.17227377	5884.994133621385

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	24
1	33	24

end0.0ms

sample1.5s

Algorithm

intervals

Results

502.0ms	1770×	body	1280	valid
245.0ms	8028×	body	80	nan
214.0ms	1183×	body	640	valid
200.0ms	4116×	body	80	valid
73.0ms	617×	body	320	valid
23.0ms	314×	body	160	valid

Details

sample51.0ms

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series10.0ms

simplify58.0ms

prune134.0ms

localize7.0ms

rewrite12.0ms

series9.0ms

simplify94.0ms

prune167.0ms

localize8.0ms

rewrite27.0ms

series19.0ms

simplify120.0ms

prune465.0ms

localize12.0ms

rewrite32.0ms

series26.0ms

simplify60.0ms

prune1.1s

regimes47.0ms

bsearch51.0ms

simplify1.0ms

end0.0ms

sample1.5s

Profiling