Details

sample61.0ms

Algorithm

intervals

Results

17.0ms	51×	body	1280	valid
10.0ms	263×	body	80	nan
9.0ms	144×	body	80	valid
8.0ms	36×	body	640	valid
3.0ms	17×	body	320	valid
1.0ms	8×	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

Filtered

1 candidates to 0 candidates (0.0%)

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: 26.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (log (+ N 1.0)) (log N))
2.9b	(log (+ N 1.0))

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:

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

series137.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (log (+ N 1.0)) (log N))
44.0ms	(log (+ N 1.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (49.0ms)

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

prune93.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Merged error: 0.0b

Counts

48 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.0b	(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))

series130.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (+ N 1.0) N)
85.0ms	(log (/ (+ N 1.0) N))

simplify102.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (21.0ms)

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

prune93.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Merged error: 0.0b

Counts

69 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
2.0b	(log (sqrt (/ (+ N 1.0) N)))
2.0b	(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:

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

series344.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (/ (+ N 1.0) N))
50.0ms	(sqrt (/ (+ N 1.0) N))
122.0ms	(log (sqrt (/ (+ N 1.0) N)))
126.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify73.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (54.0ms)

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

prune259.0ms

Filtered

130 candidates to 94 candidates (72.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	130	3	133

Merged error: 0.0b

Counts

133 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
2.0b	(log (sqrt (/ (+ N 1.0) N)))
2.1b	(log (sqrt (sqrt (/ (+ N 1.0) N))))
2.1b	(log (sqrt (sqrt (/ (+ N 1.0) N))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

102×	`sqrt-prod`
65×	`*-un-lft-identity`
63×	`log-prod`
49×	`times-frac`
44×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
13×	`pow1` `log-pow`
12×	`distribute-lft-out`
10×	`sqrt-pow1`
7×	`add-exp-log`
6×	`pow1/2` `sqrt-div`
4×	`add-cbrt-cube` `div-inv` `add-log-exp`
3×	`log-div` `rem-log-exp`
2×	`rem-sqrt-square`

Counts

4 → 131

Calls

4 calls:

5.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))
7.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
10.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (/ (+ N 1.0) N))
132.0ms	(log (sqrt (/ (+ N 1.0) N)))
184.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
180.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))

simplify85.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	303	1258
1	652	1196
2	2297	1140
3	5001	1136

prune354.0ms

Filtered

143 candidates to 101 candidates (70.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	143	3	146

Merged error: 0.0b

Counts

146 → 3

regimes18.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.3b

bsearch36.0ms

Steps

Iters	Range		Point
8	8.601567399579238	18724.121991280714	6409.532366542444

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	23
1	30	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

506.0ms	1772×	body	1280	valid
270.0ms	8059×	body	80	nan
223.0ms	1206×	body	640	valid
214.0ms	4099×	body	80	valid
73.0ms	591×	body	320	valid
26.0ms	332×	body	160	valid