Details

sample43.0ms

Algorithm

intervals

Results

12.0ms	41×	body	1280	valid
7.0ms	45×	body	640	valid
6.0ms	149×	body	80	valid
6.0ms	248×	body	80	nan
2.0ms	19×	body	320	valid
0.0ms	2×	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: 25.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (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:

8.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series140.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(- (log (+ N 1.0)) (log N))
43.0ms	(log (+ N 1.0))

simplify122.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (116.0ms)

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

prune121.0ms

Filtered

71 candidates to 43 candidates (60.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
1.4b	(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)
4.0ms	(log (/ (+ N 1.0) N))

series133.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (+ N 1.0) N)
85.0ms	(log (/ (+ N 1.0) N))

simplify106.0ms

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

prune100.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Merged error: 0.0b

Counts

74 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (log (+ N 1.0)))
0.5b	(expm1 (log1p (log (+ N 1.0))))
2.0b	(log (+ N 1.0))
22.7b	(- (expm1 (log1p (log (+ N 1.0)))) (log N))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`prod-diff`
9×	`pow1`
7×	`log-prod`
5×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-log-exp`
4×	`add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `associate--r+`
2×	`log-div` `distribute-lft-out--` `expm1-udef`
1×	`associate--l-` `sub-neg` `log1p-udef` `expm1-log1p` `flip3--` `flip3-+` `diff-log` `log1p-expm1` `rem-log-exp` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

4 → 75

Calls

4 calls:

1.0ms	(log1p (log (+ N 1.0)))
1.0ms	(expm1 (log1p (log (+ N 1.0))))
3.0ms	(log (+ N 1.0))
5.0ms	(- (expm1 (log1p (log (+ N 1.0)))) (log N))

series512.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(log1p (log (+ N 1.0)))
134.0ms	(expm1 (log1p (log (+ N 1.0))))
43.0ms	(log (+ N 1.0))
225.0ms	(- (expm1 (log1p (log (+ N 1.0)))) (log N))

simplify60.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	556	870
1	2211	669
2	5002	649

prune189.0ms

Filtered

87 candidates to 65 candidates (74.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	87	5	92

Merged error: 0.0b

Counts

92 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (+ N 1.0) N))
0.5b	(cbrt (/ (+ N 1.0) N))
1.1b	(log (cbrt (/ (+ N 1.0) N)))
1.1b	(log (cbrt (/ (+ N 1.0) N)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
62×	`*-un-lft-identity`
48×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `pow1/3` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 118

Calls

4 calls:

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

series708.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (/ (+ N 1.0) N))
136.0ms	(cbrt (/ (+ N 1.0) N))
214.0ms	(log (cbrt (/ (+ N 1.0) N)))
222.0ms	(log (cbrt (/ (+ N 1.0) N)))

simplify108.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	278	1088
1	803	1024
2	3528	998
3	5002	962

prune319.0ms

Filtered

130 candidates to 102 candidates (78.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	130	5	135

Merged error: 0.0b

Counts

135 → 5

regimes30.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.7b

bsearch32.0ms

Steps

Iters	Range		Point
9	164.2181510969774	3048118974.682059	3269.4262498147573

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample1.3s

Algorithm

intervals

Results

425.0ms	1714×	body	1280	valid
194.0ms	1248×	body	640	valid
185.0ms	7900×	body	80	nan
173.0ms	4108×	body	80	valid
63.0ms	630×	body	320	valid
21.0ms	300×	body	160	valid