Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	59×	body	1280	valid
9.0ms	46×	body	640	valid
8.0ms	230×	body	80	nan
6.0ms	124×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	13×	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: 31.3b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

1.3b	(log (+ N 1.0))
3.6b	(- (log (+ N 1.0)) (log N))

rewrite12.0ms

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:

3.0ms	(log (+ N 1.0))
7.0ms	(- (log (+ N 1.0)) (log N))

series138.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(log (+ N 1.0))
93.0ms	(- (log (+ N 1.0)) (log N))

simplify126.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	343

prune115.0ms

Filtered

71 candidates to 43 candidates (60.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	2	72

Merged error: 0.0b

Counts

72 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 0.3333333333333333 N) 0.5)
0.0b	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.7b	(/ 1 (pow N 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt` `times-frac`
39×	`prod-diff`
13×	`fma-neg`
12×	`add-exp-log` `unpow-prod-down`
8×	`associate-/r*`
6×	`div-exp`
5×	`add-cbrt-cube` `div-inv` `add-log-exp`
4×	`unpow2` `sqr-pow`
3×	`pow1` `expm1-log1p-u` `pow-to-exp` `rec-exp` `1-exp` `pow-exp` `log1p-expm1-u` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `pow-flip` `frac-2neg` `diff-log` `clear-num` `flip--` `fma-udef` `distribute-lft-out--` `inv-pow`

Counts

3 → 138

Calls

3 calls:

9.0ms	(- (/ 0.3333333333333333 N) 0.5)
1.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
5.0ms	(/ 1 (pow N 2))

series86.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(- (/ 0.3333333333333333 N) 0.5)
36.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
17.0ms	(/ 1 (pow N 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	425	1067
1	1442	713
2	5001	631

prune174.0ms

Filtered

147 candidates to 67 candidates (45.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	146	3	149

Merged error: 0.0b

Counts

149 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (log (+ N 1.0)))
1.3b	(log (+ N 1.0))
1.3b	(log (+ N 1.0))
31.6b	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`pow1` `add-sqr-sqrt` `log-prod`
7×	`add-cube-cbrt`
6×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-pow`
2×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 60

Calls

4 calls:

3.0ms	(sqrt (log (+ N 1.0)))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
1.0ms	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (log (+ N 1.0)))
46.0ms	(log (+ N 1.0))
41.0ms	(log (+ N 1.0))
205.0ms	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))

simplify113.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	332	511
1	1034	456
2	4431	417
3	5001	412

prune191.0ms

Filtered

72 candidates to 59 candidates (81.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	71	4	75

Merged error: 0.0b

Counts

75 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

1.3b	(log (+ N 1.0))
31.6b	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))
31.6b	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))
31.6b	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`log-div`
1×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out`

Counts

4 → 47

Calls

4 calls:

3.0ms	(log (+ N 1.0))
1.0ms	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))
1.0ms	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))
1.0ms	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(log (+ N 1.0))
213.0ms	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))
219.0ms	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))
210.0ms	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))

simplify59.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	181	564
1	534	466
2	1926	419
3	5002	411

prune215.0ms

Filtered

59 candidates to 54 candidates (91.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	59	4	63

Merged error: 0.0b

Counts

63 → 4

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.8b

bsearch28.0ms

Steps

Iters	Range		Point
7	2764.08540472272	53889.47736569451	4112.204171122738

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	15
1	24	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

521.0ms	1763×	body	1280	valid
262.0ms	8056×	body	80	nan
248.0ms	1259×	body	640	valid
213.0ms	4106×	body	80	valid
74.0ms	575×	body	320	valid
24.0ms	297×	body	160	valid