Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

sample42.0ms

Algorithm

intervals

Results

18.0ms	60×	body	1280	valid
7.0ms	134×	body	80	valid
7.0ms	33×	body	640	valid
3.0ms	20×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

prune2.0ms

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: 28.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (log (+ N 1.0)) (log N))
2.7b	(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 → 40

Calls

2 calls:

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

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify53.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4952	422
1	4952	422

prune78.0ms

Filtered

35 candidates to 46 candidates (-31.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 0.0b

Counts

47 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.2b	(log (/ (+ N 1.0) N))

rewrite11.0ms

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))

series8.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify44.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5054	615

prune80.0ms

Filtered

46 candidates to 66 candidates (-43.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	3	68

Merged error: 0.0b

Counts

68 → 3

localize10.0ms

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)))

rewrite25.0ms

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:

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

series17.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (/ (+ N 1.0) N))
4.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify59.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5068	1440

prune226.0ms

Filtered

94 candidates to 130 candidates (-38.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Merged error: 0.0b

Counts

133 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
2.7b	(log (sqrt (+ N 1.0)))
22.4b	(+ (- (log (sqrt (+ N 1.0))) (* 2 (log (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

60×	`log-prod`
56×	`*-un-lft-identity`
46×	`associate-+r+`
42×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`sqrt-prod`
27×	`cbrt-prod`
10×	`distribute-lft-out`
8×	`associate-+l+`
7×	`pow1` `associate--l+`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`log-pow` `add-cbrt-cube`
3×	`log-div`
2×	`flip3-+` `pow1/3` `sqrt-div` `sum-log` `flip-+`
1×	`+-commutative` `associate-+l-` `associate-+r-` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `rem-log-exp` `div-inv`

Counts

4 → 112

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
4.0ms	(log (sqrt (+ N 1.0)))
19.0ms	(+ (- (log (sqrt (+ N 1.0))) (* 2 (log (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt N)
25.0ms	(cbrt N)
6.0ms	(log (sqrt (+ N 1.0)))
35.0ms	(+ (- (log (sqrt (+ N 1.0))) (* 2 (log (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

simplify71.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5001	1694

prune200.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	124	3	127

Merged error: 0.0b

Counts

127 → 3

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.0b

bsearch22.0ms

Steps

Iters	Range		Point
9	54.98615069259875	7030692.279523352	6245.064955424139

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	32
1	20	32

end0.0ms

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

sample1.2s

Algorithm

intervals

Results

540.0ms	1766×	body	1280	valid
262.0ms	1296×	body	640	valid
223.0ms	3999×	body	80	valid
87.0ms	642×	body	320	valid
27.0ms	297×	body	160	valid

Details

analyze2.0ms

sample42.0ms

simplify2.0ms

prune2.0ms

localize7.0ms

rewrite11.0ms

series9.0ms

simplify53.0ms

prune78.0ms

localize5.0ms

rewrite11.0ms

series8.0ms

simplify44.0ms

prune80.0ms

localize10.0ms

rewrite25.0ms

series17.0ms

simplify59.0ms

prune226.0ms

localize16.0ms

rewrite31.0ms

series87.0ms

simplify71.0ms

prune200.0ms

regimes36.0ms

bsearch22.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample1.2s

Profiling