Details

sample53.0ms

Algorithm

intervals

Results

17.0ms	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))

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:

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

series138.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(log (+ N 1.0))
91.0ms	(- (log (+ N 1.0)) (log N))

simplify56.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1875	250
3	5001	247

prune89.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	2	48

Merged error: 0.0b

Counts

48 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 0.3333333333333333 N) 0.5)
0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.7b	(/ 1 (pow N 2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
58×	`times-frac`
45×	`*-un-lft-identity`
37×	`add-cube-cbrt`
33×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
12×	`div-exp`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*` `add-log-exp`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `associate-r` `pow-exp`
5×	`sub-neg` `flip3--` `frac-add` `flip--`
4×	`distribute-rgt-in` `frac-times` `associate-+l+` `distribute-lft-in` `associate-*r/` `difference-of-squares`
3×	`associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 165

Calls

4 calls:

7.0ms	(- (/ 0.3333333333333333 N) 0.5)
15.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
21.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series156.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 0.3333333333333333 N) 0.5)
35.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
73.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify80.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	597	1169
1	2754	978
2	5001	915

prune245.0ms

Filtered

177 candidates to 101 candidates (57.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	176	3	179

Merged error: 0.0b

Counts

179 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

3.6b	(log (/ (+ N 1.0) N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
15×	`*-un-lft-identity`
12×	`times-frac`
9×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log`
3×	`distribute-lft-out`
2×	`pow1` `rem-log-exp`
1×	`log-div` `div-exp` `log-pow` `add-cbrt-cube` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

4.0ms

(log (/ (+ N 1.0) N))

series82.0ms

Counts

1 → 3

Calls

1 calls:

82.0ms

(log (/ (+ N 1.0) N))

simplify58.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	167	209
1	455	196
2	1964	184
3	5002	184

prune48.0ms

Filtered

30 candidates to 20 candidates (66.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	28	5	33

Merged error: 0.0b

Counts

33 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sqrt (+ N 1.0)) N)
1.4b	(log (sqrt (+ N 1.0)))
3.8b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
42×	`times-frac`
39×	`log-prod`
37×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`sqrt-prod`
25×	`associate-+r+`
13×	`distribute-lft-out`
9×	`pow1`
7×	`associate-+l+` `log-pow` `associate-/l*`
6×	`add-exp-log` `sqrt-div`
5×	`log-div` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`associate-/r*` `add-log-exp`
2×	`associate-+l-` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log`

Counts

3 → 115

Calls

3 calls:

6.0ms	(/ (sqrt (+ N 1.0)) N)
4.0ms	(log (sqrt (+ N 1.0)))
13.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

series383.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ (sqrt (+ N 1.0)) N)
80.0ms	(log (sqrt (+ N 1.0)))
231.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

simplify45.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	458	1029
1	1402	938
2	5001	850

prune219.0ms

Filtered

124 candidates to 82 candidates (66.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	124	5	129

Merged error: 0.0b

Counts

129 → 5

regimes27.0ms

Accuracy

100% (0.0b remaining)

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

bsearch26.0ms

Steps

Iters	Range		Point
7	2764.08540472272	53889.47736569451	8097.8948115659

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

522.0ms	1763×	body	1280	valid
263.0ms	8056×	body	80	nan
245.0ms	1259×	body	640	valid
212.0ms	4106×	body	80	valid
78.0ms	575×	body	320	valid
24.0ms	297×	body	160	valid