Details

sample52.0ms

Algorithm

intervals

Results

16.0ms	56×	body	1280	valid
8.0ms	252×	body	80	nan
7.0ms	38×	body	640	valid
6.0ms	121×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	18×	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: 31.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.0b	(log (+ N 1.0))
5.0b	(- (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))

series140.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(log (+ N 1.0))
100.0ms	(- (log (+ N 1.0)) (log N))

simplify53.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (48.0ms)

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

prune105.0ms

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: 0.1b

Counts

48 → 2

localize10.0ms

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))
0.5b	(/ 1 (pow N 2))

rewrite51.0ms

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))
17.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series161.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ 0.3333333333333333 N) 0.5)
30.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
76.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
20.0ms	(/ 1 (pow N 2))

simplify81.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (62.0ms)

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

prune273.0ms

Filtered

177 candidates to 101 candidates (57.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	175	4	179

Merged error: 0.0b

Counts

179 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (pow N 2))
0.5b	(/ 1 (pow N 2))
8.5b	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
8.5b	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
22×	`add-exp-log`
16×	`associate-/r*`
14×	`sqrt-div`
12×	`div-exp`
10×	`frac-add`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp` `sqrt-prod` `associate-/l*`
4×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*l/` `clear-num` `flip-+` `div-inv` `inv-pow`

Counts

4 → 154

Calls

4 calls:

5.0ms	(/ 1 (pow N 2))
5.0ms	(/ 1 (pow N 2))
15.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
20.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (pow N 2))
16.0ms	(/ 1 (pow N 2))
54.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
62.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify62.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	413	1170
1	1727	1044
2	5001	952

prune317.0ms

Filtered

166 candidates to 82 candidates (49.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	166	4	170

Merged error: 0.0b

Counts

170 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
5.3b	(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))

series140.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (+ N 1.0) N)
87.0ms	(log (/ (+ N 1.0) N))

simplify106.0ms

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

prune97.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	65	5	70

Merged error: 0.0b

Counts

70 → 5

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.9b

bsearch30.0ms

Steps

Iters	Range		Point
8	1538.2388859235716	3249381.761613268	10531.413524966325

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

507.0ms	1728×	body	1280	valid
261.0ms	7954×	body	80	nan
242.0ms	1253×	body	640	valid
216.0ms	4117×	body	80	valid
78.0ms	615×	body	320	valid
23.0ms	287×	body	160	valid

Details

sample52.0ms

simplify5.0ms

prune2.0ms

localize7.0ms

rewrite11.0ms

series140.0ms

simplify53.0ms

prune105.0ms

localize10.0ms

rewrite51.0ms

series161.0ms

simplify81.0ms

prune273.0ms

localize13.0ms

rewrite50.0ms

series155.0ms

simplify62.0ms

prune317.0ms

localize5.0ms

rewrite12.0ms

series140.0ms

simplify106.0ms

prune97.0ms

regimes29.0ms

bsearch30.0ms

simplify1.0ms

end0.0ms

sample1.6s

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