Details

sample49.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.993897%

Results

16.0ms	53×	body	1280	valid
9.0ms	49×	body	640	valid
8.0ms	31×	body	320	valid
6.0ms	116×	body	80	valid
1.0ms	7×	body	160	valid

simplify4.0ms

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

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: 33.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.8b	(- (log (+ N 1.0)) (log N))
4.1b	(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 → 41

Calls

2 calls:

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

series10.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	232	285
1	628	264
2	2171	244
3	5001	244

prune82.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Merged error: 0.0b

Counts

48 → 3

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))
0.7b	(/ 1 (pow N 2))

rewrite49.0ms

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)
14.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
16.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series18.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (/ 0.3333333333333333 N) 0.5)
4.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
6.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
2.0ms	(/ 1 (pow N 2))

simplify74.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	597	1157
1	2754	966
2	5001	903

prune194.0ms

Filtered

101 candidates to 177 candidates (-75.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	176	4	180

Merged error: 0.0b

Counts

180 → 4

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.6b	(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))

series10.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify92.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	221	370
1	736	343
2	3220	333
3	5002	333

prune75.0ms

Filtered

46 candidates to 66 candidates (-43.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))
4.1b	(log (+ N 1.0))
4.1b	(log (+ N 1.0))
4.1b	(log (+ N 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

26×	`log-prod`
21×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`associate--l+`
7×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in`
6×	`log-div` `associate--r+` `add-log-exp`
5×	`distribute-lft-out`
4×	`add-cbrt-cube`
3×	`flip3-+` `rem-log-exp` `log-pow` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

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

series24.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	435	719
1	1434	640
2	5001	595

prune160.0ms

Filtered

67 candidates to 84 candidates (-25.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.5b

bsearch17.0ms

Steps

Iters	Range		Point
9	102.62816987946948	16863139118.531946	7710.191728627831

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.993897%

Results

512.0ms	1748×	body	1280	valid
239.0ms	1259×	body	640	valid
209.0ms	4063×	body	80	valid
80.0ms	635×	body	320	valid
26.0ms	295×	body	160	valid
0.0ms	1×	body	80	nan

Details

sample49.0ms

simplify4.0ms

prune2.0ms

localize6.0ms

rewrite11.0ms

series10.0ms

simplify55.0ms

prune82.0ms

localize10.0ms

rewrite49.0ms

series18.0ms

simplify74.0ms

prune194.0ms

localize4.0ms

rewrite11.0ms

series10.0ms

simplify92.0ms

prune75.0ms

localize11.0ms

rewrite17.0ms

series24.0ms

simplify42.0ms

prune160.0ms

regimes37.0ms

bsearch17.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling