Details

sample48.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.987794%

Results

19.0ms	66×	body	1280	valid
8.0ms	44×	body	640	valid
6.0ms	117×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	11×	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: 32.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.6b	(log (+ N 1.0))
3.1b	(- (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))

series10.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify57.0ms

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

prune81.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	4	48

Merged error: 0.0b

Counts

48 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.0b	(- (/ 0.3333333333333333 N) 0.5)
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.8b	(/ 1 (pow N 2))

rewrite54.0ms

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:

15.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
7.0ms	(- (/ 0.3333333333333333 N) 0.5)
17.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series15.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
3.0ms	(- (/ 0.3333333333333333 N) 0.5)
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

prune197.0ms

Filtered

101 candidates to 177 candidates (-75.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	176	5	181

Merged error: 0.0b

Counts

181 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (pow N 2))
18.9b	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
18.9b	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
18.9b	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
21×	`cbrt-div`
15×	`frac-add`
13×	`add-exp-log`
12×	`unpow-prod-down`
9×	`cbrt-prod`
8×	`associate-/r*`
6×	`frac-times` `flip3--` `associate-*r/` `div-exp` `add-cbrt-cube` `flip--`
4×	`pow1` `unpow2` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `flip3-+` `pow1/3` `1-exp` `associate-l/` `pow-exp` `flip-+` `associate-/l`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `div-inv` `inv-pow`

Counts

4 → 111

Calls

4 calls:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1 (pow N 2))
12.0ms	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
12.0ms	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
16.0ms	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify65.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	514	1537
1	2061	1434
2	5001	1376

prune450.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	123	5	128

Merged error: 0.0b

Counts

128 → 5

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.2b	(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))

simplify91.0ms

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

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	2	0	2
Picked	1	0	1
Done	0	2	2
Total	66	5	71

Merged error: 0.0b

Counts

71 → 5

regimes40.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch17.0ms

Steps

Iters	Range		Point
8	81.18943540732513	253778.19512877698	8492.630877905292

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	26	13

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: 99.987794%

Results

519.0ms	1762×	body	1280	valid
238.0ms	1271×	body	640	valid
212.0ms	4081×	body	80	valid
77.0ms	612×	body	320	valid
22.0ms	274×	body	160	valid
0.0ms	1×	body	80	nan

Details

sample48.0ms

simplify4.0ms

prune2.0ms

localize6.0ms

rewrite11.0ms

series10.0ms

simplify57.0ms

prune81.0ms

localize10.0ms

rewrite54.0ms

series15.0ms

simplify74.0ms

prune197.0ms

localize16.0ms

rewrite53.0ms

series42.0ms

simplify65.0ms

prune450.0ms

localize4.0ms

rewrite11.0ms

series8.0ms

simplify91.0ms

prune75.0ms

regimes40.0ms

bsearch17.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling