Details

analyze2.0ms

Algorithm: search

sample37.0ms

Algorithm

intervals

Results

15.0ms	51×	body	1280	valid
7.0ms	141×	body	80	valid
6.0ms	35×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	12×	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

prune3.0ms

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: 26.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (log (+ N 1.0)) (log N))
3.5b	(log (+ N 1.0))

rewrite10.0ms

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:

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

series154.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(- (log (+ N 1.0)) (log N))
148.0ms	(log (+ N 1.0))

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

prune76.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

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

localize5.0ms

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))

series8.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(/ (+ 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

prune70.0ms

Filtered

46 candidates to 66 candidates (-43.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Merged error: 0.0b

Counts

68 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

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))
0.4b	(/ 1 (pow N 2))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 150

Calls

3 calls:

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))

series15.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ (* (/ 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))

simplify71.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	583	1075
1	2726	892
2	5001	829

prune166.0ms

Filtered

89 candidates to 159 candidates (-78.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	157	4	161

Merged error: 0.0b

Counts

161 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (pow N 2))
21.8b	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
21.8b	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
21.8b	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite54.0ms

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))
17.0ms	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
14.0ms	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
14.0ms	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series39.0ms

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)))
13.0ms	(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify64.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (48.0ms)

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

prune461.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	123	4	127

Merged error: 0.0b

Counts

127 → 4

regimes39.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.3b

bsearch21.0ms

Steps

Iters	Range		Point
9	0.007000281397181652	12262.697333085898	8156.864740756527

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

analyze1.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

511.0ms	1763×	body	1280	valid
226.0ms	1237×	body	640	valid
203.0ms	4093×	body	80	valid
80.0ms	618×	body	320	valid
22.0ms	289×	body	160	valid

Details

analyze2.0ms

sample37.0ms

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite10.0ms

series154.0ms

simplify57.0ms

prune76.0ms

localize5.0ms

rewrite11.0ms

series8.0ms

simplify92.0ms

prune70.0ms

localize10.0ms

rewrite41.0ms

series15.0ms

simplify71.0ms

prune166.0ms

localize15.0ms

rewrite54.0ms

series39.0ms

simplify64.0ms

prune461.0ms

regimes39.0ms

bsearch21.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample1.1s

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