Details

sample44.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.987794%

Results

14.0ms	46×	body	1280	valid
9.0ms	44×	body	640	valid
8.0ms	144×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	8×	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: 26.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (log (+ N 1.0)) (log N))
3.7b	(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))

series8.0ms

Counts

2 → 6

Calls

2 calls:

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

prune77.0ms

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)
1.9b	(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))

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify93.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (18.0ms)

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

prune72.0ms

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

localize11.0ms

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))
0.3b	(/ 1 (pow N 2))

rewrite40.0ms

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))

series12.0ms

Counts

3 → 9

Calls

3 calls:

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))

simplify72.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (59.0ms)

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

prune162.0ms

Filtered

89 candidates to 159 candidates (-78.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	158	3	161

Merged error: 0.0b

Counts

161 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.3b	(/ 1 (pow N 2))
3.6b	(exp (log (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))))
23.1b	(log (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 171

Calls

4 calls:

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

series23.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
2.0ms	(/ 1 (pow N 2))
4.0ms	(exp (log (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))))
6.0ms	(log (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify83.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	731	1490
1	3211	1281
2	5001	1210

prune262.0ms

Filtered

110 candidates to 183 candidates (-66.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	183	3	186

Merged error: 0.0b

Counts

186 → 3

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.8b

bsearch17.0ms

Steps

Iters	Range		Point
9	0.026227607831048265	13207.579563402003	7746.134693397183

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.987794%

Results

520.0ms	1723×	body	1280	valid
266.0ms	1349×	body	640	valid
215.0ms	4017×	body	80	valid
83.0ms	636×	body	320	valid
25.0ms	275×	body	160	valid
0.0ms	1×	body	80	nan

Details

sample44.0ms

simplify4.0ms

prune3.0ms

localize6.0ms

rewrite11.0ms

series8.0ms

simplify55.0ms

prune77.0ms

localize5.0ms

rewrite11.0ms

series9.0ms

simplify93.0ms

prune72.0ms

localize11.0ms

rewrite40.0ms

series12.0ms

simplify72.0ms

prune162.0ms

localize16.0ms

rewrite57.0ms

series23.0ms

simplify83.0ms

prune262.0ms

regimes34.0ms

bsearch17.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling