Details

sample54.0ms

Algorithm

intervals

Results

16.0ms	56×	body	1280	valid
8.0ms	243×	body	80	nan
8.0ms	41×	body	640	valid
6.0ms	119×	body	80	valid
3.0ms	27×	body	320	valid
1.0ms	13×	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: 32.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.8b	(log (+ N 1.0))
3.9b	(- (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))

series135.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(log (+ N 1.0))
92.0ms	(- (log (+ N 1.0)) (log N))

simplify56.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (51.0ms)

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

prune97.0ms

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: 0.0b

Counts

48 → 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))
1.0b	(/ 1 (pow N 2))

rewrite49.0ms

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:

16.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
19.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
8.0ms	(/ 1 (pow N 2))

series125.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
75.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
17.0ms	(/ 1 (pow N 2))

simplify75.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	583	1087
1	2726	904
2	5001	841

prune228.0ms

Filtered

159 candidates to 89 candidates (56.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Merged error: 0b

Counts

161 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N) (* (+ (/ 0.3333333333333333 N) 0.5) 1.0)) (* (+ (/ 0.3333333333333333 N) 0.5) N))
0.2b	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
1.0b	(/ 1 (pow N 2))
17.4b	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
64×	`add-sqr-sqrt`
62×	`add-exp-log`
52×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-cbrt-cube`
31×	`associate-*l/`
26×	`prod-exp`
18×	`div-exp`
16×	`pow1` `associate-r`
14×	`associate-l`
13×	`swap-sqr`
12×	`unpow-prod-down` `associate-/l/`
10×	`frac-add` `cbrt-unprod`
9×	`associate-/r*`
8×	`cbrt-undiv`
7×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
6×	`pow-to-exp` `rec-exp` `flip3--` `1-exp` `pow-exp` `flip--` `div-inv` `associate-/l*`
4×	`pow-prod-down` `unpow2` `add-log-exp` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num` `associate-/r/` `*-commutative`
1×	`pow2` `pow-flip` `pow-plus` `pow-sqr` `pow-prod-up` `inv-pow`

Counts

4 → 192

Calls

4 calls:

31.0ms	(/ (+ (* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N) (* (+ (/ 0.3333333333333333 N) 0.5) 1.0)) (* (+ (/ 0.3333333333333333 N) 0.5) N))
14.0ms	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
5.0ms	(/ 1 (pow N 2))
17.0ms	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

series219.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (+ (* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N) (* (+ (/ 0.3333333333333333 N) 0.5) 1.0)) (* (+ (/ 0.3333333333333333 N) 0.5) N))
24.0ms	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
19.0ms	(/ 1 (pow N 2))
96.0ms	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

simplify51.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1034	1857
1	5001	1571

prune417.0ms

Filtered

204 candidates to 121 candidates (59.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	204	4	208

Merged error: 0b

Counts

208 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (pow N 2))
1.0b	(/ 1 (pow N 2))
7.8b	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
7.8b	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite54.0ms

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))
21.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
17.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (pow N 2))
16.0ms	(/ 1 (pow N 2))
61.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
56.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify69.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (48.0ms)

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

prune294.0ms

Filtered

166 candidates to 82 candidates (49.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Merged error: 0b

Counts

170 → 4

regimes22.0ms

Accuracy

100% (0.0b remaining)

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

bsearch42.0ms

Steps

Iters	Range		Point
9	0.23207878676536348	172312.70592171172	8824.451921478636

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

528.0ms	1801×	body	1280	valid
270.0ms	8097×	body	80	nan
231.0ms	1184×	body	640	valid
210.0ms	4091×	body	80	valid
78.0ms	618×	body	320	valid
24.0ms	306×	body	160	valid