Details

analyze868.0ms

Algorithm: search

sample223.0ms

Algorithm

intervals

Results

89.0ms	37×	body	2560	valid
78.0ms	85×	body	1280	valid
18.0ms	42×	body	640	valid
7.0ms	26×	body	320	valid
5.0ms	6×	body	1280	invalid
4.0ms	8×	body	640	invalid
4.0ms	53×	body	80	valid
2.0ms	13×	body	160	valid
2.0ms	5×	body	320	invalid
1.0ms	11×	body	80	invalid
1.0ms	5×	body	160	invalid
1.0ms	13×	body	80	nan

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	59	7
2	141	7
3	346	7
4	1171	7
5	5001	7

prune4.0ms

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: 48.7b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

38.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series198.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
36.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
27.0ms	(pow (+ 1.0 (/ i n)) n)
67.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify67.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune663.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	285	8	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	286	8	294

Merged error: 23.1b

Counts

294 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
11.4b	(* (pow i 2) (log 1.0))
19.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
111×	`add-sqr-sqrt`
90×	`add-cube-cbrt` `*-un-lft-identity`
56×	`associate-r`
28×	`add-exp-log`
22×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-/r*`
11×	`unswap-sqr`
9×	`prod-exp` `div-inv`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`cbrt-unprod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `-commutative` `associate-/l`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-prod-down` `clear-num` `log-pow` `flip--`

Counts

4 → 200

Calls

4 calls:

6.0ms	(* 0.5 (pow i 2))
20.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
6.0ms	(* (pow i 2) (log 1.0))
14.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series61.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.5 (pow i 2))
21.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
13.0ms	(* (pow i 2) (log 1.0))
23.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify151.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	907	3537
1	4856	3275
2	5001	3275

prune874.0ms

Filtered

157 candidates to 212 candidates (-35.0%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	201	11	212
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	202	18	220

Merged error: 11.5b

Counts

220 → 18

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
0.1b	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
10.7b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.4b	(* (pow i 2) (log 1.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`associate-l`
22×	`add-cbrt-cube`
19×	`times-frac`
12×	`pow1`
10×	`prod-exp`
8×	`associate-r` `cbrt-unprod`
6×	`log-prod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`associate-*l/` `div-inv` `associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-exp` `clear-num` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

12.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
14.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms	(* (pow i 2) (log 1.0))

series73.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
21.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
15.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
13.0ms	(* (pow i 2) (log 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	529	1979
1	2435	1684
2	5001	1679

prune425.0ms

Filtered

87 candidates to 129 candidates (-48.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	129	18	147

Merged error: 11.5b

Counts

147 → 18

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n)
0.1b	(* 100.0 (* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`associate-l`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`associate-r` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-r/` `-commutative` `flip--` `add-log-exp`
1×	`unswap-sqr`

Counts

2 → 40

Calls

2 calls:

16.0ms	(* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n)
15.0ms	(* 100.0 (* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n))

series31.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n)
16.0ms	(* 100.0 (* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n))

simplify47.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	252	736
1	1188	612
2	5001	612

prune89.0ms

Filtered

30 candidates to 46 candidates (-53.3%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	16	16
Picked	0	1	1
Done	0	1	1
Total	46	18	64

Merged error: 11.5b

Counts

64 → 18

regimes461.0ms

Accuracy

68.7% (5.6b remaining)

Error of 16.5b against oracle of 11.0b and baseline of 28.8b

bsearch379.0ms

Steps

Iters	Range		Point
9	0.09808863093133222	6951.38993561627	0.18733134105301183
5	-1.590324049603931e-10	-5.3678213925771454e-11	-1.3412065908225887e-10

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	27
1	54	27

end0.0ms

analyze858.0ms

Algorithm: search

sample6.2s

Algorithm

intervals

Results

2.5s	2807×	body	1280	valid
2.1s	972×	body	2560	valid
628.0ms	1519×	body	640	valid
178.0ms	725×	body	320	valid
124.0ms	235×	body	640	invalid
120.0ms	1616×	body	80	valid
92.0ms	110×	body	1280	invalid
56.0ms	354×	body	160	valid
53.0ms	512×	body	80	invalid
52.0ms	158×	body	320	invalid
23.0ms	7×	body	5120	valid
21.0ms	10×	body	2560	invalid
18.0ms	313×	body	80	nan
16.0ms	82×	body	160	invalid

Details

analyze868.0ms

sample223.0ms

simplify44.0ms

prune4.0ms

localize10.0ms

rewrite92.0ms

series198.0ms

simplify67.0ms

prune663.0ms

localize18.0ms

rewrite56.0ms

series61.0ms

simplify151.0ms

prune874.0ms

localize18.0ms

rewrite48.0ms

series73.0ms

simplify81.0ms

prune425.0ms

localize14.0ms

rewrite33.0ms

series31.0ms

simplify47.0ms

prune89.0ms

regimes461.0ms

bsearch379.0ms

simplify2.0ms

end0.0ms

analyze858.0ms

sample6.2s

Profiling