Details

sample2.7s

Algorithm

intervals

sampling

Space saved by range analysis: 21.655544%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

82.0ms	38×	body	2560	valid
71.0ms	88×	body	1280	valid
20.0ms	47×	body	640	valid
5.0ms	24×	body	320	valid
5.0ms	11×	body	640	invalid
3.0ms	46×	body	80	valid
2.0ms	1×	body	2560	invalid
2.0ms	13×	body	160	valid
1.0ms	15×	body	80	invalid
1.0ms	2×	body	1280	invalid
1.0ms	4×	body	320	invalid
1.0ms	11×	body	80	nan

simplify46.0ms

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

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: 48.3b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
10.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite88.0ms

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:

37.0ms	(* 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))

series192.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
37.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
27.0ms	(pow (+ 1.0 (/ i n)) n)
65.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune601.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	286	7	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	287	7	294

Merged error: 21.0b

Counts

294 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) 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)))
11.6b	(* (pow i 2) (log 1.0))
19.3b	(/ (- (+ (* 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`
102×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`associate-l`
9×	`div-inv` `add-log-exp`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`unpow-prod-down` `cbrt-unprod`
3×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 186

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
19.0ms	(* 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))

series59.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) 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)))
13.0ms	(* (pow i 2) (log 1.0))
19.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify153.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	929	3604
1	4818	3341
2	5001	3341

prune800.0ms

Filtered

150 candidates to 198 candidates (-32.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	187	11	198
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	189	16	205

Merged error: 10.3b

Counts

205 → 16

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
0.3b	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
11.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.6b	(* (pow i 2) (log 1.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
22×	`add-cbrt-cube`
20×	`associate-r`
19×	`times-frac`
12×	`pow1` `associate-l`
10×	`prod-exp`
8×	`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-*r/` `div-inv` `associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `div-sub` `associate-*l/` `pow-exp` `clear-num` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

12.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
12.0ms	(* (* 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)
6.0ms	(* (pow i 2) (log 1.0))

series68.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
24.0ms	(* (* 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))

simplify94.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	540	1985
1	2839	1693
2	5002	1693

prune404.0ms

Filtered

86 candidates to 129 candidates (-50.0%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	128	17	145

Merged error: 10.3b

Counts

145 → 17

localize24.0ms

Local error

Found 4 expressions with local error:

11.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.6b	(* (pow i 2) (log 1.0))
11.6b	(* (pow i 2) (log 1.0))
11.6b	(* (pow i 2) (log 1.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l`
21×	`add-exp-log`
18×	`log-prod`
12×	`unpow-prod-down` `associate-r` `add-cbrt-cube` `unswap-sqr`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `prod-exp`
7×	`pow1`
6×	`unpow2` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-exp` `associate-/r` `log-pow` `-commutative` `cbrt-unprod` `associate-/l*`
2×	`associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 132

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)
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(* (pow i 2) (log 1.0))

series70.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
28.0ms	(* (pow i 2) (log 1.0))
12.0ms	(* (pow i 2) (log 1.0))
13.0ms	(* (pow i 2) (log 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	299	1229
1	1359	1100
2	5002	1086

prune914.0ms

Filtered

93 candidates to 144 candidates (-54.8%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	144	17	161

Merged error: 10.3b

Counts

161 → 17

regimes302.0ms

Accuracy

61.7% (6.8b remaining)

Error of 18.0b against oracle of 11.1b and baseline of 29.0b

bsearch341.0ms

Steps

Iters	Range		Point
11	0.0008215332209713408	1.2836089123551093e+24	213.2071997229568
5	1.1223750570958262e-152	3.721099112873035e-152	2.186960948026309e-152
5	-2.95808591378959e-09	-1.3763187683271213e-09	-2.9257719524401168e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	55
1	73	55

end0.0ms

sample8.4s

Algorithm

intervals

sampling

Space saved by range analysis: 21.655544%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

2.4s	2802×	body	1280	valid
2.0s	954×	body	2560	valid
618.0ms	1541×	body	640	valid
174.0ms	735×	body	320	valid
116.0ms	224×	body	640	invalid
110.0ms	1614×	body	80	valid
64.0ms	83×	body	1280	invalid
51.0ms	348×	body	160	valid
51.0ms	162×	body	320	invalid
41.0ms	406×	body	80	invalid
39.0ms	19×	body	2560	invalid
24.0ms	6×	body	5120	valid
11.0ms	55×	body	160	invalid
10.0ms	225×	body	80	nan

Details

sample2.7s

simplify46.0ms

prune3.0ms

localize9.0ms

rewrite88.0ms

series192.0ms

simplify66.0ms

prune601.0ms

localize16.0ms

rewrite56.0ms

series59.0ms

simplify153.0ms

prune800.0ms

localize19.0ms

rewrite45.0ms

series68.0ms

simplify94.0ms

prune404.0ms

localize24.0ms

rewrite35.0ms

series70.0ms

simplify56.0ms

prune914.0ms

regimes302.0ms

bsearch341.0ms

simplify2.0ms

end0.0ms

sample8.4s

Profiling