Details

analyze2.5s

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 21.655544%

Guaranteed chance to sample good point: 59.9175%

sample210.0ms

Algorithm

intervals

Results

82.0ms	100×	body	1280	valid
79.0ms	34×	body	2560	valid
16.0ms	45×	body	640	valid
5.0ms	10×	body	640	invalid
5.0ms	23×	body	320	valid
3.0ms	46×	body	80	valid
2.0ms	2×	body	1280	invalid
2.0ms	22×	body	80	invalid
1.0ms	4×	body	320	invalid
1.0ms	8×	body	160	valid
1.0ms	4×	body	160	invalid
0.0ms	10×	body	80	nan

simplify42.0ms

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: 47.1b

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)))
1.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite83.0ms

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:

32.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
19.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series195.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
35.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
28.0ms	(pow (+ 1.0 (/ i n)) n)
66.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune574.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	289	4	293
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	289	5	294

Merged error: 24.0b

Counts

294 → 5

localize19.0ms

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)))
11.9b	(* (pow i 2) (log 1.0))
19.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite54.0ms

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))

series68.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
22.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
14.0ms	(* (pow i 2) (log 1.0))
25.0ms	(/ (- (+ (* 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

198 → 198

Iterations

Useful iterations: 1 (25.0ms)

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

prune799.0ms

Filtered

150 candidates to 198 candidates (-32.0%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	182	16	198
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	183	20	203

Merged error: 12.5b

Counts

203 → 20

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))
11.3b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.9b	(* (pow i 2) (log 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`add-exp-log`
18×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-cbrt-cube`
11×	`associate-l`
10×	`pow1`
9×	`times-frac` `add-log-exp`
8×	`prod-exp`
6×	`log-prod` `cbrt-unprod`
5×	`associate-r`
4×	`unpow-prod-down` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `sum-log` `associate-/l`
2×	`cbrt-undiv` `div-exp` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `associate-l/` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) 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)
6.0ms	(* (pow i 2) (log 1.0))

series58.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
23.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
16.0ms	(/ (- (+ (* 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))

simplify80.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	540	1516
1	2465	1293
2	5001	1289

prune379.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	17	18
Picked	0	1	1
Done	0	1	1
Total	110	20	130

Merged error: 12.5b

Counts

130 → 20

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
3.2b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
11.9b	(* (pow i 2) (log 1.0))
13.3b	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
127×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
93×	`add-cube-cbrt`
53×	`add-exp-log`
48×	`associate-r`
32×	`add-cbrt-cube`
23×	`div-exp`
21×	`associate-l`
13×	`prod-exp` `associate-/r*`
12×	`cbrt-undiv` `unswap-sqr`
10×	`div-inv`
9×	`add-log-exp`
7×	`pow1` `cbrt-unprod`
6×	`log-prod`
4×	`unpow-prod-down`
3×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `frac-times` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 215

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
14.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
6.0ms	(* (pow i 2) (log 1.0))
30.0ms	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
20.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
13.0ms	(* (pow i 2) (log 1.0))
24.0ms	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

simplify68.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1153	4360
1	5001	3911

prune761.0ms

Filtered

149 candidates to 227 candidates (-52.3%)

Pruning

20 alts after pruning (17 fresh and 3 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	16	17
Picked	0	1	1
Done	0	2	2
Total	227	20	247

Merged error: 12.5b

Counts

247 → 20

regimes606.0ms

Accuracy

66.2% (6.1b remaining)

Error of 17.2b against oracle of 11.1b and baseline of 29.1b

bsearch432.0ms

Steps

Iters	Range		Point
9	6.35902867718013e+239	6.448363558604509e+246	3.1504271704062454e+243
10	2.4322725023317916e+129	1.7022384688170886e+143	1.3298171590023524e+143
6	23.486212534144155	119.81348122388087	23.786737204236545
6	6.887435232341738e-214	4.0739848992615314e-213	4.015583309961557e-213
4	-3.2791178443538286e-28	-1.7903717444347643e-28	-3.2254347733272635e-28

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	84
1	86	84

end0.0ms

analyze2.5s

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 21.655544%

Guaranteed chance to sample good point: 59.9175%

sample6.1s

Algorithm

intervals

Results

2.4s	2768×	body	1280	valid
2.1s	974×	body	2560	valid
629.0ms	1566×	body	640	valid
173.0ms	721×	body	320	valid
129.0ms	256×	body	640	invalid
118.0ms	1617×	body	80	valid
90.0ms	106×	body	1280	invalid
56.0ms	175×	body	320	invalid
55.0ms	346×	body	160	valid
37.0ms	379×	body	80	invalid
30.0ms	8×	body	5120	valid
28.0ms	13×	body	2560	invalid
14.0ms	71×	body	160	invalid
11.0ms	186×	body	80	nan

Details

analyze2.5s

sample210.0ms

simplify42.0ms

prune3.0ms

localize9.0ms

rewrite83.0ms

series195.0ms

simplify63.0ms

prune574.0ms

localize19.0ms

rewrite54.0ms

series68.0ms

simplify151.0ms

prune799.0ms

localize16.0ms

rewrite42.0ms

series58.0ms

simplify80.0ms

prune379.0ms

localize19.0ms

rewrite67.0ms

series64.0ms

simplify68.0ms

prune761.0ms

regimes606.0ms

bsearch432.0ms

simplify3.0ms

end0.0ms

analyze2.5s

sample6.1s

Profiling