Details

sample149.0ms

Algorithm

intervals

Results

58.0ms	79×	body	1280	valid
49.0ms	25×	body	2560	valid
19.0ms	65×	body	640	valid
4.0ms	100×	body	80	valid
3.0ms	18×	body	320	valid
3.0ms	85×	body	80	nan
1.0ms	12×	body	160	valid

simplify41.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b	(pow (+ 1.0 (/ i n)) n)
9.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite549.0ms

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:

221.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
102.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
195.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

368.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
251.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
210.0ms	(pow (+ 1.0 (/ i n)) n)
349.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify60.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5001	3166

prune820.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
1.9b	(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
5.6b	(pow (+ 1.0 (/ i n)) (/ n 2))
5.6b	(pow (+ 1.0 (/ i n)) (/ n 2))

rewrite714.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`times-frac`
28×	`add-cube-cbrt`
26×	`pow-unpow`
18×	`add-exp-log`
16×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`unpow-prod-down`
6×	`prod-exp` `cbrt-unprod` `add-log-exp` `difference-of-squares`
5×	`associate-*l/` `distribute-lft-out`
4×	`sqr-pow`
3×	`flip3--` `pow-prod-down` `sqrt-prod` `flip--` `div-inv`
2×	`cbrt-undiv` `frac-times` `pow-to-exp` `pow-pow` `associate-*r/` `div-exp` `pow-exp`
1×	`sub-neg` `diff-log` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 115

Calls

4 calls:

582.0ms	(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
104.0ms	(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
12.0ms	(pow (+ 1.0 (/ i n)) (/ n 2))
11.0ms	(pow (+ 1.0 (/ i n)) (/ n 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

605.0ms	(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
260.0ms	(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
221.0ms	(pow (+ 1.0 (/ i n)) (/ n 2))
228.0ms	(pow (+ 1.0 (/ i n)) (/ n 2))

simplify66.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	552	1468
1	2135	1191
2	5001	1124

prune400.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.4b

localize13.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
5.6b	(pow (+ 1.0 (/ i n)) (/ n 2))
5.6b	(pow (+ 1.0 (/ i n)) (/ n 2))
9.2b	(/ (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) (/ i n))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

261×	`add-sqr-sqrt`
247×	`times-frac`
145×	`*-un-lft-identity`
111×	`add-cube-cbrt`
90×	`difference-of-squares`
45×	`sqrt-prod`
38×	`unpow-prod-down`
32×	`sqr-pow`
26×	`pow-unpow`
15×	`distribute-lft-out--`
14×	`div-inv`
13×	`associate-/r*`
11×	`add-exp-log`
10×	`associate-/l*`
9×	`add-cbrt-cube`
6×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r/`

Counts

4 → 246

Calls

4 calls:

101.0ms	(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
13.0ms	(pow (+ 1.0 (/ i n)) (/ n 2))
12.0ms	(pow (+ 1.0 (/ i n)) (/ n 2))
197.0ms	(/ (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

264.0ms	(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
229.0ms	(pow (+ 1.0 (/ i n)) (/ n 2))
233.0ms	(pow (+ 1.0 (/ i n)) (/ n 2))
384.0ms	(/ (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) (/ i n))

simplify119.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	939	3827
1	3857	3740
2	5001	3727

prune749.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (+ (* n (pow (+ 1.0 (/ i n)) n)) (* n (- 1.0))) i))
0.2b	(/ (+ (* n (pow (+ 1.0 (/ i n)) n)) (* n (- 1.0))) i)
1.8b	(+ (* n (pow (+ 1.0 (/ i n)) n)) (* n (- 1.0)))
5.6b	(pow (+ 1.0 (/ i n)) n)

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
25×	`times-frac`
24×	`add-cube-cbrt`
16×	`associate-r`
12×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
7×	`pow1`
6×	`add-log-exp`
4×	`unpow-prod-down` `distribute-rgt-neg-out` `associate-/l*`
3×	`pow-unpow` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-sub` `div-exp` `unsub-neg` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `-commutative` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

53.0ms	(* 100.0 (/ (+ (* n (pow (+ 1.0 (/ i n)) n)) (* n (- 1.0))) i))
71.0ms	(/ (+ (* n (pow (+ 1.0 (/ i n)) n)) (* n (- 1.0))) i)
24.0ms	(+ (* n (pow (+ 1.0 (/ i n)) n)) (* n (- 1.0)))
24.0ms	(pow (+ 1.0 (/ i n)) n)

series676.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* 100.0 (/ (+ (* n (pow (+ 1.0 (/ i n)) n)) (* n (- 1.0))) i))
169.0ms	(/ (+ (* n (pow (+ 1.0 (/ i n)) n)) (* n (- 1.0))) i)
111.0ms	(+ (* n (pow (+ 1.0 (/ i n)) n)) (* n (- 1.0)))
223.0ms	(pow (+ 1.0 (/ i n)) n)

simplify118.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	909	1582
1	4476	1435
2	5001	1421

prune368.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.8b

regimes166.0ms

Accuracy

48.5% (12.1b remaining)

Error of 31.8b against oracle of 19.7b and baseline of 43.2b

bsearch387.0ms

Steps

Iters	Range		Point
9	2.7421150748179934e+209	1.7754777225992786e+216	4.2045118870648674e+212
8	8.278373459243612e-33	2.7653121003033314e-28	2.587509873082636e-28
9	-6.956871504263554e-09	-9.165072888214816e-14	-6.8977356701701615e-09

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	103
1	116	103

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.9s	1005×	body	2560	valid
1.8s	2464×	body	1280	valid
495.0ms	1630×	body	640	valid
150.0ms	854×	body	320	valid
132.0ms	3054×	body	80	valid
75.0ms	2270×	body	80	nan
51.0ms	460×	body	160	valid