Details

Time bar (total: 16.4s)

sample133.0ms

Algorithm
intervals
Results
55.0ms76×body1280valid
36.0ms21×body2560valid
16.0ms60×body640valid
4.0ms25×body320valid
4.0ms98×body80valid
2.0ms70×body80nan
1.0ms28×body80overflowed
1.0ms11×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b
(pow (+ 1.0 (/ i n)) n)
7.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite568.0ms

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:
231.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
105.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
13.0ms
(pow (+ 1.0 (/ i n)) n)
201.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
371.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
261.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms
(pow (+ 1.0 (/ i n)) n)
353.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012263285
150013166

prune801.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
5.8b
(pow (+ 1.0 (/ i n)) n)
7.7b
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite452.0ms

Algorithm
rewrite-expression-head
Rules
717×times-frac
524×*-un-lft-identity
294×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
38×div-inv
29×associate-/r/
22×associate-/l*
18×add-exp-log
16×add-cbrt-cube
15×flip3-+ flip-+
13×associate-/r*
8×cbrt-undiv unpow-prod-down div-exp add-log-exp
6×pow1 div-sub
4×pow-unpow
2×neg-sub0 pow-to-exp associate-+r- pow-pow unsub-neg pow-exp sum-log sqr-pow
1×+-commutative frac-2neg neg-log clear-num associate-/l/
Counts
4 → 394
Calls
4 calls:
77.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
11.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
11.0ms
(pow (+ 1.0 (/ i n)) n)
325.0ms
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series2.7s

Counts
4 → 12
Calls
4 calls:
271.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
225.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
216.0ms
(pow (+ 1.0 (/ i n)) n)
2.0s
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify125.0ms

Algorithm
egg-herbie
Counts
406 → 406
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0186410059
150029637

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
0.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
1.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b
(pow (+ 1.0 (/ i n)) n)

rewrite581.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
314×add-sqr-sqrt
206×*-un-lft-identity
146×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
49×add-exp-log
32×unpow-prod-down
30×add-cbrt-cube
29×sqr-pow
28×distribute-lft-out--
23×div-exp
18×div-inv
13×associate-*l* associate-/r*
12×cbrt-undiv
10×prod-exp
8×unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
3×rec-exp pow-unpow 1-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×frac-times pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num *-commutative distribute-lft-out
Counts
4 → 310
Calls
4 calls:
243.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
197.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
104.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms
(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts
4 → 12
Calls
4 calls:
384.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
308.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
262.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
214.0ms
(pow (+ 1.0 (/ i n)) n)

simplify72.0ms

Algorithm
egg-herbie
Counts
322 → 322
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014853727
150013400

prune751.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
2.8b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
10.4b
(* (pow i 2) (log 1.0))
16.4b
(* (/ 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)))

rewrite297.0ms

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:
8.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
125.0ms
(/ (- (+ (* 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))
145.0ms
(* (/ 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)))

series564.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
147.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
148.0ms
(* (pow i 2) (log 1.0))
220.0ms
(* (/ 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)))

simplify63.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011534367
150013912

prune662.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.7b

regimes197.0ms

Accuracy

46% (13.1b remaining)

Error of 24.6b against oracle of 11.4b and baseline of 35.8b

bsearch407.0ms

Steps
ItersRangePoint
6
2.9905422499130755e-165
2.0721547055092453e-164
4.279716239820104e-165
8
1.2055374660761621e-267
4.8681767545597665e-263
1.234477812642328e-267
5
-4.0828566167469306e+260
-1.3227323216581745e+260
-1.8403630755190044e+260

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06547
16547

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.6s2251×body1280valid
1.5s791×body2560valid
474.0ms1596×body640valid
153.0ms884×body320valid
147.0ms3303×body80valid
84.0ms2479×body80nan
47.0ms422×body160valid
43.0ms985×body80overflowed
25.0ms6×body5120valid