Details

Time bar (total: 13.9s)

sample153.0ms

Algorithm
intervals
Results
59.0ms78×body1280valid
51.0ms25×body2560valid
16.0ms53×body640valid
7.0ms45×body320valid
4.0ms84×body80valid
3.0ms89×body80nan
1.0ms12×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b
(pow (+ 1.0 (/ i n)) n)
9.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite584.0ms

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:
236.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
109.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
207.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
386.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
264.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
223.0ms
(pow (+ 1.0 (/ i n)) n)
366.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify56.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012263285
150023166

prune787.0ms

Filtered
293 candidates to 223 candidates (76.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
0.5b
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b
(pow (+ 1.0 (/ i n)) n)

rewrite601.0ms

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:
206.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
253.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
110.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts
4 → 12
Calls
4 calls:
309.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
422.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
265.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
229.0ms
(pow (+ 1.0 (/ i n)) n)

simplify61.0ms

Algorithm
egg-herbie
Counts
322 → 322
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
014853727
150023400

prune748.0ms

Filtered
322 candidates to 210 candidates (65.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow i 2))
1.4b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
10.1b
(* (pow i 2) (log 1.0))
13.9b
(* (/ 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)))

rewrite497.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
136×add-sqr-sqrt
98×*-un-lft-identity
96×add-cube-cbrt
58×add-exp-log
56×associate-*r*
34×add-cbrt-cube
24×associate-*l*
23×div-exp
16×prod-exp unswap-sqr
13×associate-/r*
12×cbrt-undiv
10×div-inv
8×unpow-prod-down cbrt-unprod
7×pow1
6×log-prod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp *-commutative associate-/l*
2×pow-to-exp pow-exp associate-/r/ associate-/l/
1×frac-times flip3-- frac-2neg div-sub associate-*r/ pow-prod-down associate-*l/ clear-num log-pow flip--
Counts
4 → 229
Calls
4 calls:
6.0ms
(* 0.5 (pow i 2))
133.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
7.0ms
(* (pow i 2) (log 1.0))
340.0ms
(* (/ 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)))

series536.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 0.5 (pow i 2))
143.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
142.0ms
(* (pow i 2) (log 1.0))
226.0ms
(* (/ 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)))

simplify66.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011334294
150013845

prune727.0ms

Filtered
241 candidates to 157 candidates (65.1%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.6b

localize16.0ms

Local error

Found 4 expressions with local error:

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)
0.1b
(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
9.9b
(/ (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i)
10.1b
(* (pow i 2) (log 1.0))

rewrite350.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×add-exp-log
22×add-cbrt-cube
18×associate-*l*
16×add-cube-cbrt *-un-lft-identity
10×associate-*r*
9×pow1 prod-exp
7×cbrt-unprod
6×distribute-rgt-in log-prod distribute-lft-in times-frac unswap-sqr
4×cbrt-undiv unpow-prod-down associate-*r/ div-exp add-log-exp
3×associate-/r* *-commutative
2×sub-neg flip3-- pow-prod-down associate--l+ flip-- div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*l/ pow-exp clear-num log-pow associate-/l*
Counts
4 → 110
Calls
4 calls:
141.0ms
(* (/ (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
133.0ms
(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
65.0ms
(/ (* 100.0 (- (+ (* 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))

series639.0ms

Counts
4 → 12
Calls
4 calls:
225.0ms
(* (/ (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
119.0ms
(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
154.0ms
(/ (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i)
141.0ms
(* (pow i 2) (log 1.0))

simplify88.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
05541755
128941428
250011395

prune322.0ms

Filtered
122 candidates to 83 candidates (68.0%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.6b

regimes187.0ms

Accuracy

47% (11.8b remaining)

Error of 23.1b against oracle of 11.4b and baseline of 33.6b

bsearch287.0ms

Steps
ItersRangePoint
11
1.0812299319578903e+199
2.3876822878982117e+223
1.6485701615169504e+218
8
6.25831512931074e-67
4.832516025500173e-63
4.7711107632667577e-63
8
-118.2613039675085
-0.02423487123936656
-1.7234495065839621

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06751
16751

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.8s983×body2560valid
1.7s2440×body1280valid
476.0ms1636×body640valid
156.0ms946×body320valid
122.0ms2897×body80valid
72.0ms2306×body80nan
46.0ms428×body160valid
18.0ms5×body5120valid