Details

Time bar (total: 9.6s)

sample182.0ms

Algorithm
intervals
Results
72.0ms38×body2560valid
69.0ms95×body1280valid
18.0ms58×body640valid
4.0ms24×body320valid
3.0ms68×body80valid
2.0ms61×body80nan
2.0ms12×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550027

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 48.2b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.2b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.7b
(pow (+ 1.0 (/ i n)) n)
12.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
6×associate-*r/ associate-/r/
5×clear-num
4×frac-2neg associate-*r* div-inv associate-/l/
3×flip3-- flip--
2×associate-/r* sqr-pow
1×pow-to-exp sub-neg fma-neg div-sub un-div-inv *-commutative
Counts
4 → 29
Calls
4 calls:
7.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
4.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
3.0ms
(pow (+ 1.0 (/ i n)) n)
6.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
344.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
233.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
196.0ms
(pow (+ 1.0 (/ i n)) n)
328.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify30.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0277272
1950269
25001265

prune118.0ms

Filtered
41 candidates to 35 candidates (85.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New35641
Fresh000
Picked101
Done000
Total36642

Merged error: 24.5b

Counts
42 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma i 1.0 (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0)))))
0.0b
(* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))
0.1b
(* 100.0 (/ (+ (fma i 1.0 (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) (/ i n)))
19.3b
(/ (+ (fma i 1.0 (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) (/ i n))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-*r/
6×associate-/r/
5×clear-num
4×distribute-rgt-in sub-neg associate-+r+ frac-2neg distribute-lft-in associate-*r* div-inv associate-/l/
3×flip3-+ flip-+
2×associate-*l* associate-/r* *-commutative
1×+-commutative associate-+l+ flip3-- un-div-inv flip-- fma-udef unpow2 sqr-pow
Counts
4 → 38
Calls
4 calls:
5.0ms
(+ (fma i 1.0 (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0)))))
4.0ms
(* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))
6.0ms
(* 100.0 (/ (+ (fma i 1.0 (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) (/ i n)))
7.0ms
(/ (+ (fma i 1.0 (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) (/ i n))

series652.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (fma i 1.0 (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0)))))
181.0ms
(* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))
199.0ms
(* 100.0 (/ (+ (fma i 1.0 (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) (/ i n)))
184.0ms
(/ (+ (fma i 1.0 (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) (/ i n))

simplify37.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0276482
11161454
25002444

prune156.0ms

Filtered
50 candidates to 35 candidates (70.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New44650
Fresh145
Picked101
Done000
Total461056

Merged error: 11.6b

Counts
56 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))
0.0b
(* (/ (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))) i) n)
0.1b
(* 100.0 (* (/ (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))) i) n))
10.5b
(/ (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))) i)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
6×associate-*l/
3×frac-2neg associate-*r/ associate-*r* clear-num *-commutative div-inv
2×associate-*l*
1×fma-udef
Counts
4 → 16
Calls
4 calls:
1.0ms
(fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))
3.0ms
(* (/ (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))) i) n)
4.0ms
(* 100.0 (* (/ (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))) i) n))
2.0ms
(/ (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))) i)

series599.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))
183.0ms
(* (/ (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))) i) n)
203.0ms
(* 100.0 (* (/ (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))) i) n))
126.0ms
(/ (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))) i)

simplify84.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (81.0ms)

IterNodesCost
0176228
1619219
22995201
35002187

prune95.0ms

Filtered
28 candidates to 20 candidates (71.4%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New27128
Fresh189
Picked011
Done000
Total281038

Merged error: 11.6b

Counts
38 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))
0.1b
(* 100.0 (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))))
0.2b
(/ (/ (* 100.0 (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))) i) (/ 1 n))
10.7b
(/ (* 100.0 (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))) i)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
6×div-inv
5×associate-/l/ associate-/l*
4×frac-2neg clear-num
3×associate-/r/ *-commutative fma-udef
1×distribute-rgt-in distribute-lft-in times-frac associate-/r*
Counts
4 → 23
Calls
4 calls:
1.0ms
(fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))
2.0ms
(* 100.0 (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))))
5.0ms
(/ (/ (* 100.0 (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))) i) (/ 1 n))
3.0ms
(/ (* 100.0 (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))) i)

series556.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))
115.0ms
(* 100.0 (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n))))
206.0ms
(/ (/ (* 100.0 (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))) i) (/ 1 n))
145.0ms
(/ (* 100.0 (fma (- 0.5 (* 0.5 (log 1.0))) (pow i 2) (fma i 1.0 (* (log 1.0) n)))) i)

simplify177.0ms

Algorithm
egg-herbie
Counts
35 → 35
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0229311
1874288
24913273
35001273

prune72.0ms

Filtered
35 candidates to 20 candidates (57.1%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New33235
Fresh178
Picked011
Done011
Total341145

Merged error: 11.6b

Counts
45 → 11

regimes136.0ms

Accuracy

66.3% (6.0b remaining)

Error of 17.0b against oracle of 11.0b and baseline of 28.8b

bsearch300.0ms

Steps
ItersRangePoint
9
8.842130359288541e+276
8.124587968450558e+285
2.3738362736714574e+285
8
7.73626891890573e+237
1.8079044960271525e+241
3.509593677294075e+238
7
3.3738295839295406e-08
2.5653698016906928e-06
2.5190799162811194e-06
10
-0.0748897710117716
-1.528326527761479e-12
-0.007772809334100071

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05841
15841

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.1s2952×body1280valid
1.8s956×body2560valid
562.0ms1817×body640valid
155.0ms893×body320valid
114.0ms2419×body80valid
83.0ms2225×body80nan
45.0ms412×body160valid
8.0ms2×body5120valid