Details

Time bar (total: 13.1s)

sample198.0ms

Algorithm
intervals
Results
78.0ms93×body1280valid
69.0ms33×body2560valid
21.0ms53×body640valid
8.0ms29×body320valid
6.0ms83×body80valid
3.0ms66×body80nan
2.0ms17×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

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: 48.0b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.5b
(pow (+ 1.0 (/ i n)) n)
10.9b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
305×add-sqr-sqrt
222×*-un-lft-identity
156×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
48×unpow-prod-down
33×sqr-pow
28×distribute-lft-out--
24×prod-diff
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
8×fma-neg
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
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
Counts
4 → 321
Calls
4 calls:
33.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms
(pow (+ 1.0 (/ i n)) n)
16.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts
4 → 12
Calls
4 calls:
489.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
248.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
210.0ms
(pow (+ 1.0 (/ i n)) n)
342.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify69.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune706.0ms

Filtered
333 candidates to 242 candidates (72.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New3276333
Fresh000
Picked101
Done000
Total3286334

Merged error: 19.8b

Counts
334 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
0.1b
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
12.4b
(* (pow i 2) (log 1.0))
20.1b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite33.0ms

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
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ pow-prod-down pow-exp clear-num log-pow fma-udef
Counts
4 → 186
Calls
4 calls:
1.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
13.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 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))
5.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series627.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
214.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
132.0ms
(* (pow i 2) (log 1.0))
186.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify116.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07343209
137502968
250012968

prune671.0ms

Filtered
198 candidates to 152 candidates (76.8%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New18612198
Fresh145
Picked101
Done000
Total18816204

Merged error: 8.5b

Counts
204 → 16

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
0.1b
(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
11.7b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
12.4b
(* (pow i 2) (log 1.0))

rewrite18.0ms

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
8×prod-exp
6×log-prod cbrt-unprod
5×associate-*r*
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* associate-/l*
2×cbrt-undiv div-exp *-commutative unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ associate-*l/ pow-exp clear-num log-pow fma-udef div-inv
Counts
4 → 98
Calls
4 calls:
1.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
6.0ms
(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
3.0ms
(/ (fma i 1.0 (- (fma 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))

series573.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
207.0ms
(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
138.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
135.0ms
(* (pow i 2) (log 1.0))

simplify63.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04061369
117341164
250031157

prune307.0ms

Filtered
110 candidates to 74 candidates (67.3%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1082110
Fresh31215
Picked011
Done000
Total11115126

Merged error: 8.5b

Counts
126 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n))
3.8b
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
12.4b
(* (pow i 2) (log 1.0))
14.3b
(/ (* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)) i)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
22×add-sqr-sqrt add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity associate-*l*
12×pow1
10×prod-exp
8×associate-*r* cbrt-unprod
6×log-prod
5×unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in times-frac div-exp associate-/r* *-commutative
2×unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow div-inv associate-/l*
Counts
4 → 101
Calls
4 calls:
5.0ms
(* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n))
3.0ms
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
6.0ms
(* (pow i 2) (log 1.0))
6.0ms
(/ (* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)) i)

series668.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n))
152.0ms
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
142.0ms
(* (pow i 2) (log 1.0))
210.0ms
(/ (* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)) i)

simplify69.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04401420
121761157
250011157

prune270.0ms

Filtered
113 candidates to 73 candidates (64.6%)
Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1112113
Fresh11213
Picked011
Done011
Total11216128

Merged error: 8.5b

Counts
128 → 16

regimes404.0ms

Accuracy

63.3% (6.6b remaining)

Error of 17.7b against oracle of 11.0b and baseline of 29.1b

bsearch797.0ms

Steps
ItersRangePoint
10
0.23207878676536348
4.21737757242384e+15
203.39871032850647
4
3.907456749990429e-214
6.094218886842199e-214
6.025882570065581e-214
9
-3.3602540314246e-239
-2.1926783248178302e-246
-3.31557411309755e-239
7
-4.2879479194182286e-190
-5.378668933057223e-192
-4.2320413708144426e-190
7
-3.4402871636077537
-0.05202343663643454
-0.9493973613575561

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07196
17196

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.4s2820×body1280valid
2.1s1012×body2560valid
708.0ms1770×body640valid
222.0ms903×body320valid
175.0ms2419×body80valid
94.0ms2124×body80nan
73.0ms465×body160valid
25.0ms6×body5120valid