Details

Time bar (total: 11.9s)

sample166.0ms

Algorithm
intervals
Results
67.0ms32×body2560valid
61.0ms88×body1280valid
13.0ms45×body640valid
4.0ms94×body80valid
4.0ms24×body320valid
3.0ms90×body80nan
2.0ms15×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.6b
(pow (+ 1.0 (/ i n)) n)
9.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite611.0ms

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:
228.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
127.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
223.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
350.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
239.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
202.0ms
(pow (+ 1.0 (/ i n)) n)
332.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify62.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune873.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.4b

localize16.0ms

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)))
9.9b
(* (pow i 2) (log 1.0))
17.4b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite38.0ms

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:
0.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
18.0ms
(* 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)))
7.0ms
(* (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))

series641.0ms

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)))))
215.0ms
(* 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)))
136.0ms
(* (pow i 2) (log 1.0))
194.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify127.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07343209
137502968
250012968

prune745.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 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))
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)
9.4b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
9.9b
(* (pow i 2) (log 1.0))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
22×add-cbrt-cube
20×associate-*r*
19×times-frac
12×pow1 associate-*l*
10×prod-exp
8×cbrt-unprod
6×log-prod 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 div-exp associate-/r* *-commutative associate-/l*
2×associate-*r/ div-inv unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*l/ pow-exp clear-num log-pow
Counts
4 → 122
Calls
4 calls:
7.0ms
(* 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))
15.0ms
(* (* 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)
2.0ms
(/ (fma i 1.0 (- (fma 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))

series660.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* 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))
222.0ms
(* (* 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)
137.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
144.0ms
(* (pow i 2) (log 1.0))

simplify74.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
04881787
123721525
250021522

prune437.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 11.3b

localize17.0ms

Local error

Found 4 expressions with local error:

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))))))
2.5b
(* (* 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)
9.9b
(* (pow i 2) (log 1.0))
13.2b
(/ (* (* 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) i)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
22×add-sqr-sqrt add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity
12×pow1 associate-*l*
10×associate-*r* prod-exp
8×cbrt-unprod
6×log-prod
5×unswap-sqr
4×distribute-rgt-in expm1-log1p-u unpow-prod-down distribute-lft-in pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp associate-/r* *-commutative
2×fma-udef unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow div-inv associate-/l*
Counts
4 → 103
Calls
4 calls:
3.0ms
(* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
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)
6.0ms
(* (pow i 2) (log 1.0))
7.0ms
(/ (* (* 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)

series618.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
158.0ms
(* (* 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)
137.0ms
(* (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)

simplify73.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
04511430
125021162
250011159

prune303.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.3b

regimes294.0ms

Accuracy

47.5% (12.1b remaining)

Error of 22.6b against oracle of 10.5b and baseline of 33.6b

bsearch299.0ms

Steps
ItersRangePoint
11
3.4015986104447535e-172
7.536207518846309e-153
1.6252547660245352e-162
5
1.297677126524779e-204
2.9494229738237948e-204
2.918972662683953e-204
8
-1.3829131679288303e-259
-6.98766638603121e-263
-8.483643462012967e-263
5
-1.3050201109302798e+106
-3.910903516244074e+105
-3.9724448286356644e+105

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06955
16955

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s2542×body1280valid
1.7s951×body2560valid
455.0ms1561×body640valid
137.0ms832×body320valid
131.0ms3077×body80valid
70.0ms2295×body80nan
47.0ms466×body160valid
17.0ms4×body5120valid