Details

Time bar (total: 14.6s)

sample173.0ms

Algorithm
intervals
Results
62.0ms73×body1280valid
52.0ms24×body2560valid
23.0ms53×body640valid
9.0ms30×body320valid
8.0ms108×body80valid
4.0ms72×body80nan
2.0ms15×body160valid

simplify42.0ms

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: 42.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.5b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
9.0b
(pow (+ 1.0 (/ i n)) n)

rewrite618.0ms

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:
231.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
129.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
227.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
12.0ms
(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts
4 → 12
Calls
4 calls:
360.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
247.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
343.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
207.0ms
(pow (+ 1.0 (/ i n)) n)

simplify64.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013193734
150013446

prune874.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.0b

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))
1.5b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
9.0b
(pow (+ 1.0 (/ i n)) n)

rewrite629.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
330×add-sqr-sqrt
230×*-un-lft-identity
162×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
49×add-exp-log
48×unpow-prod-down
33×sqr-pow
30×add-cbrt-cube
28×distribute-lft-out--
24×prod-diff
23×div-exp
18×div-inv
13×associate-*l* associate-/r*
12×cbrt-undiv
10×prod-exp
8×fma-neg unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
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
Counts
4 → 350
Calls
4 calls:
246.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
224.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
129.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.1s

Counts
4 → 12
Calls
4 calls:
355.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
289.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
242.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
208.0ms
(pow (+ 1.0 (/ i n)) n)

simplify73.0ms

Algorithm
egg-herbie
Counts
362 → 362
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015764180
150023683

prune791.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.5 (pow i 2) (* (log 1.0) n))
4.2b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n))
13.6b
(* (/ 100.0 i) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
14.1b
(* (pow i 2) (log 1.0))

rewrite50.0ms

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
7×pow1 cbrt-unprod
6×log-prod
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp associate-/l*
2×associate-/r/ *-commutative unpow2 sqr-pow
1×frac-times pow-to-exp frac-2neg associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num log-pow fma-udef
Counts
4 → 215
Calls
4 calls:
0.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
5.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n))
28.0ms
(* (/ 100.0 i) (/ (fma i 1.0 (- (fma 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))

series564.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
151.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n))
217.0ms
(* (/ 100.0 i) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
138.0ms
(* (pow i 2) (log 1.0))

simplify64.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09663799
150013400

prune747.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.5b

localize21.0ms

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))))) n) (/ 1 i)))
4.1b
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
13.5b
(* (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n) (/ 1 i))
14.1b
(* (pow i 2) (log 1.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
65×add-exp-log
38×add-cbrt-cube
37×prod-exp
27×add-sqr-sqrt
21×pow1 associate-*r*
19×add-cube-cbrt *-un-lft-identity cbrt-unprod
15×associate-*l*
10×pow-prod-down
9×times-frac
8×div-exp
6×log-prod
5×unswap-sqr
4×cbrt-undiv expm1-log1p-u unpow-prod-down rec-exp 1-exp associate-*r/ *-commutative log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×un-div-inv unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow div-inv
Counts
4 → 129
Calls
4 calls:
23.0ms
(* 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) (/ 1 i)))
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)
10.0ms
(* (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n) (/ 1 i))
7.0ms
(* (pow i 2) (log 1.0))

series714.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(* 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) (/ 1 i)))
154.0ms
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
196.0ms
(* (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n) (/ 1 i))
144.0ms
(* (pow i 2) (log 1.0))

simplify84.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05871937
127781534
250011521

prune338.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 12.5b

regimes196.0ms

Accuracy

40.1% (13.3b remaining)

Error of 24.4b against oracle of 11.1b and baseline of 33.3b

bsearch349.0ms

Steps
ItersRangePoint
7
3.08233935006482e-177
4.6633733187569337e-175
1.0241992467778217e-176
7
2.485172904982384e-300
3.7216408253122465e-298
2.527653028095778e-300
9
-4.678446177901538e+200
-3.5200299588200005e+195
-3.5588588888448117e+195

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06975
16975

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.1s2457×body1280valid
2.1s1010×body2560valid
702.0ms1666×body640valid
224.0ms855×body320valid
218.0ms2987×body80valid
124.0ms2284×body80nan
75.0ms461×body160valid
30.0ms8×body5120valid