Details

Time bar (total: 13.6s)

sample181.0ms

Algorithm
intervals
Results
69.0ms78×body1280valid
61.0ms25×body2560valid
19.0ms53×body640valid
9.0ms45×body320valid
4.0ms84×body80valid
4.0ms89×body80nan
1.0ms12×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize9.0ms

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))

rewrite673.0ms

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:
233.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
182.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
228.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.4s

Counts
4 → 12
Calls
4 calls:
360.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
256.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
407.0ms
(pow (+ 1.0 (/ i n)) n)
348.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013193734
150023446

prune853.0ms

Filtered
333 candidates to 242 candidates (72.7%)
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)

rewrite647.0ms

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:
228.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
252.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
133.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts
4 → 12
Calls
4 calls:
305.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
378.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
254.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
217.0ms
(pow (+ 1.0 (/ i n)) n)

simplify74.0ms

Algorithm
egg-herbie
Counts
362 → 362
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
015764180
150013683

prune824.0ms

Filtered
362 candidates to 229 candidates (63.3%)
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
(fma 0.5 (pow i 2) (* (log 1.0) n))
1.4b
(/ (fma i 1.0 (- (fma 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) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))

rewrite56.0ms

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))
7.0ms
(* (pow i 2) (log 1.0))
33.0ms
(* (/ 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)))

series595.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(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))
145.0ms
(* (pow i 2) (log 1.0))
229.0ms
(* (/ 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)))

simplify131.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09653799
149503397
250013397

prune757.0ms

Filtered
227 candidates to 152 candidates (67.0%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.6b

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)))))) i) n)
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))))))
9.9b
(/ (* 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)
10.1b
(* (pow i 2) (log 1.0))

rewrite30.0ms

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×log-prod times-frac unswap-sqr
4×cbrt-undiv distribute-rgt-in expm1-log1p-u unpow-prod-down distribute-lft-in div-exp log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
2×pow-prod-down fma-udef div-inv 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:
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)
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))))))
4.0ms
(/ (* 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)
7.0ms
(* (pow i 2) (log 1.0))

series640.0ms

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)))))) i) n)
124.0ms
(* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
153.0ms
(/ (* 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)
143.0ms
(* (pow i 2) (log 1.0))

simplify69.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04661519
123141249
250011249

prune333.0ms

Filtered
122 candidates to 80 candidates (65.6%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.6b

regimes180.0ms

Accuracy

47% (11.8b remaining)

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

bsearch280.0ms

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
05747
15747

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s983×body2560valid
1.7s2440×body1280valid
468.0ms1636×body640valid
156.0ms946×body320valid
120.0ms2897×body80valid
73.0ms2306×body80nan
43.0ms428×body160valid
18.0ms5×body5120valid