Details

Time bar (total: 16.8s)

sample156.0ms

Algorithm
intervals
Results
72.0ms38×body2560valid
48.0ms67×body1280valid
11.0ms43×body640valid
5.0ms32×body320valid
4.0ms102×body80valid
2.0ms74×body80nan
1.0ms15×body160valid

simplify44.0ms

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: 38.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.3b
(pow (+ 1.0 (/ i n)) n)
12.1b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite622.0ms

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:
234.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
130.0ms
(- (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))

series1.2s

Counts
4 → 12
Calls
4 calls:
439.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
248.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
204.0ms
(pow (+ 1.0 (/ i n)) n)
352.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify68.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013193734
150023446

prune825.0ms

Filtered
333 candidates to 242 candidates (72.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
0.1b
(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
1.6b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.3b
(pow (+ 1.0 (/ i n)) n)

rewrite717.0ms

Algorithm
rewrite-expression-head
Rules
1689×times-frac
1113×add-sqr-sqrt
854×*-un-lft-identity
678×add-cube-cbrt
330×associate-*r*
246×difference-of-squares
102×unpow-prod-down
87×sqr-pow
82×distribute-lft-out--
80×div-inv
59×add-exp-log
34×add-cbrt-cube
32×div-exp
25×associate-/l*
24×prod-diff
16×cbrt-undiv
13×associate-/r*
9×prod-exp
8×fma-neg
7×pow1 unswap-sqr
6×add-log-exp
5×cbrt-unprod distribute-lft-out
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u
3×pow-unpow associate-*l*
2×div-sub associate-/r/
1×pow-to-exp sub-neg flip3-- pow-pow frac-2neg diff-log associate-*r/ pow-prod-down pow-exp clear-num *-commutative flip-- associate-/l/
Counts
4 → 826
Calls
4 calls:
300.0ms
(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
192.0ms
(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
131.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts
4 → 12
Calls
4 calls:
366.0ms
(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
344.0ms
(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
249.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
205.0ms
(pow (+ 1.0 (/ i n)) n)

simplify167.0ms

Algorithm
egg-herbie
Counts
838 → 838
Iterations

Useful iterations: 1 (60.0ms)

IterNodesCost
0323611841
1500111227

prune2.0s

Filtered
838 candidates to 524 candidates (62.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.0b

localize16.0ms

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) (/ 1 n)))
0.2b
(/ (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) (/ 1 n))
11.2b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
11.9b
(* (pow i 2) (log 1.0))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
846×times-frac
428×add-sqr-sqrt
399×*-un-lft-identity
397×add-cube-cbrt
178×associate-*r*
65×add-exp-log
57×div-inv
38×add-cbrt-cube
33×div-exp
17×cbrt-undiv
16×associate-/r* associate-/l*
12×prod-exp
11×associate-*l* unswap-sqr
7×pow1
6×log-prod cbrt-unprod
4×expm1-log1p-u unpow-prod-down rec-exp 1-exp log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×frac-2neg clear-num associate-/r/ *-commutative unpow2 sqr-pow
1×pow-to-exp associate-*r/ pow-prod-down pow-exp log-pow associate-/l/
Counts
4 → 496
Calls
4 calls:
58.0ms
(* 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) (/ 1 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))))) i) (/ 1 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))

series690.0ms

Counts
4 → 12
Calls
4 calls:
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) (/ 1 n)))
202.0ms
(/ (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) (/ 1 n))
135.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
139.0ms
(* (pow i 2) (log 1.0))

simplify133.0ms

Algorithm
egg-herbie
Counts
508 → 508
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0201610576
150029933

prune1.7s

Filtered
508 candidates to 336 candidates (66.1%)
Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.0b

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))))) i) n)
0.1b
(* (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n) 100.0)
11.2b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
11.9b
(* (pow i 2) (log 1.0))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
22×associate-*l* add-cbrt-cube
19×times-frac
12×pow1
10×associate-*r* 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-*l/ associate-/r* *-commutative associate-/l*
2×div-inv unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow
Counts
4 → 122
Calls
4 calls:
7.0ms
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
12.0ms
(* (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n) 100.0)
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)
7.0ms
(* (pow i 2) (log 1.0))

series699.0ms

Counts
4 → 12
Calls
4 calls:
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)
222.0ms
(* (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n) 100.0)
143.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
140.0ms
(* (pow i 2) (log 1.0))

simplify66.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04771779
120401510
250011503

prune394.0ms

Filtered
134 candidates to 92 candidates (68.7%)
Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 7.0b

regimes429.0ms

Accuracy

51.4% (10.8b remaining)

Error of 21.7b against oracle of 10.9b and baseline of 33.2b

bsearch592.0ms

Steps
ItersRangePoint
8
4.857585983193909e-119
1.2526148682615025e-114
6.931508871390016e-118
9
-64698196.670160554
-0.37949367736095085
-1.4720208733212128
7
-1117730599.3323822
-64698196.670160554
-1052610260.2415111
8
-1.6575157961979843e+24
-2.0257957255525243e+20
-2.7376334279782315e+20
5
-1.155399601105498e+98
-5.129643794534772e+97
-1.0664791814828006e+98
10
-7.67426779176068e+146
-2.077318348352935e+129
-8.254710623414133e+133

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07787
18187
28187

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.9s1000×body2560valid
1.7s2443×body1280valid
640.0ms1551×body640valid
140.0ms883×body320valid
132.0ms3144×body80valid
73.0ms2296×body80nan
45.0ms445×body160valid
33.0ms9×body5120valid