Details

Time bar (total: 17.1s)

sample169.0ms

Algorithm
intervals
Results
64.0ms78×body1280valid
53.0ms24×body2560valid
20.0ms55×body640valid
7.0ms106×body80valid
6.0ms28×body320valid
3.0ms69×body80nan
2.0ms16×body160valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.2b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.2b
(pow (+ 1.0 (/ i n)) n)
8.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

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:
317.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
186.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms
(pow (+ 1.0 (/ i n)) n)
522.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
337.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
220.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
185.0ms
(pow (+ 1.0 (/ i n)) n)
315.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)))
0.0b
(* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n))
1.2b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.2b
(pow (+ 1.0 (/ i n)) n)

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
42×*-un-lft-identity
35×add-sqr-sqrt
34×add-cbrt-cube
33×prod-exp
30×add-cube-cbrt
24×prod-diff
21×unpow-prod-down
19×pow1
17×cbrt-unprod
16×associate-*l*
10×associate-*l/
9×times-frac associate-*r/ pow-prod-down
8×fma-neg div-exp
6×add-log-exp sqr-pow
5×flip3-- flip-- distribute-lft-out
4×cbrt-undiv expm1-log1p-u frac-times rec-exp 1-exp log1p-expm1-u
3×pow-unpow difference-of-squares
2×associate-*r* *-commutative
1×pow-to-exp sub-neg pow-pow diff-log pow-exp div-inv distribute-lft-out--
Counts
4 → 149
Calls
4 calls:
1.4s
(* 100.0 (* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)))
562.0ms
(* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n))
190.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)

series1.1s

Counts
4 → 12
Calls
4 calls:
329.0ms
(* 100.0 (* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)))
322.0ms
(* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n))
228.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
196.0ms
(pow (+ 1.0 (/ i n)) n)

simplify87.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07001572
133701190
250021180

prune492.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (* (/ 1 i) (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)))
2.4b
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
12.8b
(* (pow i 2) (log 1.0))
12.9b
(* (/ 1 i) (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
65×add-exp-log
38×add-cbrt-cube
37×prod-exp
27×add-sqr-sqrt associate-*l*
21×pow1
19×add-cube-cbrt *-un-lft-identity cbrt-unprod
10×pow-prod-down
9×times-frac associate-*r*
8×div-exp
6×log-prod
5×unswap-sqr
4×cbrt-undiv expm1-log1p-u unpow-prod-down rec-exp 1-exp *-commutative log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×associate-*l/ unpow2 sqr-pow
1×pow-to-exp associate-*r/ pow-exp log-pow div-inv
Counts
4 → 127
Calls
4 calls:
55.0ms
(* 100.0 (* (/ 1 i) (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)))
7.0ms
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
13.0ms
(* (pow i 2) (log 1.0))
24.0ms
(* (/ 1 i) (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n))

series638.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(* 100.0 (* (/ 1 i) (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) 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))))) n)
131.0ms
(* (pow i 2) (log 1.0))
179.0ms
(* (/ 1 i) (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n))

simplify81.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
05611912
125331513
250011505

prune631.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.2b

localize19.0ms

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
(* 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))
12.2b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
12.8b
(* (pow i 2) (log 1.0))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
24×associate-*l*
22×add-cbrt-cube
19×times-frac
12×pow1
10×prod-exp
8×associate-*r* 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-*l/ div-inv unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ pow-exp clear-num log-pow
Counts
4 → 122
Calls
4 calls:
14.0ms
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
26.0ms
(* 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))
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)
13.0ms
(* (pow i 2) (log 1.0))

series623.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
188.0ms
(* 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))
123.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
136.0ms
(* (pow i 2) (log 1.0))

simplify69.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04771789
119011520
250011513

prune699.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 12.2b

regimes314.0ms

Accuracy

44.5% (12.9b remaining)

Error of 23.7b against oracle of 10.8b and baseline of 34.1b

bsearch719.0ms

Steps
ItersRangePoint
9
1.4132788863622532e-206
3.299107912687795e-197
1.3264644651248639e-198
9
-5.1582382664008115e-229
-1.4281663542957573e-234
-1.4508071834264677e-234
9
-2.52020065333125e+99
-1.181987030892061e+91
-2.8822367339188696e+97
7
-2.2138820721712034e+132
-9.063407043561957e+130
-2.1887173671760445e+132
8
-7.242891634590126e+196
-1.3129567736428036e+194
-1.6947020516616556e+196

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06976
16976

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.9s2392×body1280valid
1.9s961×body2560valid
619.0ms1679×body640valid
200.0ms3162×body80valid
189.0ms829×body320valid
108.0ms2217×body80nan
62.0ms436×body160valid
20.0ms6×body5120valid