Details

Time bar (total: 1.1m)

sample146.0ms

Algorithm
intervals
Results
60.0ms32×body2560valid
46.0ms75×body1280valid
10.0ms40×body640valid
7.0ms108×body80valid
5.0ms36×body320valid
3.0ms83×body80nan
2.0ms18×body160valid

simplify39.0ms

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: 39.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.3b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b
(pow (+ 1.0 (/ i n)) n)
11.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite649.0ms

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:
244.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
136.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
13.0ms
(pow (+ 1.0 (/ i n)) n)
234.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts
4 → 12
Calls
4 calls:
347.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
231.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
223.0ms
(pow (+ 1.0 (/ i n)) n)
513.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013193734
150023446

prune847.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.8b

localize15.0ms

Local error

Found 4 expressions with local error:

2.2b
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
5.8b
(pow (+ 1.0 (/ i n)) n)
11.4b
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite515.0ms

Algorithm
rewrite-expression-head
Rules
717×times-frac
528×*-un-lft-identity
296×add-sqr-sqrt add-cube-cbrt
116×distribute-lft-out
38×div-inv
29×associate-/r/
22×associate-/l*
18×add-exp-log
16×add-cbrt-cube
15×flip3-+ flip-+
13×associate-/r*
12×unpow-prod-down
8×cbrt-undiv fma-def div-exp add-log-exp
6×pow1 div-sub
4×expm1-log1p-u pow-unpow log1p-expm1-u
3×sqr-pow
2×neg-sub0 pow-to-exp associate-+r- pow-pow unsub-neg pow-exp sum-log
1×+-commutative frac-2neg neg-log clear-num associate-/l/
Counts
4 → 410
Calls
4 calls:
94.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
12.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
12.0ms
(pow (+ 1.0 (/ i n)) n)
368.0ms
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series2.6s

Counts
4 → 12
Calls
4 calls:
259.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
221.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
204.0ms
(pow (+ 1.0 (/ i n)) n)
2.0s
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify127.0ms

Algorithm
egg-herbie
Counts
422 → 422
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0188610118
150019695

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.8b

localize31.0ms

Local error

Found 4 expressions with local error:

5.8b
(pow (+ 1.0 (/ i n)) n)
5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
11.4b
(/ (/ (/ (+ (pow (pow (+ 1.0 (/ i n)) (* 2 n)) 3) (pow (- (* 1.0 1.0)) 3)) (fma (- (* 1.0 1.0)) (- (- (* 1.0 1.0)) (pow (+ 1.0 (/ i n)) (* 2 n))) (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite943.0ms

Algorithm
rewrite-expression-head
Rules
6117×times-frac
4655×*-un-lft-identity
2101×add-sqr-sqrt add-cube-cbrt
1277×distribute-lft-out
684×unpow-prod-down
672×cube-prod
202×div-inv
168×sum-cubes
130×associate-/l*
29×associate-/r/
28×add-exp-log
25×add-cbrt-cube
15×cbrt-undiv div-exp
14×flip3-+ flip-+
13×associate-/r*
7×pow1
6×div-sub
5×pow-unpow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
2×cube-neg
1×frac-2neg unsub-neg clear-num associate-/l/
Counts
4 → 1917
Calls
4 calls:
12.0ms
(pow (+ 1.0 (/ i n)) n)
12.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
12.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
653.0ms
(/ (/ (/ (+ (pow (pow (+ 1.0 (/ i n)) (* 2 n)) 3) (pow (- (* 1.0 1.0)) 3)) (fma (- (* 1.0 1.0)) (- (- (* 1.0 1.0)) (pow (+ 1.0 (/ i n)) (* 2 n))) (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series44.6s

Counts
4 → 12
Calls
4 calls:
196.0ms
(pow (+ 1.0 (/ i n)) n)
205.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
205.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
44.0s
(/ (/ (/ (+ (pow (pow (+ 1.0 (/ i n)) (* 2 n)) 3) (pow (- (* 1.0 1.0)) 3)) (fma (- (* 1.0 1.0)) (- (- (* 1.0 1.0)) (pow (+ 1.0 (/ i n)) (* 2 n))) (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify913.0ms

Algorithm
egg-herbie
Counts
1929 → 1929
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
05001114779

prune4.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.8b

localize41.0ms

Local error

Found 4 expressions with local error:

5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
16×unpow-prod-down *-un-lft-identity
8×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt
4×expm1-log1p-u pow-to-exp pow-unpow pow-pow pow-exp add-cbrt-cube log1p-expm1-u distribute-lft-out add-log-exp sqr-pow
Counts
4 → 72
Calls
4 calls:
11.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
11.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
12.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
15.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))

series949.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
193.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
195.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
367.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))

simplify48.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0121528
1412508
21729504
35001504

prune594.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.8b

regimes163.0ms

Accuracy

45.2% (11.9b remaining)

Error of 33.3b against oracle of 21.4b and baseline of 43.0b

bsearch845.0ms

Steps
ItersRangePoint
7
8.639792360287736e-11
7.241082556785e-09
7.147085067578077e-09
7
2.7499475250696328e-134
7.422960692703227e-133
2.8738884927185156e-134
6
8.896230187054732e-198
8.190807967914936e-197
8.057002382378186e-197
9
2.78333567540328e-277
5.2293129153053376e-272
1.6479702105467177e-275
7
-3.2963305767896758e-273
-9.078934504337964e-275
-1.1313305452296457e-274
10
-1530624.207495954
-2.4048977341445043e-11
-1.2132993654259578

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0109257
1112257
2115257
3115257

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.7s961×body2560valid
1.7s2501×body1280valid
437.0ms1585×body640valid
138.0ms885×body320valid
125.0ms3123×body80valid
71.0ms2336×body80nan
46.0ms457×body160valid
13.0ms4×body5120valid