Details

Time bar (total: 16.9s)

sample169.0ms

Algorithm
intervals
Results
70.0ms33×body2560valid
57.0ms85×body1280valid
13.0ms46×body640valid
5.0ms113×body80valid
4.0ms27×body320valid
3.0ms1×body5120valid
2.0ms63×body80nan
1.0ms9×body160valid

simplify41.0ms

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: 40.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.6b
(pow (+ 1.0 (/ i n)) n)
12.1b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite873.0ms

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:
322.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
186.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
328.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
339.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
229.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
190.0ms
(pow (+ 1.0 (/ i n)) n)
324.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify68.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune793.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.6b
(pow (+ 1.0 (/ i n)) n)
4.6b
(pow (+ 1.0 (/ i n)) n)
4.6b
(pow (+ 1.0 (/ i n)) n)

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×add-sqr-sqrt
29×unpow-prod-down
26×add-cube-cbrt
24×prod-diff
9×pow-unpow
8×fma-neg sqr-pow
7×pow1 add-exp-log distribute-lft-out
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow-to-exp pow-pow pow-exp difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 110
Calls
4 calls:
189.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
18.0ms
(pow (+ 1.0 (/ i n)) n)
20.0ms
(pow (+ 1.0 (/ i n)) n)

series831.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
204.0ms
(pow (+ 1.0 (/ i n)) n)
196.0ms
(pow (+ 1.0 (/ i n)) n)
197.0ms
(pow (+ 1.0 (/ i n)) n)

simplify150.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 3 (134.0ms)

IterNodesCost
0277905
1898707
24735678
35001657

prune360.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.9b

localize14.0ms

Local error

Found 4 expressions with local error:

3.7b
(cbrt (+ 1.0 (/ i n)))
3.7b
(cbrt (+ 1.0 (/ i n)))
3.7b
(cbrt (+ 1.0 (/ i n)))
12.1b
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
55×*-un-lft-identity
49×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
12×cbrt-prod
9×add-exp-log add-cbrt-cube
6×cbrt-div
5×div-inv
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ pow1/3 div-exp flip-+ distribute-lft-out associate-/l*
1×frac-2neg clear-num associate-/r/
Counts
4 → 120
Calls
4 calls:
8.0ms
(cbrt (+ 1.0 (/ i n)))
8.0ms
(cbrt (+ 1.0 (/ i n)))
8.0ms
(cbrt (+ 1.0 (/ i n)))
9.0ms
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))

series1.4s

Counts
4 → 12
Calls
4 calls:
235.0ms
(cbrt (+ 1.0 (/ i n)))
223.0ms
(cbrt (+ 1.0 (/ i n)))
232.0ms
(cbrt (+ 1.0 (/ i n)))
702.0ms
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))

simplify67.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05522490
120712369
250022335

prune493.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
4.6b
(pow (+ 1.0 (/ i n)) (* 2 n))
4.6b
(pow (+ 1.0 (/ i n)) n)
12.1b
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite675.0ms

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:
130.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
18.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
17.0ms
(pow (+ 1.0 (/ i n)) n)
481.0ms
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series2.5s

Counts
4 → 12
Calls
4 calls:
242.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
201.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
202.0ms
(pow (+ 1.0 (/ i n)) n)
1.8s
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify118.0ms

Algorithm
egg-herbie
Counts
422 → 422
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0188610118
150019695

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.9b

regimes229.0ms

Accuracy

46.2% (11.0b remaining)

Error of 32.9b against oracle of 21.8b and baseline of 42.3b

bsearch796.0ms

Steps
ItersRangePoint
11
9.114942375872904
1.7627780978962467e+26
9.279004486906034
2
-3.7772777444549045e-293
-3.4254484264047055e-293
-3.6453417501860803e-293
6
-5.437880838921468e-241
-8.799282718950662e-242
-1.0190934966261474e-241
9
-2.9824033774138834e-226
-2.6435658756109646e-232
-2.8828508567879816e-226
8
-4.738015710750703e-202
-1.9291273829153054e-206
-1.9646845915022113e-206
8
-0.0004774284186052567
-4.58106554975698e-07
-0.0004726437827530885

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
092153
192153

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.9s1003×body2560valid
1.7s2393×body1280valid
476.0ms1614×body640valid
152.0ms902×body320valid
141.0ms3211×body80valid
71.0ms2265×body80nan
42.0ms410×body160valid
26.0ms7×body5120valid