Details

Time bar (total: 16.8s)

sample168.0ms

Algorithm
intervals
Results
67.0ms33×body2560valid
57.0ms85×body1280valid
13.0ms46×body640valid
5.0ms113×body80valid
4.0ms27×body320valid
3.0ms1×body5120valid
2.0ms63×body80nan
1.0ms9×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.1b

localize9.0ms

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))

rewrite893.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
289×add-sqr-sqrt
198×*-un-lft-identity
140×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
32×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
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 distribute-lft-out
Counts
4 → 281
Calls
4 calls:
356.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
171.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms
(pow (+ 1.0 (/ i n)) n)
327.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts
4 → 12
Calls
4 calls:
529.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
224.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
198.0ms
(pow (+ 1.0 (/ i n)) n)
317.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify62.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012263285
150013166

prune794.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.9b

localize16.0ms

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)

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
15×add-sqr-sqrt
13×unpow-prod-down
10×add-cube-cbrt
9×pow-unpow
7×pow1 add-exp-log
6×add-log-exp
4×add-cbrt-cube sqr-pow
3×pow-to-exp pow-pow pow-exp distribute-lft-out difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 70
Calls
4 calls:
171.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms
(pow (+ 1.0 (/ i n)) n)
20.0ms
(pow (+ 1.0 (/ i n)) n)
21.0ms
(pow (+ 1.0 (/ i n)) n)

series810.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
193.0ms
(pow (+ 1.0 (/ i n)) n)
195.0ms
(pow (+ 1.0 (/ i n)) n)
195.0ms
(pow (+ 1.0 (/ i n)) n)

simplify64.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0192470
1556461
22075455
35001449

prune276.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (log (exp (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)

rewrite592.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
13×add-sqr-sqrt
12×unpow-prod-down
11×add-cube-cbrt
9×pow-unpow
8×pow1
7×add-exp-log
5×add-log-exp
4×add-cbrt-cube
3×pow-to-exp log-prod pow-pow pow-exp associate--l+ distribute-lft-out sqr-pow
2×distribute-lft-out--
1×sub-neg flip3-- diff-log log-pow flip-- difference-of-squares
Counts
4 → 72
Calls
4 calls:
531.0ms
(- (log (exp (pow (+ 1.0 (/ i n)) n))) 1.0)
22.0ms
(pow (+ 1.0 (/ i n)) n)
19.0ms
(pow (+ 1.0 (/ i n)) n)
19.0ms
(pow (+ 1.0 (/ i n)) n)

series800.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(- (log (exp (pow (+ 1.0 (/ i n)) n))) 1.0)
190.0ms
(pow (+ 1.0 (/ i n)) n)
190.0ms
(pow (+ 1.0 (/ i n)) n)
193.0ms
(pow (+ 1.0 (/ i n)) n)

simplify63.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
0201511
1573474
22094468
35001462

prune339.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.9b

localize16.0ms

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))

rewrite724.0ms

Algorithm
rewrite-expression-head
Rules
717×times-frac
524×*-un-lft-identity
294×add-sqr-sqrt add-cube-cbrt
115×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*
8×cbrt-undiv unpow-prod-down div-exp add-log-exp
6×pow1 div-sub
4×pow-unpow
2×neg-sub0 pow-to-exp associate-+r- pow-pow unsub-neg pow-exp sum-log sqr-pow
1×+-commutative frac-2neg neg-log clear-num associate-/l/
Counts
4 → 394
Calls
4 calls:
126.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
20.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
19.0ms
(pow (+ 1.0 (/ i n)) n)
526.0ms
(/ (/ (+ (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:
250.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
204.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
203.0ms
(pow (+ 1.0 (/ i n)) n)
1.9s
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify121.0ms

Algorithm
egg-herbie
Counts
406 → 406
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0186410059
150029637

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.9b

regimes231.0ms

Accuracy

46.3% (11.0b remaining)

Error of 32.9b against oracle of 21.9b and baseline of 42.4b

bsearch828.0ms

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

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0112164
1116164
2117164
3117164

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.9s1003×body2560valid
1.7s2393×body1280valid
464.0ms1614×body640valid
150.0ms902×body320valid
136.0ms3211×body80valid
70.0ms2265×body80nan
43.0ms410×body160valid
26.0ms7×body5120valid