Details

Time bar (total: 6.9m)

sample147.0ms

Algorithm
intervals
Results
55.0ms78×body1280valid
46.0ms24×body2560valid
15.0ms57×body640valid
5.0ms32×body320valid
4.0ms97×body80valid
3.0ms1×body5120valid
2.0ms57×body80nan
2.0ms15×body160valid

simplify40.0ms

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: 42.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0b
(pow (+ 1.0 (/ i n)) n)
8.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite907.0ms

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:
338.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
193.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms
(pow (+ 1.0 (/ i n)) n)
335.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
367.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
252.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
222.0ms
(pow (+ 1.0 (/ i n)) n)
351.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify60.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune926.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
7.0b
(pow (+ 1.0 (/ i n)) n)
7.0b
(pow (+ 1.0 (/ i n)) (* 2 n))
8.7b
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite705.0ms

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:
137.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
18.0ms
(pow (+ 1.0 (/ i n)) n)
18.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
503.0ms
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series2.9s

Counts
4 → 12
Calls
4 calls:
256.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
216.0ms
(pow (+ 1.0 (/ i n)) n)
221.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
2.2s
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify117.0ms

Algorithm
egg-herbie
Counts
422 → 422
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0188610118
150019695

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize26.0ms

Local error

Found 4 expressions with local error:

7.0b
(pow (+ 1.0 (/ i n)) n)
7.0b
(pow (+ 1.0 (/ i n)) (* 2 n))
7.0b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
8.7b
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (- (* 1.0 1.0)) (- (* 1.0 1.0))))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite945.0ms

Algorithm
rewrite-expression-head
Rules
3405×times-frac
2121×*-un-lft-identity
1275×add-sqr-sqrt add-cube-cbrt
423×distribute-lft-out
150×div-inv
141×associate-/r/
78×associate-/l*
70×flip3-+ flip-+
28×add-exp-log
25×add-cbrt-cube
15×cbrt-undiv div-exp
13×associate-/r*
12×unpow-prod-down
9×div-sub
7×pow1
5×pow-unpow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
1×neg-sub0 associate-+r- frac-2neg unsub-neg clear-num associate-/l/
Counts
4 → 1190
Calls
4 calls:
20.0ms
(pow (+ 1.0 (/ i n)) n)
18.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
19.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
760.0ms
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (- (* 1.0 1.0)) (- (* 1.0 1.0))))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series15.5s

Counts
4 → 12
Calls
4 calls:
214.0ms
(pow (+ 1.0 (/ i n)) n)
212.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
220.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
14.8s
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (- (* 1.0 1.0)) (- (* 1.0 1.0))))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify608.0ms

Algorithm
egg-herbie
Counts
1202 → 1202
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
0500157884

prune3.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize31.0ms

Local error

Found 4 expressions with local error:

7.0b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
7.0b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
7.0b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
7.5b
(/ (/ i n) (cbrt (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (- (* 1.0 1.0)) (- (* 1.0 1.0))))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))))

rewrite630.0ms

Algorithm
rewrite-expression-head
Rules
3471×times-frac
2155×*-un-lft-identity
1309×add-sqr-sqrt add-cube-cbrt
1092×cbrt-prod
423×distribute-lft-out
153×div-inv
141×associate-/r/
81×associate-/r*
70×flip3-+ flip-+
13×associate-/l*
12×add-exp-log unpow-prod-down
7×pow1 add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv pow-to-exp pow-unpow pow-pow div-exp pow-exp sqr-pow
1×cbrt-div frac-2neg clear-num associate-/l/
Counts
4 → 1219
Calls
4 calls:
19.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
19.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
18.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
438.0ms
(/ (/ i n) (cbrt (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (- (* 1.0 1.0)) (- (* 1.0 1.0))))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))))

series6.2m

Counts
4 → 12
Calls
4 calls:
206.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
209.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
206.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
6.2m
(/ (/ i n) (cbrt (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (- (* 1.0 1.0)) (- (* 1.0 1.0))))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))))

simplify503.0ms

Algorithm
egg-herbie
Counts
1231 → 1231
Iterations

Useful iterations: 1 (49.0ms)

IterNodesCost
0377063110
1500163015

prune5.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

regimes135.0ms

Accuracy

48% (11.0b remaining)

Error of 32.7b against oracle of 21.7b and baseline of 42.9b

bsearch387.0ms

Steps
ItersRangePoint
9
4.0934292270240455e-202
7.54522698597779e-194
1.4804598641216222e-197
10
1.7737628767255715e-237
1.519103788223036e-224
1.49643453067125e-224
9
-1.4303290161078484e-293
-8.576442143435e-299
-8.67638754664335e-297
7
-4.3463433571433286e+38
-9.263934665448618e+36
-4.096260797826322e+37
2
-1.0374203462869247e+178
-8.775060660017807e+177
-8.974953510374238e+177

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0108174
1122174
2135174
3152174
4153174
5153174

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s1003×body2560valid
1.6s2404×body1280valid
432.0ms1632×body640valid
140.0ms916×body320valid
121.0ms3049×body80valid
67.0ms2253×body80nan
46.0ms442×body160valid
32.0ms9×body5120valid