Details

Time bar (total: 15.8s)

sample164.0ms

Algorithm
intervals
Results
61.0ms32×body2560valid
61.0ms83×body1280valid
15.0ms56×body640valid
5.0ms26×body320valid
4.0ms92×body80valid
2.0ms61×body80nan
2.0ms16×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: 44.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.9b
(pow (+ 1.0 (/ i n)) n)
10.9b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite822.0ms

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:
329.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
159.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
300.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
376.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
254.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
215.0ms
(pow (+ 1.0 (/ i n)) n)
360.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify55.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012263285
150013166

prune803.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
0.0b
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
1.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.9b
(pow (+ 1.0 (/ i n)) n)

rewrite839.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
29×*-un-lft-identity
28×associate-*r*
22×times-frac
19×add-exp-log add-cube-cbrt
18×add-cbrt-cube
12×pow1 difference-of-squares
8×unpow-prod-down
7×prod-exp cbrt-unprod
6×add-log-exp
5×sqr-pow
4×associate-*l* pow-prod-down distribute-lft-out--
3×pow-unpow
2×cbrt-undiv associate-*r/ div-exp *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log associate-*l/ pow-exp flip-- div-inv distribute-lft-out
Counts
4 → 99
Calls
4 calls:
307.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
353.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
158.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)

series1.0s

Counts
4 → 12
Calls
4 calls:
159.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
379.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
260.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
224.0ms
(pow (+ 1.0 (/ i n)) n)

simplify68.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0561927
12792821
25001820

prune270.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
11.0b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.6b
(* (pow i 2) (log 1.0))

rewrite558.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×add-exp-log
17×add-cube-cbrt *-un-lft-identity
16×add-cbrt-cube
9×pow1 times-frac associate-*l*
8×prod-exp
7×associate-*r*
6×log-prod cbrt-unprod
4×unpow-prod-down unswap-sqr
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* associate-/l* add-log-exp
2×cbrt-undiv div-exp *-commutative associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ associate-*l/ pow-exp clear-num log-pow flip-- div-inv
Counts
3 → 85
Calls
3 calls:
285.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
257.0ms
(/ (- (+ (* 1.0 i) (+ (* 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))

series491.0ms

Counts
3 → 9
Calls
3 calls:
210.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
137.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
144.0ms
(* (pow i 2) (log 1.0))

simplify63.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04561354
121071143
250021139

prune281.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 i)))
0.3b
(* (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 i))) n)
11.2b
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 i))
11.6b
(* (pow i 2) (log 1.0))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
55×add-exp-log
34×add-cbrt-cube
32×add-sqr-sqrt
31×prod-exp
21×pow1 associate-*r*
20×*-un-lft-identity
19×add-cube-cbrt
17×cbrt-unprod
15×associate-*r/ associate-*l*
12×associate-*l/
11×times-frac
10×pow-prod-down
7×unswap-sqr
6×frac-times log-prod flip3-- div-exp flip--
4×unpow-prod-down *-commutative add-log-exp
3×cbrt-undiv distribute-rgt-in rec-exp distribute-lft-in 1-exp un-div-inv
2×unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow div-inv
Counts
4 → 133
Calls
4 calls:
483.0ms
(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 i)))
1.2s
(* (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 i))) n)
403.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 i))
14.0ms
(* (pow i 2) (log 1.0))

series649.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 i)))
213.0ms
(* (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 i))) n)
134.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 i))
146.0ms
(* (pow i 2) (log 1.0))

simplify102.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
06622348
134961921
250021908

prune373.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 12.2b

regimes404.0ms

Accuracy

52.4% (10.9b remaining)

Error of 21.5b against oracle of 10.7b and baseline of 33.5b

bsearch519.0ms

Steps
ItersRangePoint
8
5.5413977021021364e-204
5.854389425032826e-200
5.06196450596402e-200
10
-6.071180404494044e-306
4.010022869839558e-300
5.964212362723236e-309
6
-1.312921234409977e+17
-17398359074955834.0
-1.0363019718914387e+17
9
-1.1951520515514796e+115
-4.1275081529303654e+108
-1.1745123512936853e+115
7
-4.412166578960519e+130
-4.90358144502769e+128
-5.170598455267975e+128

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08780
18780

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.9s999×body2560valid
1.8s2545×body1280valid
465.0ms1576×body640valid
133.0ms798×body320valid
131.0ms3071×body80valid
71.0ms2231×body80nan
45.0ms445×body160valid
19.0ms5×body5120valid