Details

Time bar (total: 13.3s)

sample217.0ms

Algorithm
intervals
Results
81.0ms83×body1280valid
79.0ms32×body2560valid
21.0ms56×body640valid
6.0ms26×body320valid
6.0ms92×body80valid
3.0ms61×body80nan
3.0ms16×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1607
21457
33647
412487
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))

rewrite857.0ms

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:
311.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
179.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
331.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
363.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
269.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
217.0ms
(pow (+ 1.0 (/ i n)) n)
346.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify65.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune1.0s

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)

rewrite866.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
35×add-cube-cbrt
28×associate-*r*
24×unpow-prod-down prod-diff
22×times-frac
19×add-exp-log
18×add-cbrt-cube
12×pow1 difference-of-squares
9×sqr-pow
8×fma-neg
7×prod-exp cbrt-unprod
6×add-log-exp
5×distribute-lft-out
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u 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
Counts
4 → 139
Calls
4 calls:
294.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
339.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
209.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)

series983.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
364.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
257.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
209.0ms
(pow (+ 1.0 (/ i n)) n)

simplify91.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06551376
132011082
250021080

prune315.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

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 expm1-log1p-u distribute-lft-in pow-prod-down associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp *-commutative unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ associate-*l/ pow-exp clear-num log-pow div-inv
Counts
3 → 88
Calls
3 calls:
25.0ms
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
5.0ms
(/ (fma i 1.0 (- (fma 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))

series498.0ms

Counts
3 → 9
Calls
3 calls:
216.0ms
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
143.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
140.0ms
(* (pow i 2) (log 1.0))

simplify57.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
03981207
117511023
250021016

prune302.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite138.0ms

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-*l*
11×times-frac
10×pow-prod-down
7×associate-*r/ unswap-sqr
6×log-prod div-exp
4×expm1-log1p-u unpow-prod-down *-commutative log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in rec-exp distribute-lft-in 1-exp un-div-inv
2×associate-*l/ unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow div-inv
Counts
4 → 129
Calls
4 calls:
25.0ms
(* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 i)))
79.0ms
(* (* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 i))) n)
14.0ms
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 i))
16.0ms
(* (pow i 2) (log 1.0))

series652.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 i)))
213.0ms
(* (* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 i))) n)
137.0ms
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 i))
145.0ms
(* (pow i 2) (log 1.0))

simplify82.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
05771909
126751525
250011510

prune357.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 12.2b

regimes194.0ms

Accuracy

52.4% (10.9b remaining)

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

bsearch498.0ms

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
07673
17673

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.8s999×body2560valid
1.8s2545×body1280valid
451.0ms1576×body640valid
129.0ms3071×body80valid
128.0ms798×body320valid
69.0ms2231×body80nan
45.0ms445×body160valid
19.0ms5×body5120valid