Details

Time bar (total: 18.7s)

sample157.0ms

Algorithm
intervals
Results
62.0ms91×body1280valid
55.0ms31×body2560valid
12.0ms43×body640valid
6.0ms92×body80valid
4.0ms23×body320valid
3.0ms95×body80nan
2.0ms20×body160valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
12515
25815
313715
432715
599815
6417715
done500015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.7b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.2b
(pow (+ 1.0 (/ i n)) n)
9.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite591.0ms

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:
237.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
111.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
211.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
357.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
245.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
206.0ms
(pow (+ 1.0 (/ i n)) n)
340.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify399.0ms

Counts
293 → 293
Iterations

Useful iterations: done (389.0ms)

IterNodesCost
04376469
112356125
done50016097

prune815.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
1.7b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.2b
(pow (+ 1.0 (/ i n)) n)

rewrite591.0ms

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:
246.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
217.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
112.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)

series965.0ms

Counts
4 → 12
Calls
4 calls:
363.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
149.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
244.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
208.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.0s

Counts
111 → 111
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02241903
15711812
225641596
done50001592

prune260.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.4b

localize19.0ms

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)))) 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)))) i)) n)
10.8b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.4b
(* (pow i 2) (log 1.0))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
22×add-cbrt-cube
20×associate-*r*
19×times-frac
12×pow1 associate-*l*
10×prod-exp
8×cbrt-unprod
6×log-prod unswap-sqr
4×unpow-prod-down pow-prod-down add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*r/ div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*l/ pow-exp clear-num log-pow flip--
Counts
4 → 117
Calls
4 calls:
125.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
143.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
127.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms
(* (pow i 2) (log 1.0))

series629.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
205.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
135.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
139.0ms
(* (pow i 2) (log 1.0))

simplify886.0ms

Counts
129 → 129
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
02183765
15483686
225333149
done50003149

prune408.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt 100.0) (* (sqrt 100.0) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)))
0.3b
(* (* (sqrt 100.0) (* (sqrt 100.0) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))) n)
10.8b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.4b
(* (pow i 2) (log 1.0))

rewrite634.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
31×add-cbrt-cube
26×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
19×pow1
17×prod-exp
15×associate-*l* cbrt-unprod
9×times-frac pow-prod-down
8×associate-*r*
6×log-prod
4×unpow-prod-down associate-*r/ add-log-exp unswap-sqr
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* sqrt-prod *-commutative associate-/l*
2×associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*l/ pow-exp clear-num log-pow flip-- div-inv
Counts
4 → 112
Calls
4 calls:
108.0ms
(* (sqrt 100.0) (* (sqrt 100.0) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)))
389.0ms
(* (* (sqrt 100.0) (* (sqrt 100.0) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))) n)
127.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms
(* (pow i 2) (log 1.0))

series958.0ms

Counts
4 → 12
Calls
4 calls:
291.0ms
(* (sqrt 100.0) (* (sqrt 100.0) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)))
400.0ms
(* (* (sqrt 100.0) (* (sqrt 100.0) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))) n)
129.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
137.0ms
(* (pow i 2) (log 1.0))

simplify906.0ms

Counts
124 → 124
Iterations

Useful iterations: 2 (199.0ms)

IterNodesCost
02374011
15993656
226592965
done50012965

prune519.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.3b

regimes197.0ms

Accuracy

53.7% (10.8b remaining)

Error of 21.4b against oracle of 10.6b and baseline of 33.9b

bsearch191.0ms

Steps
ItersRangePoint
6
2.0126860685752985e-10
2.7764519059011607e-09
2.7217117903300314e-09
11
-1011077464093715.9
-1.3606912768451591e-05
-1.4961350298470049

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04389
15989
done5989

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s984×body2560valid
1.7s2487×body1280valid
453.0ms1595×body640valid
137.0ms857×body320valid
133.0ms3098×body80valid
69.0ms2196×body80nan
44.0ms446×body160valid
15.0ms4×body5120valid