Details

Time bar (total: 17.0s)

sample159.0ms

Algorithm
intervals
Results
64.0ms91×body1280valid
56.0ms31×body2560valid
13.0ms43×body640valid
4.0ms92×body80valid
4.0ms23×body320valid
3.0ms95×body80nan
2.0ms20×body160valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
12515
25815
313715
431915
593915
6375915
done500015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize14.0ms

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))

rewrite581.0ms

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:
236.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
108.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
205.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
348.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
240.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
205.0ms
(pow (+ 1.0 (/ i n)) n)
348.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.2s

Counts
293 → 293
Iterations

Useful iterations: 2 (648.0ms)

IterNodesCost
04376469
112216125
237725875
done50005875

prune800.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.6b

localize12.0ms

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)

rewrite672.0ms

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:
341.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
210.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
106.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.0s

Counts
4 → 12
Calls
4 calls:
411.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
144.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
242.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
205.0ms
(pow (+ 1.0 (/ i n)) n)

simplify841.0ms

Counts
111 → 111
Iterations

Useful iterations: done (836.0ms)

IterNodesCost
02241903
15601812
217231596
done50001592

prune268.0ms

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))

rewrite401.0ms

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:
124.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
141.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
125.0ms
(/ (- (+ (* 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))

series624.0ms

Counts
4 → 12
Calls
4 calls:
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))
213.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
132.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
136.0ms
(* (pow i 2) (log 1.0))

simplify787.0ms

Counts
129 → 129
Iterations

Useful iterations: 2 (322.0ms)

IterNodesCost
02183765
15393686
220193149
done50003149

prune407.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 100.0 (+ (* 50.0 i) (* 100.0 (/ (* (log 1.0) n) i))))
0.3b
(* (- (+ 100.0 (+ (* 50.0 i) (* 100.0 (/ (* (log 1.0) n) i)))) (* 50.0 (* i (log 1.0)))) n)

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
6×add-sqr-sqrt *-un-lft-identity
4×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*r* associate-*l* sum-log
2×associate-*l/
1×+-commutative associate-+r+ flip3-- flip3-+ pow-prod-down prod-exp *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out unswap-sqr
Counts
2 → 34
Calls
2 calls:
6.0ms
(+ 100.0 (+ (* 50.0 i) (* 100.0 (/ (* (log 1.0) n) i))))
147.0ms
(* (- (+ 100.0 (+ (* 50.0 i) (* 100.0 (/ (* (log 1.0) n) i)))) (* 50.0 (* i (log 1.0)))) n)

series207.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(+ 100.0 (+ (* 50.0 i) (* 100.0 (/ (* (log 1.0) n) i))))
150.0ms
(* (- (+ 100.0 (+ (* 50.0 i) (* 100.0 (/ (* (log 1.0) n) i)))) (* 50.0 (* i (log 1.0)))) n)

simplify373.0ms

Counts
40 → 40
Iterations

Useful iterations: done (372.0ms)

IterNodesCost
0911062
12501009
2970917
done5002857

prune99.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.3b

regimes183.0ms

Accuracy

53.4% (10.8b remaining)

Error of 21.4b against oracle of 10.6b and baseline of 33.7b

bsearch188.0ms

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
03979
15379
done5379

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.8s984×body2560valid
1.7s2487×body1280valid
466.0ms1595×body640valid
142.0ms857×body320valid
130.0ms3098×body80valid
72.0ms2196×body80nan
45.0ms446×body160valid
15.0ms4×body5120valid