Details

Time bar (total: 25.7s)

sample218.0ms

Algorithm
intervals
Results
79.0ms31×body2560valid
72.0ms69×body1280valid
23.0ms57×body640valid
7.0ms96×body80valid
7.0ms26×body320valid
4.0ms74×body80nan
4.0ms1×body5120valid
2.0ms11×body160valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
25915
314015
434715
5151415
done500015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.9b
(pow (+ 1.0 (/ i n)) n)
10.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.2s

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:
534.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
228.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
22.0ms
(pow (+ 1.0 (/ i n)) n)
428.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts
4 → 12
Calls
4 calls:
537.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
323.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
294.0ms
(pow (+ 1.0 (/ i n)) n)
543.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify832.0ms

Counts
293 → 293
Iterations

Useful iterations: done (812.0ms)

IterNodesCost
04376469
114166211
done50005919

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
0.3b
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.9b
(pow (+ 1.0 (/ i n)) n)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
340×times-frac
314×add-sqr-sqrt
206×*-un-lft-identity
146×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
49×add-exp-log
32×unpow-prod-down
30×add-cbrt-cube
29×sqr-pow
28×distribute-lft-out--
23×div-exp
18×div-inv
13×associate-*l* associate-/r*
12×cbrt-undiv
10×prod-exp
8×unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
3×rec-exp pow-unpow 1-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×frac-times pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num *-commutative distribute-lft-out
Counts
4 → 310
Calls
4 calls:
490.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
560.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
235.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms
(pow (+ 1.0 (/ i n)) n)

series1.6s

Counts
4 → 12
Calls
4 calls:
496.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
474.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
344.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
313.0ms
(pow (+ 1.0 (/ i n)) n)

simplify960.0ms

Counts
322 → 322
Iterations

Useful iterations: done (945.0ms)

IterNodesCost
04677463
116796787
done50005995

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
4.7b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
12.2b
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
12.8b
(* (pow i 2) (log 1.0))

rewrite800.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
127×add-sqr-sqrt
95×*-un-lft-identity
93×add-cube-cbrt
53×add-exp-log
48×associate-*r*
32×add-cbrt-cube
23×div-exp
21×associate-*l*
13×prod-exp associate-/r*
12×cbrt-undiv unswap-sqr
10×div-inv
9×add-log-exp
7×pow1 cbrt-unprod
6×log-prod
4×unpow-prod-down
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp sum-log associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×+-commutative frac-times pow-to-exp associate-+r+ flip3-- frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num log-pow flip-- flip-+
Counts
4 → 215
Calls
4 calls:
34.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
351.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
386.0ms
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
17.0ms
(* (pow i 2) (log 1.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
475.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
258.0ms
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
228.0ms
(* (pow i 2) (log 1.0))

simplify677.0ms

Counts
227 → 227
Iterations

Useful iterations: done (664.0ms)

IterNodesCost
03798307
112437916
done50006996

prune991.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (* n (+ (* 1.0 i) (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))) i))
4.5b
(* n (+ (* 1.0 i) (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
12.0b
(/ (* n (+ (* 1.0 i) (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))) i)
12.8b
(* (pow i 2) (log 1.0))

rewrite548.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×add-exp-log
22×add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
14×associate-*r* associate-*l*
9×pow1 prod-exp
7×cbrt-unprod
6×log-prod times-frac unswap-sqr
5×associate-*r/
4×cbrt-undiv distribute-rgt-in unpow-prod-down distribute-lft-in div-exp add-log-exp
3×associate-/r* *-commutative
2×flip3-+ pow-prod-down flip-+ div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow associate-/l*
Counts
4 → 106
Calls
4 calls:
200.0ms
(* 100.0 (/ (* n (+ (* 1.0 i) (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))) i))
253.0ms
(* n (+ (* 1.0 i) (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
73.0ms
(/ (* n (+ (* 1.0 i) (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))) i)
19.0ms
(* (pow i 2) (log 1.0))

series849.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(* 100.0 (/ (* n (+ (* 1.0 i) (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))) i))
167.0ms
(* n (+ (* 1.0 i) (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
253.0ms
(/ (* n (+ (* 1.0 i) (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))) i)
213.0ms
(* (pow i 2) (log 1.0))

simplify1.5s

Counts
118 → 118
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02063221
15653149
231932401
done50002399

prune417.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.3b

regimes318.0ms

Accuracy

45.9% (12.2b remaining)

Error of 23.1b against oracle of 10.9b and baseline of 33.4b

bsearch372.0ms

Steps
ItersRangePoint
9
1.4677799112160757e-106
1.1702822108249084e-100
1.4887262418381814e-106
9
-3.387992976769487e-240
-2.0488175508739457e-248
-3.040807945417772e-242
8
-3.3100924427793195e+98
-7.40491600406347e+94
-2.2600474911734306e+95

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
041101
157101
done57101

end0.0ms

sample6.6s

Algorithm
intervals
Results
2.6s2451×body1280valid
2.2s1008×body2560valid
661.0ms1652×body640valid
293.0ms862×body320valid
267.0ms2950×body80valid
130.0ms2281×body80nan
57.0ms424×body160valid
29.0ms6×body5120valid