Details

Time bar (total: 20.8s)

sample264.0ms

Algorithm
intervals
Results
91.0ms82×body1280valid
78.0ms29×body2560valid
48.0ms48×body640valid
8.0ms107×body80valid
8.0ms25×body320valid
5.0ms73×body80nan
2.0ms12×body160valid

simplify45.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b
(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:
490.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
198.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
35.0ms
(pow (+ 1.0 (/ i n)) n)
434.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts
4 → 12
Calls
4 calls:
464.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
351.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
296.0ms
(pow (+ 1.0 (/ i n)) n)
490.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify109.0ms

Counts
293 → 293

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n)))
0.1b
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) (/ i n)))
11.9b
(* (pow i 2) (log 1.0))
18.2b
(/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) (/ i n))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
144×times-frac
102×add-sqr-sqrt
87×add-cube-cbrt *-un-lft-identity
48×associate-*r*
23×add-exp-log
20×add-cbrt-cube
13×associate-/r*
11×associate-*l*
9×div-inv add-log-exp
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×unpow-prod-down cbrt-unprod associate-/l/
3×distribute-rgt-in distribute-lft-in sum-log associate-/l*
2×flip3-+ associate-*l/ associate-/r/ *-commutative frac-sub flip-+ unpow2 sqr-pow
1×+-commutative pow-to-exp associate-+r+ flip3-- frac-2neg div-sub associate-*r/ pow-prod-down pow-exp clear-num log-pow flip--
Counts
4 → 188
Calls
4 calls:
45.0ms
(+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n)))
446.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) (/ i n)))
22.0ms
(* (pow i 2) (log 1.0))
583.0ms
(/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) (/ i n))

series829.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n)))
298.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) (/ i n)))
232.0ms
(* (pow i 2) (log 1.0))
249.0ms
(/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) (/ i n))

simplify106.0ms

Counts
200 → 200

prune885.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 7.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i) n)
0.1b
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i) n))
11.2b
(/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i)
11.9b
(* (pow i 2) (log 1.0))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
24×associate-*l*
22×add-cbrt-cube
19×times-frac
12×pow1
10×prod-exp
8×associate-*r* cbrt-unprod
6×log-prod unswap-sqr
4×unpow-prod-down pow-prod-down associate-*l/ associate-/l/ add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×frac-sub div-inv unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg flip3-+ div-sub associate-*r/ pow-exp clear-num log-pow flip-- flip-+
Counts
4 → 119
Calls
4 calls:
596.0ms
(* (/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i) n)
430.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i) n))
578.0ms
(/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i)
21.0ms
(* (pow i 2) (log 1.0))

series910.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(* (/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i) n)
264.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i) n))
196.0ms
(/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i)
201.0ms
(* (pow i 2) (log 1.0))

simplify81.0ms

Counts
131 → 131

prune612.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 7.5b

localize53.0ms

Local error

Found 4 expressions with local error:

11.2b
(/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i)
11.9b
(* (pow i 2) (log 1.0))
11.9b
(* (pow i 2) (log 1.0))
11.9b
(* (pow i 2) (log 1.0))

rewrite648.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity
24×associate-*l*
21×add-exp-log
18×log-prod
12×unpow-prod-down associate-*r* add-cbrt-cube unswap-sqr
9×distribute-rgt-in distribute-lft-in times-frac prod-exp
7×pow1
6×unpow2 sqr-pow
4×associate-/l/ add-log-exp
3×pow-to-exp pow-exp associate-/r* log-pow *-commutative cbrt-unprod associate-/l*
2×associate-*l/ frac-sub
1×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp clear-num flip-- flip-+ div-inv
Counts
4 → 134
Calls
4 calls:
578.0ms
(/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i)
21.0ms
(* (pow i 2) (log 1.0))
21.0ms
(* (pow i 2) (log 1.0))
22.0ms
(* (pow i 2) (log 1.0))

series807.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ (- (+ (* 1.0 i) (+ (* (/ 1.0 2.0) (pow i 2)) (* (log 1.0) n))) (* (/ 1.0 2.0) (* (pow i 2) (log 1.0)))) i)
216.0ms
(* (pow i 2) (log 1.0))
220.0ms
(* (pow i 2) (log 1.0))
195.0ms
(* (pow i 2) (log 1.0))

simplify57.0ms

Counts
146 → 146

prune638.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 7.5b

regimes276.0ms

Accuracy

57% (10.9b remaining)

Error of 19.2b against oracle of 8.3b and baseline of 33.7b

bsearch340.0ms

Steps
ItersRangePoint
11
0.0033763382367094055
5.206713059748268e+29
0.10387405912847383
5
-2.921513544512531
-0.7794201341187467
-0.9131486383075667

simplify85.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
2.5s2473×body1280valid
2.3s961×body2560valid
788.0ms1602×body640valid
466.0ms2281×body80nan
333.0ms8×body5120valid
235.0ms3083×body80valid
202.0ms822×body320valid
97.0ms429×body160valid