Details

Time bar (total: 3.1m)

sample379.0ms

Algorithm
intervals
Results
134.0ms85×body1280valid
119.0ms33×body2560valid
65.0ms49×body640valid
19.0ms37×body320valid
11.0ms85×body80valid
8.0ms60×body80nan
5.0ms17×body160valid

simplify160.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
160.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.1b

localize17.0ms

Local error

Found 4 expressions with local error:

11.6b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
6.1b
(pow (+ 1 (/ i n)) n)
1.3b
(- (pow (+ 1 (/ i n)) n) 1)
0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite592.0ms

Algorithm
rewrite-expression-head
Rules
584×times-frac
485×add-sqr-sqrt
366×*-un-lft-identity
224×add-cube-cbrt
174×associate-*r*
168×difference-of-squares
88×unpow-prod-down
85×sqr-pow
84×difference-of-sqr-1
29×div-inv
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
13×associate-/r* associate-/l*
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×insert-posit16
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp clear-num sub-neg pow-pow frac-2neg diff-log div-sub pow-prod-down pow-exp associate-*r/ *-commutative distribute-lft-out
Counts
4 → 453
Calls
4 calls:
Slowest
259.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
198.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
101.0ms
(- (pow (+ 1 (/ i n)) n) 1)
17.0ms
(pow (+ 1 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
427.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
426.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
287.0ms
(- (pow (+ 1 (/ i n)) n) 1)
284.0ms
(pow (+ 1 (/ i n)) n)

simplify2.3m

Counts
595 → 465
Calls
595 calls:
Slowest
828.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (* (cbrt (/ i n)) (cbrt (/ i n))))
629.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (cbrt i) (cbrt n)))
534.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (cbrt i) (sqrt n)))
528.0ms
(/ (- (pow (+ 1 (/ i n)) (/ n 2)) 1) (/ i (cbrt n)))
525.0ms
(/ (- (pow (sqrt (+ 1 (/ i n))) n) 1) (/ (cbrt i) (cbrt n)))

prune3.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.4b

localize21.0ms

Local error

Found 4 expressions with local error:

18.1b
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
0.3b
(* 1/6 i)
0.1b
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
0.1b
(* (* i i) (+ (* 1/6 i) 1/2))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
97×add-sqr-sqrt
85×*-un-lft-identity add-cube-cbrt
50×associate-*r*
25×add-cbrt-cube add-exp-log
13×pow1 associate-/r*
9×div-inv
7×associate-*l* prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow-prod-down unswap-sqr
4×insert-posit16 add-log-exp
3×associate-*r/ *-commutative associate-/l*
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in
Counts
4 → 183
Calls
4 calls:
Slowest
33.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
27.0ms
(* (* i i) (+ (* 1/6 i) 1/2))
16.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
5.0ms
(* 1/6 i)

series237.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
72.0ms
(* (* i i) (+ (* 1/6 i) 1/2))
66.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
27.0ms
(* 1/6 i)

simplify24.7s

Counts
194 → 195
Calls
194 calls:
Slowest
526.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
506.0ms
(* (* (* 100 100) 100) (/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ (* (* i i) i) (* (* n n) n))))
503.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ (cbrt i) (cbrt n)))
434.0ms
(* (* (* 100 100) 100) (/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (* (* (/ i n) (/ i n)) (/ i n))))
305.0ms
(/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ (* (* i i) i) (* (* n n) n)))

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.1b

localize19.0ms

Local error

Found 4 expressions with local error:

2.4b
(* n (+ 100 (* i (+ (* 50/3 i) 50))))
0.5b
(* 50/3 i)
0.1b
(* i (+ (* 50/3 i) 50))
0.0b
(+ (* 50/3 i) 50)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
6×add-log-exp
4×associate-*r/ insert-posit16
3×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
2×distribute-rgt-in distribute-lft-in
1×+-commutative sum-log
Counts
4 → 77
Calls
4 calls:
Slowest
17.0ms
(* i (+ (* 50/3 i) 50))
10.0ms
(* n (+ 100 (* i (+ (* 50/3 i) 50))))
6.0ms
(+ (* 50/3 i) 50)
5.0ms
(* 50/3 i)

series166.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
65.0ms
(* i (+ (* 50/3 i) 50))
51.0ms
(* n (+ 100 (* i (+ (* 50/3 i) 50))))
34.0ms
(+ (* 50/3 i) 50)
15.0ms
(* 50/3 i)

simplify2.1s

Counts
50 → 89
Calls
50 calls:
Slowest
220.0ms
(* (* (* n n) n) (* (* (+ 100 (* i (+ (* 50/3 i) 50))) (+ 100 (* i (+ (* 50/3 i) 50)))) (+ 100 (* i (+ (* 50/3 i) 50)))))
172.0ms
(+ (* (* 50/3 i) (* 50/3 i)) (- (* 50 50) (* (* 50/3 i) 50)))
151.0ms
(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))
151.0ms
(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))
149.0ms
(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))

prune537.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.0b

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b
(* n (+ 100 (* (+ (* 50/3 i) 50) i)))
0.5b
(* 50/3 i)
0.1b
(* (+ (* 50/3 i) 50) i)
0.0b
(+ (* 50/3 i) 50)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
6×add-log-exp
4×insert-posit16
3×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
2×associate-*l/ associate-*r/
1×distribute-rgt-in +-commutative sum-log distribute-lft-in
Counts
4 → 75
Calls
4 calls:
Slowest
21.0ms
(* (+ (* 50/3 i) 50) i)
10.0ms
(* n (+ 100 (* (+ (* 50/3 i) 50) i)))
6.0ms
(+ (* 50/3 i) 50)
5.0ms
(* 50/3 i)

series164.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
60.0ms
(* (+ (* 50/3 i) 50) i)
48.0ms
(* n (+ 100 (* (+ (* 50/3 i) 50) i)))
37.0ms
(+ (* 50/3 i) 50)
19.0ms
(* 50/3 i)

simplify2.3s

Counts
47 → 87
Calls
47 calls:
Slowest
270.0ms
(* (+ (pow (* 50/3 i) 3) (pow 50 3)) i)
194.0ms
(* (* (* n n) n) (* (* (+ 100 (* (+ (* 50/3 i) 50) i)) (+ 100 (* (+ (* 50/3 i) 50) i))) (+ 100 (* (+ (* 50/3 i) 50) i))))
159.0ms
(* (- (* (* 50/3 i) (* 50/3 i)) (* 50 50)) i)
153.0ms
(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))
152.0ms
(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))

prune466.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.0b

regimes396.0ms

Accuracy

57% (10.6b remaining)

Error of 19.0b against oracle of 8.3b and baseline of 33.1b

bsearch257.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
2.8s2568×body1280valid
2.3s950×body2560valid
849.0ms1546×body640valid
387.0ms913×body320valid
297.0ms3050×body80valid
175.0ms2151×body80nan
87.0ms456×body160valid
20.0ms5×body5120valid