Details

Time bar (total: 3.2m)

sample265.0ms

Algorithm
intervals
Results
105.0ms69×body1280valid
78.0ms28×body2560valid
29.0ms46×body640valid
12.0ms97×body80valid
12.0ms28×body320valid
8.0ms68×body80nan
5.0ms1×body5120valid
3.0ms10×body160valid

simplify190.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
190.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize26.0ms

Local error

Found 4 expressions with local error:

9.7b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
7.1b
(pow (+ 1 (/ i n)) n)
1.2b
(- (pow (+ 1 (/ i n)) n) 1)
0.1b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite507.0ms

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
195.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
195.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
89.0ms
(- (pow (+ 1 (/ i n)) n) 1)
17.0ms
(pow (+ 1 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
426.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
415.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
273.0ms
(pow (+ 1 (/ i n)) n)
250.0ms
(- (pow (+ 1 (/ i n)) n) 1)

simplify2.4m

Counts
595 → 465
Calls
595 calls:
Slowest
1.0s
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) (cbrt n)))
625.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (cbrt i) (cbrt n)))
619.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (cbrt i) n))
617.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) (sqrt n)))
605.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ i (sqrt n)))

prune3.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.9b

localize23.0ms

Local error

Found 4 expressions with local error:

7.1b
(pow (+ 1 (/ i n)) n)
1.2b
(- (pow (+ 1 (/ i n)) n) 1)
0.1b
(* (* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) i)) n)
0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) i))

rewrite365.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
47×*-un-lft-identity
46×associate-*r*
40×times-frac
25×add-cube-cbrt
24×difference-of-squares
19×add-exp-log
18×add-cbrt-cube
16×unpow-prod-down
13×sqr-pow
12×pow1 difference-of-sqr-1
7×prod-exp cbrt-unprod
6×add-log-exp
4×associate-*l* pow-prod-down insert-posit16 distribute-lft-out--
3×pow-unpow
2×cbrt-undiv div-exp associate-*r/ *-commutative unswap-sqr
1×pow-to-exp sub-neg pow-pow flip3-- diff-log associate-*l/ pow-exp div-inv flip-- distribute-lft-out
Counts
4 → 127
Calls
4 calls:
Slowest
154.0ms
(* (* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) i)) n)
133.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) i))
69.0ms
(- (pow (+ 1 (/ i n)) n) 1)
8.0ms
(pow (+ 1 (/ i n)) n)

series873.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
306.0ms
(* (* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) i)) n)
221.0ms
(- (pow (+ 1 (/ i n)) n) 1)
213.0ms
(pow (+ 1 (/ i n)) n)
133.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) i))

simplify17.3s

Counts
102 → 139
Calls
102 calls:
Slowest
619.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt i))
369.0ms
(* (sqrt 100) (/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (sqrt i)))
368.0ms
(* (sqrt 100) (/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (sqrt i)))
365.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) i)
364.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) i)

prune919.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize20.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i)
3.3b
(* (* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i)) n)
0.4b
(* 1/6 i)
0.1b
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
22×add-cbrt-cube add-exp-log
19×times-frac associate-*r*
13×pow1
8×prod-exp cbrt-unprod
7×associate-*l*
5×pow-prod-down
4×insert-posit16 add-log-exp
3×cbrt-undiv associate-/r* div-exp *-commutative associate-/l* unswap-sqr
2×associate-*r/ div-inv associate-/l/
1×clear-num frac-2neg flip3-+ associate-*l/ flip-+
Counts
4 → 104
Calls
4 calls:
Slowest
28.0ms
(* (* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i)) n)
27.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i)
13.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i))
5.0ms
(* 1/6 i)

series189.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
73.0ms
(* (* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i)) n)
51.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i)
50.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i))
15.0ms
(* 1/6 i)

simplify8.5s

Counts
82 → 116
Calls
82 calls:
Slowest
412.0ms
(* (* (* (* 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))
354.0ms
(* (* (* 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)))
256.0ms
(* (* 100 (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) n)
247.0ms
(+ (log (* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i))) (log n))
213.0ms
(* (* (* (* 100 100) 100) (* (* (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i) (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i)) (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) i))) (* (* n n) n))

prune769.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.6b

localize17.0ms

Local error

Found 3 expressions with local error:

3.3b
(* (+ (* (+ (* 50/3 i) 50) i) 100) n)
0.5b
(* 50/3 i)
0.0b
(* (+ (* 50/3 i) 50) i)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cbrt-cube associate-*r* associate-*l* add-exp-log add-cube-cbrt
4×associate-*l/
3×pow-prod-down prod-exp *-commutative cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×flip3-+ flip-+
Counts
3 → 61
Calls
3 calls:
Slowest
36.0ms
(* (+ (* (+ (* 50/3 i) 50) i) 100) n)
21.0ms
(* (+ (* 50/3 i) 50) i)
5.0ms
(* 50/3 i)

series119.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
65.0ms
(* (+ (* 50/3 i) 50) i)
39.0ms
(* (+ (* (+ (* 50/3 i) 50) i) 100) n)
15.0ms
(* 50/3 i)

simplify2.9s

Counts
40 → 70
Calls
40 calls:
Slowest
536.0ms
(* (+ (pow (* 50/3 i) 3) (pow 50 3)) i)
444.0ms
(* (+ (pow (* (+ (* 50/3 i) 50) i) 3) (pow 100 3)) n)
355.0ms
(* (- (* (* (+ (* 50/3 i) 50) i) (* (+ (* 50/3 i) 50) i)) (* 100 100)) n)
161.0ms
(* (- (* (* 50/3 i) (* 50/3 i)) (* 50 50)) i)
152.0ms
(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))

prune383.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.5b

regimes316.0ms

Accuracy

56.5% (10.5b remaining)

Error of 18.9b against oracle of 8.4b and baseline of 32.5b

bsearch539.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
2.8s2476×body1280valid
2.4s1043×body2560valid
860.0ms1592×body640valid
308.0ms849×body320valid
308.0ms2979×body80valid
236.0ms2230×body80nan
102.0ms403×body160valid
50.0ms8×body5120valid