Details

Time bar (total: 3.8m)

sample344.0ms

Algorithm
intervals
Results
157.0ms92×body1280valid
94.0ms26×body2560valid
36.0ms50×body640valid
15.0ms30×body320valid
11.0ms82×body80valid
9.0ms66×body80nan
5.0ms17×body160valid

simplify156.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
156.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.5b

localize20.0ms

Local error

Found 4 expressions with local error:

10.2b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
5.9b
(pow (+ 1 (/ i n)) n)
1.4b
(- (pow (+ 1 (/ i n)) n) 1)
0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite515.0ms

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
207.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
188.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
93.0ms
(- (pow (+ 1 (/ i n)) n) 1)
9.0ms
(pow (+ 1 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
395.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
360.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
314.0ms
(pow (+ 1 (/ i n)) n)
306.0ms
(- (pow (+ 1 (/ i n)) n) 1)

simplify2.5m

Counts
654 → 465
Calls
654 calls:
Slowest
949.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (cbrt i) (sqrt n)))
705.0ms
(- (pow (pow (+ 1 (/ i n)) n) 3) (pow 1 3))
678.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (* (cbrt i) (cbrt i)) (sqrt n)))
672.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) (cbrt n)))
668.0ms
(* 100 (/ (+ (pow (sqrt (+ 1 (/ i n))) n) 1) (* (cbrt (/ i n)) (cbrt (/ i n)))))

prune3.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.5b

localize21.0ms

Local error

Found 4 expressions with local error:

17.2b
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
0.3b
(* 1/6 i)
0.1b
(* (* i i) (+ (* 1/6 i) 1/2))
0.1b
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))

rewrite81.0ms

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
29.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
25.0ms
(* (* i i) (+ (* 1/6 i) 1/2))
16.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
8.0ms
(* 1/6 i)

series226.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
71.0ms
(* (* i i) (+ (* 1/6 i) 1/2))
71.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
68.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
15.0ms
(* 1/6 i)

simplify30.9s

Counts
239 → 195
Calls
239 calls:
Slowest
501.0ms
(* 100 (/ (* (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))) (/ (sqrt i) (sqrt n))))
501.0ms
(* (* (* 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))))
426.0ms
(* (* (* 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))))
396.0ms
(/ (* (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n))))
324.0ms
(* 100 (/ (* (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (cbrt (+ i (* (* i i) (+ (* 1/6 i) 1/2))))) (/ (* (cbrt i) (cbrt i)) (* (cbrt n) (cbrt n)))))

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1/6 i)
0.1b
(* (* i n) (+ 1/2 (* 1/6 i)))
0.1b
(* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n))
0.0b
(+ (* (* i n) (+ 1/2 (* 1/6 i))) n)

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×associate-*r/ insert-posit16
3×distribute-rgt-in distribute-lft-in flip3-+ *-commutative flip-+
2×associate-+l+ unswap-sqr
1×+-commutative sum-log
Counts
4 → 79
Calls
4 calls:
Slowest
49.0ms
(* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n))
17.0ms
(* (* i n) (+ 1/2 (* 1/6 i)))
14.0ms
(+ (* (* i n) (+ 1/2 (* 1/6 i))) n)
9.0ms
(* 1/6 i)

series125.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
45.0ms
(* (* i n) (+ 1/2 (* 1/6 i)))
33.0ms
(* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n))
31.0ms
(+ (* (* i n) (+ 1/2 (* 1/6 i))) n)
15.0ms
(* 1/6 i)

simplify8.9s

Counts
95 → 91
Calls
95 calls:
Slowest
334.0ms
(* (* (* 100 100) 100) (* (* (+ (* (* i n) (+ 1/2 (* 1/6 i))) n) (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)) (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))
245.0ms
(* 100 (+ (pow (* (* i n) (+ 1/2 (* 1/6 i))) 3) (pow n 3)))
242.0ms
(* (* (* (* i n) (+ 1/2 (* 1/6 i))) (* (* i n) (+ 1/2 (* 1/6 i)))) (* (* i n) (+ 1/2 (* 1/6 i))))
236.0ms
(* (* (* (* i i) i) (* (* n n) n)) (* (* (+ 1/2 (* 1/6 i)) (+ 1/2 (* 1/6 i))) (+ 1/2 (* 1/6 i))))
226.0ms
(exp (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))

prune582.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.4b

localize35.0ms

Local error

Found 4 expressions with local error:

11.2b
(cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))
11.2b
(cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))
11.2b
(cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))
0.5b
(* (cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n))) (cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*r/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-+ pow1/3 flip-+
8×*-un-lft-identity add-cube-cbrt
7×cbrt-prod
6×add-exp-log
4×frac-times add-cbrt-cube swap-sqr associate-*r* associate-*l* insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 76
Calls
4 calls:
Slowest
62.0ms
(* (cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n))) (cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n))))
19.0ms
(cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))
18.0ms
(cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))
18.0ms
(cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(* (cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n))) (cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n))))
107.0ms
(cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))
107.0ms
(cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))
106.0ms
(cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))

simplify17.2s

Counts
101 → 88
Calls
101 calls:
Slowest
414.0ms
(* (cbrt (cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))) (cbrt (cbrt (* 100 (+ (* (* i n) (+ 1/2 (* 1/6 i))) n)))))
412.0ms
(* (cbrt (* 100 (- (* (* (* i n) (+ 1/2 (* 1/6 i))) (* (* i n) (+ 1/2 (* 1/6 i)))) (* n n)))) (cbrt (* 100 (+ (pow (* (* i n) (+ 1/2 (* 1/6 i))) 3) (pow n 3)))))
395.0ms
(* (cbrt (* 100 (+ (pow (* (* i n) (+ 1/2 (* 1/6 i))) 3) (pow n 3)))) (cbrt (* 100 (- (* (* (* i n) (+ 1/2 (* 1/6 i))) (* (* i n) (+ 1/2 (* 1/6 i)))) (* n n)))))
355.0ms
(+ (* (pow n 1/3) (cbrt 100)) (+ (* 1/36 (* (* (pow i 2) (cbrt 100)) (pow n 1/3))) (* 1/6 (* (* i (cbrt 100)) (pow n 1/3)))))
354.0ms
(+ (* (pow n 1/3) (cbrt 100)) (+ (* 1/36 (* (* (pow i 2) (cbrt 100)) (pow n 1/3))) (* 1/6 (* (* i (cbrt 100)) (pow n 1/3)))))

prune690.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.4b

regimes527.0ms

Accuracy

57.6% (10.9b remaining)

Error of 19.9b against oracle of 9.0b and baseline of 34.7b

bsearch1.2s

end0.0ms

sample7.0s

Algorithm
intervals
Results
2.6s2518×body1280valid
2.1s929×body2560valid
832.0ms1540×body640valid
395.0ms504×body160valid
335.0ms3030×body80valid
275.0ms888×body320valid
178.0ms2276×body80nan
41.0ms11×body5120valid