2d06b8d9-a946-4126-8e73-07f31360dfcf 18 6 12 decimal

&[DATE] &[TIME] - &[FILENAME]

Step 1: assign the arc length integrand

3 appVersion 0.98.6179 ≡ Timing 2min 40 s ≡ acc 100 ≡ 31 mat

arc length integrand
of x^n [n fractional] x f 1 x n^x diff (2^+ sqrt :

ε 1015 -^:

Step 2: the wild arc length integration

x f x int maple n 3^x * 1 n 2^1 - n + (x ln * exp 2^* + sqrt * 1 n 3^2 - n + (* + 1 n 3^1 - n + (* + (1 n 2^1 - n + (x ln * exp 2^* + sqrt * / x int 1 n 3^1 - n + (* + (* + 1 n 3^1 - n + (* + /

Step 3: assign/transit wild arc length integration Step 4: validate the integrator [u] in the range [x]

x n arc n 3^x * 1 n 2^1 - n + (x ln * exp (2^* + sqrt * 1 n 3^2 - n + (* + 1 n 3^1 - n + (* + (1 n 2^1 - n + (u ln * exp (2^* + sqrt * / u ε x int 1 n 3^1 - n + (* + (* + 1 n 3^1 - n + (* + / :

x c 1 ε x ≤ (x 1 ≤ (& cases :

113 / arc 0.816563

t0 1 time :

x 1 3 / ^ x c * x 1 3 / arc x c * 2 1 sys

==================================

1 time t0 - 108 s *

# f L Δ N Δinc X 0 : i 1 N range X i 1 + el L Δ i * + : X 1 el L : 21 line for i 1 X rows range vy i el X i el f eval : for X vy augment 41 line :

x Φ x 13 / arc :

t0 1 time :

Observe . . .

Canvas plot runs 145 times the

integration in 110 s. The eval(,)

discretizer runs 100 times the

integration in 47 s. Equivalently

eval(,) is ~ 1.6 times faster.

subtile . . .

arc(x,n):=eval(,) has NO effect

on the canvas.

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L ε : Δ 0.01 : N 99 : 13 mat ARC x Φ L Δ N Δinc : ARC 11 el 0 : 31 sys

===========================

1 time t0 - 47 s *

ARC

ARC 00 0.01 0.0036 0.02 0.006 0.03 0.009 0.04 0.0124 0.05 0.0163 0.06 0.0205 72 mat

ARC rows 147145 * 110100 * / / 21 mat 100 1.61 21 mat