d7f3ba91-d155-4a97-80b6-bf3a5ef63dd6 41 4 5 decimal

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

x erf 2 π sqrt / t 2^- exp t 0 x int * ≡

must be vectorized x erf vectorize x 02 int 1.437

1rst derivative ...
is simply the integrand x D 2 π sqrt / x 2^- exp * :

3 specifics wrt erf(x) . . .

1. Vectorized integrator.

2. X_Y plot mystic/unique

3. eval(solve)

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Antiderivative,
integral curve. z int z z erf * z 2^- exp π sqrt / + :

n 2 :

'n' derivative x D x n diff 4 x 2^- exp * 12 x 2^* - (* π sqrt / -

constrain the plot ["] x u 12 - x ≤ (x 2 ≤ (& cases :

x erf x u * x D x D x 1 diff 0.5 x D x 3 diff * 4 1 sys x D x 0 diff

x y XY x y / - :

x 1.5 - 1.5 1.49 - range :

erf XY x erf 3 1 sys

a 0.5 : b 1 : xn b a + (2 / : 31 line

xx f xx erf xx - eval :

ε 1010 -^:

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

sanity

xn 0.617446879

xn f 41011 -^*

n 27

Antiderivative,
integral curve. z int z z erf * z 2^- exp π sqrt / + :

0 int 1 π sqrt / ≡

0 int 0.564

x int 0 0 int + 30 red 1 5 mat 2 1 sys

Cumulative integration between limits a 0 : b 2 : 12 mat a b Σ b int a int - : 21 line

a b Σ 1.43678843916719

option: integral accuracy 10000 x erf vectorize x a b int 1.43678843916719

__The recalcitrant solve bloc__

sol x erf vectorize 1 x / - 0 ≡ x 1 1.3 solve : #

sol 1.1255

x erf vectorize 1 x / - 0 ≡ x 1 1.3 solve 1.1255

sol x erf vectorize 1 x / - 0 ≡ x 1 1.3 solve eval : 1.1255

x erf 1 x / 2 1 sys x 2 ^ 1 x / 2 1 sys

sol x 2^1 x / - 0 ≡ x 0.5 1.5 solve : 1