d7f3ba91-d155-4a97-80b6-bf3a5ef63dd6 27 3 5 decimal

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

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

x erf vectorize x 02 int 1.437

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

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 1 : 12 mat a b Σ b int a int - : 21 line

a b Σ 0.486064958112255

option: integral accuracy 1000 x erf vectorize x a b int 0.486064958112257

Romberg integrator ... NFG for erf(x) f a b Int x f x a b int 32 / b a - (* w G w 01 int * ≡ (memo ≡ w s b a - (34 / 2 w * 1 - (* 14 / 2 w * 1 - (3^* - 12 / + (* a + : w G w s f vectorize 12 w * 1 - (2^- (* : 32 / b a - (* w G w 01 int * 41 line :

x f x erf vectorize :

f a b Int 0.48606495811223

__The recalcitrant solve bloc__

x erf vectorize x - 0 ≡ x 0.615 0.62 solve 0.617

x erf vectorize 1 x / - 0 ≡ x 1 1.3 solve 1.12545238897753

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

x erf 1 x / 2 1 sys

x 1.12545238897753 :

x erf 1 x / - 5.526 107 -^*