Asymptote B

Average Error: 0.0 → 0.0

Time: 1.3s

Precision: binary64

Math

\[\frac{1}{x - 1} + \frac{x}{x + 1} \]

↓

\[\frac{1}{x + -1} + {\left(\frac{1 + x}{x}\right)}^{-1} \]

FPCore

(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))

↓

(FPCore (x)
 :precision binary64
 (+ (/ 1.0 (+ x -1.0)) (pow (/ (+ 1.0 x) x) -1.0)))

C

double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}

↓

double code(double x) {
	return (1.0 / (x + -1.0)) + pow(((1.0 + x) / x), -1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / (x - 1.0d0)) + (x / (x + 1.0d0))
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / (x + (-1.0d0))) + (((1.0d0 + x) / x) ** (-1.0d0))
end function

Java

public static double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}

↓

public static double code(double x) {
	return (1.0 / (x + -1.0)) + Math.pow(((1.0 + x) / x), -1.0);
}

Python

def code(x):
	return (1.0 / (x - 1.0)) + (x / (x + 1.0))

↓

def code(x):
	return (1.0 / (x + -1.0)) + math.pow(((1.0 + x) / x), -1.0)

Julia

function code(x)
	return Float64(Float64(1.0 / Float64(x - 1.0)) + Float64(x / Float64(x + 1.0)))
end

↓

function code(x)
	return Float64(Float64(1.0 / Float64(x + -1.0)) + (Float64(Float64(1.0 + x) / x) ^ -1.0))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / (x - 1.0)) + (x / (x + 1.0));
end

↓

function tmp = code(x)
	tmp = (1.0 / (x + -1.0)) + (((1.0 + x) / x) ^ -1.0);
end

Wolfram

code[x_] := N[(N[(1.0 / N[(x - 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(N[(1.0 / N[(x + -1.0), $MachinePrecision]), $MachinePrecision] + N[Power[N[(N[(1.0 + x), $MachinePrecision] / x), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

2. Applied egg-rr 0.0

   \[\leadsto \frac{1}{x - 1} + \color{blue}{{\left(\frac{x + 1}{x}\right)}^{-1}} \]

3. Final simplification 0.0

   \[\leadsto \frac{1}{x + -1} + {\left(\frac{1 + x}{x}\right)}^{-1} \]

Reproduce

herbie shell --seed 2022153 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))