Average Error: 29.1 → 0.0
Time: 3.6s
Precision: binary64
\[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
↓
\[\frac{-3 + \frac{-1}{x}}{\frac{x + 1}{x} \cdot \left(-1 + x\right)} \]
(FPCore (x) :precision binary64 (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (/ (+ -3.0 (/ -1.0 x)) (* (/ (+ x 1.0) x) (+ -1.0 x))))
double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}
↓
double code(double x) {
	return (-3.0 + (-1.0 / x)) / (((x + 1.0) / x) * (-1.0 + x));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x / (x + 1.0d0)) - ((x + 1.0d0) / (x - 1.0d0))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = ((-3.0d0) + ((-1.0d0) / x)) / (((x + 1.0d0) / x) * ((-1.0d0) + x))
end function

public static double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}
↓
public static double code(double x) {
	return (-3.0 + (-1.0 / x)) / (((x + 1.0) / x) * (-1.0 + x));
}

def code(x):
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0))
↓
def code(x):
	return (-3.0 + (-1.0 / x)) / (((x + 1.0) / x) * (-1.0 + x))

function code(x)
	return Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x - 1.0)))
end
↓
function code(x)
	return Float64(Float64(-3.0 + Float64(-1.0 / x)) / Float64(Float64(Float64(x + 1.0) / x) * Float64(-1.0 + x)))
end

function tmp = code(x)
	tmp = (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
end
↓
function tmp = code(x)
	tmp = (-3.0 + (-1.0 / x)) / (((x + 1.0) / x) * (-1.0 + x));
end

code[x_] := N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[(-3.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{x}{x + 1} - \frac{x + 1}{x - 1}
↓
\frac{-3 + \frac{-1}{x}}{\frac{x + 1}{x} \cdot \left(-1 + x\right)}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.1

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

  2. Applied egg-rr28.9

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

  3. Taylor expanded in x around 0 0.0

    \[\leadsto \frac{\color{blue}{-\left(3 + \frac{1}{x}\right)}}{\frac{x + 1}{x} \cdot \left(x + -1\right)} \]

  4. Simplified0.0

    \[\leadsto \frac{\color{blue}{-3 + \frac{-1}{x}}}{\frac{x + 1}{x} \cdot \left(x + -1\right)} \]

  5. Final simplification0.0

    \[\leadsto \frac{-3 + \frac{-1}{x}}{\frac{x + 1}{x} \cdot \left(-1 + x\right)} \]

Reproduce

herbie shell --seed 2022206 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))