Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1} \]
↓
\[\sqrt[3]{{\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right)}^{3}} \]
(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (cbrt (pow (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x))) 3.0)))
double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
double code(double x) {
	return cbrt(pow(((1.0 / (x - 1.0)) + (x / (1.0 + x))), 3.0));
}

public static double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
public static double code(double x) {
	return Math.cbrt(Math.pow(((1.0 / (x - 1.0)) + (x / (1.0 + x))), 3.0));
}

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

code[x_] := N[(N[(1.0 / N[(x - 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[Power[N[Power[N[(N[(1.0 / N[(x - 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]

\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right)}^{3}}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022146 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))