Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1} \]
↓
\[\sqrt[3]{{\left(-1 + x\right)}^{-3}} + \frac{x}{x + 1} \]
(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (+ (cbrt (pow (+ -1.0 x) -3.0)) (/ x (+ x 1.0))))
double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
double code(double x) {
	return cbrt(pow((-1.0 + x), -3.0)) + (x / (x + 1.0));
}

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), -3.0)) + (x / (x + 1.0));
}

function code(x)
	return Float64(Float64(1.0 / Float64(x - 1.0)) + Float64(x / Float64(x + 1.0)))
end
↓
function code(x)
	return Float64(cbrt((Float64(-1.0 + x) ^ -3.0)) + Float64(x / Float64(x + 1.0)))
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[(N[Power[N[Power[N[(-1.0 + x), $MachinePrecision], -3.0], $MachinePrecision], 1/3], $MachinePrecision] + N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

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 add-exp-log_binary6447.8

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

  3. Applied 1-exp_binary6447.8

    \[\leadsto \frac{\color{blue}{e^{0}}}{e^{\log \left(x - 1\right)}} + \frac{x}{x + 1} \]

  4. Applied div-exp_binary6447.8

    \[\leadsto \color{blue}{e^{0 - \log \left(x - 1\right)}} + \frac{x}{x + 1} \]

  5. Simplified47.8

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

  6. Applied add-cbrt-cube_binary6447.8

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2022137 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))