Average Error: 0.0 → 0.0
Time: 3.3s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1} \]
↓
\[\sqrt[3]{{\left(\frac{x}{x + 1} + \frac{x + 1}{\mathsf{fma}\left(x, x, -1\right)}\right)}^{3}} \]
(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (cbrt (pow (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (fma x x -1.0))) 3.0)))
double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
double code(double x) {
	return cbrt(pow(((x / (x + 1.0)) + ((x + 1.0) / fma(x, x, -1.0))), 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(x / Float64(x + 1.0)) + Float64(Float64(x + 1.0) / fma(x, x, -1.0))) ^ 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[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x + 1.0), $MachinePrecision] / N[(x * x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]

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

Error

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2022211 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))