Average Error: 15.4 → 0.9
Time: 4.0s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{\sqrt{0.5}} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}\right) \]
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (cbrt g) (* (cbrt (sqrt 0.5)) (cbrt (/ (sqrt 0.5) a)))))
double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}
↓
double code(double g, double a) {
	return cbrt(g) * (cbrt(sqrt(0.5)) * cbrt((sqrt(0.5) / a)));
}

public static double code(double g, double a) {
	return Math.cbrt((g / (2.0 * a)));
}
↓
public static double code(double g, double a) {
	return Math.cbrt(g) * (Math.cbrt(Math.sqrt(0.5)) * Math.cbrt((Math.sqrt(0.5) / a)));
}

function code(g, a)
	return cbrt(Float64(g / Float64(2.0 * a)))
end
↓
function code(g, a)
	return Float64(cbrt(g) * Float64(cbrt(sqrt(0.5)) * cbrt(Float64(sqrt(0.5) / a))))
end

code[g_, a_] := N[Power[N[(g / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]
↓
code[g_, a_] := N[(N[Power[g, 1/3], $MachinePrecision] * N[(N[Power[N[Sqrt[0.5], $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(N[Sqrt[0.5], $MachinePrecision] / a), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{\sqrt{0.5}} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}\right)

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.4

    \[\sqrt[3]{\frac{g}{2 \cdot a}} \]

  2. Applied div-inv_binary6415.4

    \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}} \]

  3. Applied cbrt-prod_binary640.8

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}} \]

  4. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\sqrt[3]{\frac{0.5}{a}}} \]

  5. Applied *-un-lft-identity_binary640.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{\color{blue}{1 \cdot a}}} \]

  6. Applied add-sqr-sqrt_binary640.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{\color{blue}{\sqrt{0.5} \cdot \sqrt{0.5}}}{1 \cdot a}} \]

  7. Applied times-frac_binary640.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\color{blue}{\frac{\sqrt{0.5}}{1} \cdot \frac{\sqrt{0.5}}{a}}} \]

  8. Applied cbrt-prod_binary640.9

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{\frac{\sqrt{0.5}}{1}} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}\right)} \]

  9. Simplified0.9

    \[\leadsto \sqrt[3]{g} \cdot \left(\color{blue}{\sqrt[3]{\sqrt{0.5}}} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}\right) \]

  10. Final simplification0.9

    \[\leadsto \sqrt[3]{g} \cdot \left(\sqrt[3]{\sqrt{0.5}} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}\right) \]

Reproduce

herbie shell --seed 2022138 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))