?

Average Error: 15.9 → 0.9
Time: 1.6min
Precision: binary64
Cost: 25984

?

\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{{a}^{-1}} \cdot \sqrt[3]{0.5}\right) \]
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (cbrt g) (* (cbrt (pow a -1.0)) (cbrt 0.5))))
double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}
↓
double code(double g, double a) {
	return cbrt(g) * (cbrt(pow(a, -1.0)) * cbrt(0.5));
}

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.pow(a, -1.0)) * Math.cbrt(0.5));
}

function code(g, a)
	return cbrt(Float64(g / Float64(2.0 * a)))
end
↓
function code(g, a)
	return Float64(cbrt(g) * Float64(cbrt((a ^ -1.0)) * cbrt(0.5)))
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[Power[a, -1.0], $MachinePrecision], 1/3], $MachinePrecision] * N[Power[0.5, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{{a}^{-1}} \cdot \sqrt[3]{0.5}\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 15.9

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

  2. Simplified15.9

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

  3. Applied egg-rr0.8

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

  4. Applied egg-rr0.9

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

Alternatives

Alternative 1
Error0.9
Cost19904
\[\sqrt[3]{g} \cdot \frac{\sqrt[3]{0.1111111111111111 \cdot \frac{-0.5}{-0.037037037037037035 \cdot a}}}{\sqrt[3]{3}} \]
Alternative 2
Error0.9
Cost19520
\[\sqrt[3]{g} \cdot \frac{\sqrt[3]{0.5}}{\sqrt[3]{a}} \]
Alternative 3
Error0.9
Cost13376
\[\sqrt[3]{g} \cdot \frac{\sqrt[3]{\frac{-0.5}{-0.037037037037037035 \cdot a}}}{3} \]
Alternative 4
Error0.8
Cost13248
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{0.018518518518518517}{a \cdot 0.037037037037037035}} \]
Alternative 5
Error0.8
Cost13120
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{a}} \]
Alternative 6
Error15.9
Cost6720
\[\sqrt[3]{0.5 \cdot \frac{g}{a}} \]

Error

Reproduce?

herbie shell --seed 2023033 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))