2-ancestry mixing, zero discriminant

Average Accuracy: 76.0% → 98.6%

Time: 7.5s

Precision: binary64

Cost: 19520

Math

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

↓

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

FPCore

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))

↓

(FPCore (g a) :precision binary64 (* (cbrt g) (/ (cbrt 0.5) (cbrt a))))

C

double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}

↓

double code(double g, double a) {
	return cbrt(g) * (cbrt(0.5) / cbrt(a));
}

Java

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(0.5) / Math.cbrt(a));
}

Julia

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

↓

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

Wolfram

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[0.5, 1/3], $MachinePrecision] / N[Power[a, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.4%

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

2. Applied egg-rr 98.7%

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

   [Start] 77.4	\[ \sqrt[3]{\frac{g}{2 \cdot a}} \]
   associate-/r* [=>] 77.4	\[ \sqrt[3]{\color{blue}{\frac{\frac{g}{2}}{a}}} \]
   cbrt-div [=>] 98.7	\[ \color{blue}{\frac{\sqrt[3]{\frac{g}{2}}}{\sqrt[3]{a}}} \]
   div-inv [=>] 98.7	\[ \frac{\sqrt[3]{\color{blue}{g \cdot \frac{1}{2}}}}{\sqrt[3]{a}} \]
   metadata-eval [=>] 98.7	\[ \frac{\sqrt[3]{g \cdot \color{blue}{0.5}}}{\sqrt[3]{a}} \]

3. Applied egg-rr 98.7%

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

   [Start] 98.7	\[ \frac{\sqrt[3]{g \cdot 0.5}}{\sqrt[3]{a}} \]
   div-inv [=>] 98.7	\[ \color{blue}{\sqrt[3]{g \cdot 0.5} \cdot \frac{1}{\sqrt[3]{a}}} \]
   cbrt-prod [=>] 98.6	\[ \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{0.5}\right)} \cdot \frac{1}{\sqrt[3]{a}} \]
   associate-*l* [=>] 98.7	\[ \color{blue}{\sqrt[3]{g} \cdot \left(\sqrt[3]{0.5} \cdot \frac{1}{\sqrt[3]{a}}\right)} \]

4. Simplified 98.8%

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

   [Start] 98.7	\[ \sqrt[3]{g} \cdot \left(\sqrt[3]{0.5} \cdot \frac{1}{\sqrt[3]{a}}\right) \]
   associate-*r/ [=>] 98.8	\[ \sqrt[3]{g} \cdot \color{blue}{\frac{\sqrt[3]{0.5} \cdot 1}{\sqrt[3]{a}}} \]
   *-rgt-identity [=>] 98.8	\[ \sqrt[3]{g} \cdot \frac{\color{blue}{\sqrt[3]{0.5}}}{\sqrt[3]{a}} \]

5. Final simplification 98.8%

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

Alternatives

Alternative 1
Accuracy	98.6%
Cost	19520

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

Alternative 2
Accuracy	98.7%
Cost	13120

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

Alternative 3
Accuracy	98.7%
Cost	13120

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

Alternative 4
Accuracy	75.9%
Cost	6848

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

Alternative 5
Accuracy	76.0%
Cost	6720

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

Alternative 6
Accuracy	76.0%
Cost	6720

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

Reproduce

herbie shell --seed 2023160 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))