2-ancestry mixing, zero discriminant

Average Accuracy: 75.2% → 98.7%

Time: 7.6s

Precision: binary64

Cost: 13120

Math

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

↓

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

FPCore

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

↓

(FPCore (g a) :precision binary64 (/ (cbrt (* g 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 * 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 * 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(Float64(g * 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[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[a, 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.2%

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

2. Applied egg-rr 98.7%

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

   [Start] 75.2	\[ \sqrt[3]{\frac{g}{2 \cdot a}} \]
   associate-/r* [=>] 75.2	\[ \sqrt[3]{\color{blue}{\frac{\frac{g}{2}}{a}}} \]
   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. Final simplification 98.7%

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

Alternatives

Alternative 1
Accuracy	98.7%
Cost	13120

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

Alternative 2
Accuracy	98.7%
Cost	13120

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

Alternative 3
Accuracy	75.2%
Cost	6720

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

Reproduce

herbie shell --seed 2023138 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))