2-ancestry mixing, zero discriminant

Average Error: 15.5 → 0.9

Time: 39.2s

Precision: binary64

Cost: 19648

Math

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

↓

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

FPCore

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

↓

(FPCore (g a) :precision binary64 (* (* (cbrt (/ 1.0 a)) (cbrt g)) (cbrt 0.5)))

C

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

↓

double code(double g, double a) {
	return (cbrt((1.0 / a)) * cbrt(g)) * cbrt(0.5);
}

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((1.0 / a)) * Math.cbrt(g)) * Math.cbrt(0.5);
}

Julia

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

↓

function code(g, a)
	return Float64(Float64(cbrt(Float64(1.0 / a)) * cbrt(g)) * cbrt(0.5))
end

Wolfram

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

↓

code[g_, a_] := N[(N[(N[Power[N[(1.0 / a), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[g, 1/3], $MachinePrecision]), $MachinePrecision] * N[Power[0.5, 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.5

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

2. Simplified 15.5

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

   [Start] 15.5	\[ \sqrt[3]{\frac{g}{2 \cdot a}} \]
   rational_best-simplify-54 [=>] 15.5	\[ \sqrt[3]{\color{blue}{\frac{\frac{g}{2}}{a}}} \]

3. Applied egg-rr 15.5

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

4. Applied egg-rr 0.9

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

5. Final simplification 0.9

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

Alternatives

Alternative 1
Error	0.9
Cost	13120

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

Alternative 2
Error	15.5
Cost	6720

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

Reproduce

herbie shell --seed 2023099 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))