2-ancestry mixing, zero discriminant

Average Error: 25.02% → 1.35%

Time: 5.4s

Precision: binary64

Cost: 13376

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Derivation

1. Initial program 25.02

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

2. Applied egg-rr 1.41

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

3. Applied egg-rr 61.91

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

4. Simplified 61.82

   \[\leadsto \color{blue}{{\left(\sqrt{\sqrt[3]{\frac{a}{g \cdot 0.5}}}\right)}^{-2}} \]
   Proof

   [Start] 61.91	\[ {\left(\sqrt{\sqrt[3]{\frac{\frac{a}{0.5}}{g}}}\right)}^{-1} \cdot {\left(\sqrt{\sqrt[3]{\frac{\frac{a}{0.5}}{g}}}\right)}^{-1} \]
   pow-sqr [=>] 61.85	\[ \color{blue}{{\left(\sqrt{\sqrt[3]{\frac{\frac{a}{0.5}}{g}}}\right)}^{\left(2 \cdot -1\right)}} \]
   associate-/l/ [=>] 61.82	\[ {\left(\sqrt{\sqrt[3]{\color{blue}{\frac{a}{g \cdot 0.5}}}}\right)}^{\left(2 \cdot -1\right)} \]
   metadata-eval [=>] 61.82	\[ {\left(\sqrt{\sqrt[3]{\frac{a}{g \cdot 0.5}}}\right)}^{\color{blue}{-2}} \]

5. Applied egg-rr 1.35

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

6. Final simplification 1.35

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

Alternatives

Alternative 1
Error	1.32%
Cost	13248

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

Alternative 2
Error	1.33%
Cost	13120

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

Alternative 3
Error	1.28%
Cost	13120

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

Alternative 4
Error	24.97%
Cost	6720

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

Alternative 5
Error	25.02%
Cost	6720

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

Reproduce

herbie shell --seed 2023104 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))