2-ancestry mixing, zero discriminant

Average Error: 15.2 → 0.9

Time: 5.9s

Precision: binary64

Cost: 13376

Math

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

↓

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

FPCore

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

↓

(FPCore (g a)
 :precision binary64
 (/ (/ 1.0 (cbrt (* a 2.0))) (cbrt (/ 1.0 g))))

C

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

↓

double code(double g, double a) {
	return (1.0 / cbrt((a * 2.0))) / cbrt((1.0 / g));
}

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 * 2.0))) / Math.cbrt((1.0 / g));
}

Julia

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

↓

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

Derivation

1. Initial program 15.2

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

2. Applied egg-rr 0.9

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

3. Simplified 0.8

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

   [Start] 0.9	\[ \sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}} \]
   associate-*r/ [=>] 0.8	\[ \color{blue}{\frac{\sqrt[3]{g} \cdot 1}{\sqrt[3]{2 \cdot a}}} \]
   *-rgt-identity [=>] 0.8	\[ \frac{\color{blue}{\sqrt[3]{g}}}{\sqrt[3]{2 \cdot a}} \]
   *-commutative [=>] 0.8	\[ \frac{\sqrt[3]{g}}{\sqrt[3]{\color{blue}{a \cdot 2}}} \]

4. Applied egg-rr 1.2

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

5. Applied egg-rr 0.9

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

6. Applied egg-rr 34.4

   \[\leadsto \frac{\frac{1}{\sqrt[3]{a \cdot 2}}}{\color{blue}{{\left(\frac{1}{g}\right)}^{0.3333333333333333}}} \]

7. Simplified 0.9

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

   [Start] 34.4	\[ \frac{\frac{1}{\sqrt[3]{a \cdot 2}}}{{\left(\frac{1}{g}\right)}^{0.3333333333333333}} \]
   unpow1/3 [=>] 0.9	\[ \frac{\frac{1}{\sqrt[3]{a \cdot 2}}}{\color{blue}{\sqrt[3]{\frac{1}{g}}}} \]

8. Final simplification 0.9

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

Alternatives

Alternative 1
Error	15.3
Cost	13120

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

Alternative 2
Error	0.8
Cost	13120

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

Alternative 3
Error	0.8
Cost	13120

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

Alternative 4
Error	15.2
Cost	6720

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

Alternative 5
Error	15.2
Cost	6720

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

Reproduce

herbie shell --seed 2023027 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))