2-ancestry mixing, zero discriminant

Average Accuracy: 75.1% → 98.7%

Time: 6.9s

Precision: binary64

Cost: 19648

Math

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

↓

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

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

Derivation

1. Initial program 75.1%

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

2. Applied egg-rr 98.7%

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

   [Start] 75.1	\[ \sqrt[3]{\frac{g}{2 \cdot a}} \]
   associate-/r* [=>] 75.1	\[ \sqrt[3]{\color{blue}{\frac{\frac{g}{2}}{a}}} \]
   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%

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

   [Start] 98.7	\[ \frac{\sqrt[3]{g \cdot 0.5}}{\sqrt[3]{a}} \]
   div-inv [=>] 98.7	\[ \color{blue}{\sqrt[3]{g \cdot 0.5} \cdot \frac{1}{\sqrt[3]{a}}} \]
   *-commutative [=>] 98.7	\[ \color{blue}{\frac{1}{\sqrt[3]{a}} \cdot \sqrt[3]{g \cdot 0.5}} \]

4. Applied egg-rr 45.7%

   \[\leadsto \color{blue}{\left({\left(\frac{1}{a}\right)}^{0.16666666666666666} \cdot {\left(\frac{1}{a}\right)}^{0.16666666666666666}\right)} \cdot \sqrt[3]{g \cdot 0.5} \]
   Proof

   [Start] 98.7	\[ \frac{1}{\sqrt[3]{a}} \cdot \sqrt[3]{g \cdot 0.5} \]
   add-cbrt-cube [=>] 98.4	\[ \color{blue}{\sqrt[3]{\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}}} \cdot \sqrt[3]{g \cdot 0.5} \]
   pow1/3 [=>] 45.7	\[ \color{blue}{{\left(\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}^{0.3333333333333333}} \cdot \sqrt[3]{g \cdot 0.5} \]
   sqr-pow [=>] 45.7	\[ \color{blue}{\left({\left(\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)} \cdot {\left(\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)}\right)} \cdot \sqrt[3]{g \cdot 0.5} \]
   un-div-inv [=>] 45.7	\[ \left({\color{blue}{\left(\frac{\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}}{\sqrt[3]{a}}\right)}}^{\left(\frac{0.3333333333333333}{2}\right)} \cdot {\left(\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)}\right) \cdot \sqrt[3]{g \cdot 0.5} \]
   frac-times [=>] 45.7	\[ \left({\left(\frac{\color{blue}{\frac{1 \cdot 1}{\sqrt[3]{a} \cdot \sqrt[3]{a}}}}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)} \cdot {\left(\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)}\right) \cdot \sqrt[3]{g \cdot 0.5} \]
   metadata-eval [=>] 45.7	\[ \left({\left(\frac{\frac{\color{blue}{1}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)} \cdot {\left(\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)}\right) \cdot \sqrt[3]{g \cdot 0.5} \]
   associate-/l/ [=>] 45.7	\[ \left({\color{blue}{\left(\frac{1}{\sqrt[3]{a} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)}\right)}}^{\left(\frac{0.3333333333333333}{2}\right)} \cdot {\left(\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)}\right) \cdot \sqrt[3]{g \cdot 0.5} \]
   *-commutative [<=] 45.7	\[ \left({\left(\frac{1}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)} \cdot {\left(\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)}\right) \cdot \sqrt[3]{g \cdot 0.5} \]
   add-cube-cbrt [<=] 45.7	\[ \left({\left(\frac{1}{\color{blue}{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)} \cdot {\left(\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)}\right) \cdot \sqrt[3]{g \cdot 0.5} \]
   metadata-eval [=>] 45.7	\[ \left({\left(\frac{1}{a}\right)}^{\color{blue}{0.16666666666666666}} \cdot {\left(\left(\frac{1}{\sqrt[3]{a}} \cdot \frac{1}{\sqrt[3]{a}}\right) \cdot \frac{1}{\sqrt[3]{a}}\right)}^{\left(\frac{0.3333333333333333}{2}\right)}\right) \cdot \sqrt[3]{g \cdot 0.5} \]

5. Simplified 98.7%

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

   [Start] 45.7	\[ \left({\left(\frac{1}{a}\right)}^{0.16666666666666666} \cdot {\left(\frac{1}{a}\right)}^{0.16666666666666666}\right) \cdot \sqrt[3]{g \cdot 0.5} \]
   pow-sqr [=>] 45.7	\[ \color{blue}{{\left(\frac{1}{a}\right)}^{\left(2 \cdot 0.16666666666666666\right)}} \cdot \sqrt[3]{g \cdot 0.5} \]
   metadata-eval [=>] 45.7	\[ {\left(\frac{1}{a}\right)}^{\color{blue}{0.3333333333333333}} \cdot \sqrt[3]{g \cdot 0.5} \]
   unpow1/3 [=>] 98.7	\[ \color{blue}{\sqrt[3]{\frac{1}{a}}} \cdot \sqrt[3]{g \cdot 0.5} \]

6. Applied egg-rr 98.7%

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

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

7. Final simplification 98.7%

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

Alternatives

Alternative 1
Accuracy	98.7%
Cost	13248

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

Alternative 2
Accuracy	98.7%
Cost	13248

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

Alternative 3
Accuracy	98.7%
Cost	13120

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

Alternative 4
Accuracy	98.7%
Cost	13120

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

Alternative 5
Accuracy	75.0%
Cost	6848

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

Alternative 6
Accuracy	75.0%
Cost	6720

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

Alternative 7
Accuracy	74.3%
Cost	6720

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

Reproduce

herbie shell --seed 2023129 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))