2-ancestry mixing, zero discriminant

Average Error: 15.5 → 0.9

Time: 6.4s

Precision: binary64

Cost: 13376

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

function code(g, a)
	return Float64(1.0 / Float64(cbrt(Float64(2.0 / g)) / Float64(1.0 / cbrt(a))))
end

Wolfram

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

↓

code[g_, a_] := N[(1.0 / N[(N[Power[N[(2.0 / g), $MachinePrecision], 1/3], $MachinePrecision] / N[(1.0 / N[Power[a, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.5

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

2. Applied egg-rr 15.5

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

3. Applied egg-rr 0.9

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

4. Applied egg-rr 0.9

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

5. Final simplification 0.9

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

Alternatives

Alternative 1
Error	0.8
Cost	13120

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

Alternative 2
Error	15.5
Cost	6848

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

Alternative 3
Error	15.5
Cost	6848

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

Alternative 4
Error	15.5
Cost	6720

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

Alternative 5
Error	15.5
Cost	6720

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

Reproduce

herbie shell --seed 2023039 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))