2-ancestry mixing, zero discriminant

Average Accuracy: 76.3% → 98.6%

Time: 6.8s

Precision: binary64

Cost: 13248

• Unsound rule application detected in e-graph. Results may not be sound.

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 78.0%

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

2. Applied egg-rr 98.8%

   \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}} \]
   Step-by-step derivation

   [Start] 78.0	\[ \sqrt[3]{\frac{g}{2 \cdot a}} \]
   cbrt-div [=>] 98.7	\[ \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}} \]
   div-inv [=>] 98.8	\[ \color{blue}{\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}} \]

3. Simplified 98.8%

   \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{a \cdot 2}}} \]
   Step-by-step derivation

   [Start] 98.8	\[ \sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}} \]
   *-commutative [=>] 98.8	\[ \sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{\color{blue}{a \cdot 2}}} \]

4. Final simplification 98.8%

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

Alternatives

Alternative 1
Accuracy	98.7%
Cost	13120

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

Alternative 2
Accuracy	98.7%
Cost	13120

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

Alternative 3
Accuracy	76.2%
Cost	6848

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

Alternative 4
Accuracy	76.3%
Cost	6720

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

Alternative 5
Accuracy	76.3%
Cost	6720

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

Alternative 6
Accuracy	3.2%
Cost	6592

\[\sqrt[3]{g} \cdot 0 \]

Reproduce

herbie shell --seed 2023159 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))