2-ancestry mixing, zero discriminant

Percentage Accurate: 76.0% → 98.7%

Time: 5.5s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \sqrt[3]{\frac{g}{2 \cdot a}} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Initial Program: 76.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\frac{g}{2 \cdot a}} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. cbrt-div 98.7%

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

   2. div-inv 98.7%

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

3. Applied egg-rr 98.7%

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

   1. associate-*r/ 98.7%

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

   2. *-rgt-identity 98.7%

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

   3. *-commutative 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{a}} \end{array} \]

FPCore

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

C

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

Java

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

Julia

function code(g, a)
	return Float64(cbrt(g) * cbrt(Float64(0.5 / a)))
end

Wolfram

code[g_, a_] := N[(N[Power[g, 1/3], $MachinePrecision] * N[Power[N[(0.5 / a), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. div-inv 76.2%

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

   2. cbrt-prod 98.6%

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

   3. associate-/r* 98.6%

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

   4. metadata-eval 98.6%

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

3. Applied egg-rr 98.6%

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

4. Final simplification 98.6%

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

Alternative 3: 76.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{g \cdot \frac{0.5}{a}} \end{array} \]

FPCore

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

C

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

Java

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

Julia

function code(g, a)
	return cbrt(Float64(g * Float64(0.5 / a)))
end

Wolfram

code[g_, a_] := N[Power[N[(g * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]

Derivation

1. Initial program 76.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. expm1-log1p-u 58.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)\right)} \]

   2. expm1-udef 22.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)} - 1} \]

   3. log1p-udef 22.6%

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

   4. add-exp-log 40.5%

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

   5. *-un-lft-identity 40.5%

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

   6. times-frac 40.5%

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

   7. metadata-eval 40.5%

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

3. Applied egg-rr 40.5%

   \[\leadsto \color{blue}{\left(1 + \sqrt[3]{0.5 \cdot \frac{g}{a}}\right) - 1} \]
4. Step-by-step derivation

   1. +-commutative 40.5%

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

   2. associate--l+ 76.2%

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

   3. metadata-eval 76.2%

      \[\leadsto \sqrt[3]{0.5 \cdot \frac{g}{a}} + \color{blue}{0} \]

   4. +-rgt-identity 76.2%

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

   5. associate-*r/ 76.2%

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

   6. associate-*l/ 76.2%

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

5. Simplified 76.2%

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

6. Final simplification 76.2%

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

Alternative 4: 76.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\frac{g}{a \cdot 2}} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.2%

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

2. Final simplification 76.2%

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

Alternative 5: 4.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{g} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (cbrt g))

C

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

Java

public static double code(double g, double a) {
	return Math.cbrt(g);
}

Julia

function code(g, a)
	return cbrt(g)
end

Wolfram

code[g_, a_] := N[Power[g, 1/3], $MachinePrecision]

Derivation

1. Initial program 76.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. clear-num 74.3%

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

   2. cbrt-div 75.8%

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

   3. metadata-eval 75.8%

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

   4. *-un-lft-identity 75.8%

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

   5. times-frac 75.8%

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

   6. metadata-eval 75.8%

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

3. Applied egg-rr 75.8%

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

   1. associate-*r/ 75.8%

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

   2. associate-*l/ 75.4%

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

5. Simplified 75.4%

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

   1. associate-*l/ 75.8%

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

   2. *-commutative 75.8%

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

   3. cbrt-div 98.7%

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

   4. div-inv 98.7%

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

   5. metadata-eval 98.7%

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

   6. div-inv 98.7%

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

   7. add-log-exp 4.6%

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

   8. div-inv 4.6%

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

   9. metadata-eval 4.6%

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

   10. exp-lft-sqr 4.6%

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

   11. log-prod 4.6%

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

   12. add-log-exp 14.0%

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

   13. add-log-exp 98.7%

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

7. Applied egg-rr 98.7%

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

   1. associate-*r/ 98.7%

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

   2. *-rgt-identity 98.7%

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

9. Simplified 98.7%

   \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{g}}}} \]
10. Step-by-step derivation

    1. associate-/r/ 98.7%

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

11. Applied egg-rr 4.8%

    \[\leadsto \color{blue}{\left(a + a\right) \cdot \sqrt[3]{g}} \]

13. Simplified 5.0%

    \[\leadsto \color{blue}{\sqrt[3]{g}} \]

14. Final simplification 5.0%

    \[\leadsto \sqrt[3]{g} \]

Alternative 6: 3.2% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (g a) :precision binary64 0.0)

C

double code(double g, double a) {
	return 0.0;
}

Fortran

real(8) function code(g, a)
    real(8), intent (in) :: g
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double g, double a) {
	return 0.0;
}

Python

def code(g, a):
	return 0.0

Julia

function code(g, a)
	return 0.0
end

MATLAB

function tmp = code(g, a)
	tmp = 0.0;
end

Wolfram

code[g_, a_] := 0.0

Derivation

1. Initial program 76.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Step-by-step derivation

   1. clear-num 74.3%

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

   2. cbrt-div 75.8%

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

   3. metadata-eval 75.8%

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

   4. *-un-lft-identity 75.8%

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

   5. times-frac 75.8%

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

   6. metadata-eval 75.8%

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

3. Applied egg-rr 75.8%

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

   1. associate-*r/ 75.8%

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

   2. associate-*l/ 75.4%

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

5. Simplified 75.4%

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

   1. associate-*l/ 75.8%

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

   2. *-commutative 75.8%

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

   3. cbrt-div 98.7%

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

   4. div-inv 98.7%

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

   5. metadata-eval 98.7%

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

   6. div-inv 98.7%

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

   7. add-log-exp 4.6%

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

   8. div-inv 4.6%

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

   9. metadata-eval 4.6%

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

   10. exp-lft-sqr 4.6%

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

   11. log-prod 4.6%

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

   12. add-log-exp 14.0%

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

   13. add-log-exp 98.7%

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

7. Applied egg-rr 98.7%

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

   1. associate-*r/ 98.7%

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

   2. *-rgt-identity 98.7%

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

9. Simplified 98.7%

   \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{g}}}} \]
10. Step-by-step derivation

    1. flip-+ 0.0%

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

    2. difference-of-squares 0.0%

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

    3. +-inverses 0.0%

       \[\leadsto \frac{1}{\frac{\sqrt[3]{\frac{\left(a + a\right) \cdot \color{blue}{0}}{a - a}}}{\sqrt[3]{g}}} \]

    4. metadata-eval 0.0%

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

    5. +-inverses 0.0%

       \[\leadsto \frac{1}{\frac{\sqrt[3]{\frac{\left(a + a\right) \cdot \log 1}{\color{blue}{0}}}}{\sqrt[3]{g}}} \]

    6. metadata-eval 0.0%

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

    7. associate-*r/ 0.0%

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

    8. metadata-eval 0.0%

       \[\leadsto \frac{1}{\frac{\sqrt[3]{\left(a + a\right) \cdot \frac{\color{blue}{0}}{\log 1}}}{\sqrt[3]{g}}} \]

    9. +-inverses 0.0%

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

    10. metadata-eval 0.0%

        \[\leadsto \frac{1}{\frac{\sqrt[3]{\left(a + a\right) \cdot \frac{a \cdot a - a \cdot a}{\color{blue}{0}}}}{\sqrt[3]{g}}} \]

    11. +-inverses 0.0%

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

    12. flip-+ 4.6%

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

    13. flip-+ 0.0%

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

    14. difference-of-squares 0.0%

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

    15. +-inverses 0.0%

        \[\leadsto \frac{1}{\frac{\sqrt[3]{\frac{\left(a + a\right) \cdot \color{blue}{0}}{a - a} \cdot \left(a + a\right)}}{\sqrt[3]{g}}} \]

    16. metadata-eval 0.0%

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

    17. +-inverses 0.0%

        \[\leadsto \frac{1}{\frac{\sqrt[3]{\frac{\left(a + a\right) \cdot \log 1}{\color{blue}{0}} \cdot \left(a + a\right)}}{\sqrt[3]{g}}} \]

    18. metadata-eval 0.0%

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

    19. associate-*r/ 0.0%

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

    20. metadata-eval 0.0%

        \[\leadsto \frac{1}{\frac{\sqrt[3]{\left(\left(a + a\right) \cdot \frac{\color{blue}{0}}{\log 1}\right) \cdot \left(a + a\right)}}{\sqrt[3]{g}}} \]

    21. +-inverses 0.0%

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

    22. metadata-eval 0.0%

        \[\leadsto \frac{1}{\frac{\sqrt[3]{\left(\left(a + a\right) \cdot \frac{a \cdot a - a \cdot a}{\color{blue}{0}}\right) \cdot \left(a + a\right)}}{\sqrt[3]{g}}} \]

    23. +-inverses 0.0%

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

    24. flip-+ 5.5%

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

11. Applied egg-rr 6.4%

    \[\leadsto \frac{1}{\frac{\color{blue}{a + a}}{\sqrt[3]{g}}} \]
12. Step-by-step derivation

    1. clear-num 6.4%

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

    2. flip-+ 0.0%

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

    3. +-inverses 0.0%

       \[\leadsto \frac{\sqrt[3]{g}}{\frac{\color{blue}{0}}{a - a}} \]

    4. metadata-eval 0.0%

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

    5. +-inverses 0.0%

       \[\leadsto \frac{\sqrt[3]{g}}{\frac{\log 1}{\color{blue}{0}}} \]

    6. metadata-eval 0.0%

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

    7. associate-/r/ 0.0%

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

    8. metadata-eval 0.0%

       \[\leadsto \frac{\sqrt[3]{g}}{\color{blue}{0}} \cdot \log 1 \]

    9. metadata-eval 0.0%

       \[\leadsto \frac{\sqrt[3]{g}}{0} \cdot \color{blue}{0} \]

13. Applied egg-rr 0.0%

    \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{0} \cdot 0} \]

15. Simplified 3.3%

    \[\leadsto \color{blue}{0} \]

16. Final simplification 3.3%

    \[\leadsto 0 \]

Reproduce

herbie shell --seed 2023182 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))