2-ancestry mixing, zero discriminant

Percentage Accurate: 75.4% → 98.7%

Time: 2.7s

Alternatives: 5

Speedup: 0.9×

Specification

Math

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

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: 75.4% accurate, 1.0× speedup

Math

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

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, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.4%

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

   1. lift-cbrt.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. cbrt-div N/A

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

   4. lower-/.f64 N/A

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

   5. lower-cbrt.f64 N/A

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

   6. lower-cbrt.f64 98.7%

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

   7. lift-*.f64 N/A

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

   8. count-2-rev N/A

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

   9. lower-+.f64 98.7%

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

3. Applied rewrites 98.7%

   \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{a + a}}} \]
4. Add Preprocessing

Alternative 2: 75.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.4%

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

   1. lift-cbrt.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. cbrt-div N/A

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

   4. lower-/.f64 N/A

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

   5. lower-cbrt.f64 N/A

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

   6. lower-cbrt.f64 98.7%

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

   7. lift-*.f64 N/A

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

   8. count-2-rev N/A

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

   9. lower-+.f64 98.7%

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

3. Applied rewrites 98.7%

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

   1. lift-/.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. count-2 N/A

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

   5. cbrt-prod N/A

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

   6. lift-cbrt.f64 N/A

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

   7. associate-/r* N/A

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

   8. lift-cbrt.f64 N/A

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

   9. cbrt-div N/A

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

   10. mult-flip-rev N/A

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

   11. metadata-eval N/A

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

   12. *-commutative N/A

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

   13. lift-*.f64 N/A

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

   14. lift-cbrt.f64 N/A

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

   15. div-flip-rev N/A

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

   16. lift-/.f64 N/A

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

   17. lift-/.f64 98.7%

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

   18. lift-/.f64 N/A

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

   19. lift-cbrt.f64 N/A

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

   20. lift-cbrt.f64 N/A

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

   21. cbrt-undiv N/A

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

   22. lift-*.f64 N/A

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

   23. *-commutative N/A

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

   24. associate-/r* N/A

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

   25. div-flip-rev N/A

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

   26. lift-/.f64 N/A

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

5. Applied rewrites 75.1%

   \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{\frac{a + a}{g}}}} \]
6. Add Preprocessing

Alternative 3: 75.3% accurate, 1.0× speedup

Math

\[\frac{0.7937005259840998}{\sqrt[3]{\frac{a}{g}}} \]

FPCore

(FPCore (g a) :precision binary64 (/ 0.7937005259840998 (cbrt (/ a g))))

C

double code(double g, double a) {
	return 0.7937005259840998 / cbrt((a / g));
}

Java

public static double code(double g, double a) {
	return 0.7937005259840998 / Math.cbrt((a / g));
}

Julia

function code(g, a)
	return Float64(0.7937005259840998 / cbrt(Float64(a / g)))
end

Wolfram

code[g_, a_] := N[(0.7937005259840998 / N[Power[N[(a / g), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.4%

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

   1. lift-cbrt.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-/r* N/A

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

   6. mult-flip N/A

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

   7. cbrt-prod N/A

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

   8. cbrt-undiv N/A

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

   9. lower-*.f64 N/A

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

   10. cbrt-undiv N/A

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

   11. lower-cbrt.f64 N/A

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

   12. lower-/.f64 N/A

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

   13. lower-cbrt.f64 N/A

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

   14. metadata-eval 75.3%

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

3. Applied rewrites 75.3%

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

4. Evaluated real constant 75.3%

   \[\leadsto \sqrt[3]{\frac{g}{a}} \cdot \color{blue}{0.7937005259840998} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\sqrt[3]{\frac{g}{a}} \cdot \frac{7149018786131517}{9007199254740992}} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\frac{7149018786131517}{9007199254740992} \cdot \sqrt[3]{\frac{g}{a}}} \]

   3. lift-cbrt.f64 N/A

      \[\leadsto \frac{7149018786131517}{9007199254740992} \cdot \color{blue}{\sqrt[3]{\frac{g}{a}}} \]

   4. lift-/.f64 N/A

      \[\leadsto \frac{7149018786131517}{9007199254740992} \cdot \sqrt[3]{\color{blue}{\frac{g}{a}}} \]

   5. div-flip-rev N/A

      \[\leadsto \frac{7149018786131517}{9007199254740992} \cdot \sqrt[3]{\color{blue}{\frac{1}{\frac{a}{g}}}} \]

   6. lift-/.f64 N/A

      \[\leadsto \frac{7149018786131517}{9007199254740992} \cdot \sqrt[3]{\frac{1}{\color{blue}{\frac{a}{g}}}} \]

   7. cbrt-undiv N/A

      \[\leadsto \frac{7149018786131517}{9007199254740992} \cdot \color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{\frac{a}{g}}}} \]

   8. metadata-eval N/A

      \[\leadsto \frac{7149018786131517}{9007199254740992} \cdot \frac{\color{blue}{1}}{\sqrt[3]{\frac{a}{g}}} \]

   9. lift-cbrt.f64 N/A

      \[\leadsto \frac{7149018786131517}{9007199254740992} \cdot \frac{1}{\color{blue}{\sqrt[3]{\frac{a}{g}}}} \]

   10. mult-flip-rev N/A

       \[\leadsto \color{blue}{\frac{\frac{7149018786131517}{9007199254740992}}{\sqrt[3]{\frac{a}{g}}}} \]

   11. lower-/.f64 75.0%

       \[\leadsto \color{blue}{\frac{0.7937005259840998}{\sqrt[3]{\frac{a}{g}}}} \]

6. Applied rewrites 75.0%

   \[\leadsto \color{blue}{\frac{0.7937005259840998}{\sqrt[3]{\frac{a}{g}}}} \]
7. Add Preprocessing

Alternative 4: 75.1% accurate, 1.0× speedup

Math

\[\sqrt[3]{\frac{g}{a}} \cdot 0.7937005259840998 \]

FPCore

(FPCore (g a) :precision binary64 (* (cbrt (/ g a)) 0.7937005259840998))

C

double code(double g, double a) {
	return cbrt((g / a)) * 0.7937005259840998;
}

Java

public static double code(double g, double a) {
	return Math.cbrt((g / a)) * 0.7937005259840998;
}

Julia

function code(g, a)
	return Float64(cbrt(Float64(g / a)) * 0.7937005259840998)
end

Wolfram

code[g_, a_] := N[(N[Power[N[(g / a), $MachinePrecision], 1/3], $MachinePrecision] * 0.7937005259840998), $MachinePrecision]

Derivation

1. Initial program 75.4%

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

   1. lift-cbrt.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-/r* N/A

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

   6. mult-flip N/A

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

   7. cbrt-prod N/A

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

   8. cbrt-undiv N/A

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

   9. lower-*.f64 N/A

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

   10. cbrt-undiv N/A

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

   11. lower-cbrt.f64 N/A

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

   12. lower-/.f64 N/A

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

   13. lower-cbrt.f64 N/A

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

   14. metadata-eval 75.3%

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

3. Applied rewrites 75.3%

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

4. Evaluated real constant 75.3%

   \[\leadsto \sqrt[3]{\frac{g}{a}} \cdot \color{blue}{0.7937005259840998} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.4%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

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

   3. lower-+.f64 75.4%

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

3. Applied rewrites 75.4%

   \[\leadsto \sqrt[3]{\frac{g}{\color{blue}{a + a}}} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2025191 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))