Average Error: 15.6 → 0.9
Time: 4.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right)
double f(double g, double a) {
        double r159749 = g;
        double r159750 = 2.0;
        double r159751 = a;
        double r159752 = r159750 * r159751;
        double r159753 = r159749 / r159752;
        double r159754 = cbrt(r159753);
        return r159754;
}
↓
double f(double g, double a) {
        double r159755 = g;
        double r159756 = cbrt(r159755);
        double r159757 = 1.0;
        double r159758 = 2.0;
        double r159759 = r159757 / r159758;
        double r159760 = cbrt(r159759);
        double r159761 = a;
        double r159762 = r159757 / r159761;
        double r159763 = cbrt(r159762);
        double r159764 = r159760 * r159763;
        double r159765 = r159756 * r159764;
        return r159765;
}

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.6

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  2. Using strategy rm

  3. Applied div-inv15.6

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

  4. Applied cbrt-prod0.9

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity0.9

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

  7. Applied times-frac0.8

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

  8. Applied cbrt-prod0.9

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

  9. Applied associate-*r*0.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{1}{a}}}\]
  10. Using strategy rm

  11. Applied associate-*l*0.9

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

  12. Final simplification0.9

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))