Average Error: 15.2 → 0.9
Time: 11.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{{\left(\sqrt[3]{0.5}\right)}^{3} \cdot \frac{1}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \sqrt[3]{{\left(\sqrt[3]{0.5}\right)}^{3} \cdot \frac{1}{a}}
double f(double g, double a) {
        double r126502 = g;
        double r126503 = 2.0;
        double r126504 = a;
        double r126505 = r126503 * r126504;
        double r126506 = r126502 / r126505;
        double r126507 = cbrt(r126506);
        return r126507;
}
↓
double f(double g, double a) {
        double r126508 = g;
        double r126509 = cbrt(r126508);
        double r126510 = 0.5;
        double r126511 = cbrt(r126510);
        double r126512 = 3.0;
        double r126513 = pow(r126511, r126512);
        double r126514 = 1.0;
        double r126515 = a;
        double r126516 = r126514 / r126515;
        double r126517 = r126513 * r126516;
        double r126518 = cbrt(r126517);
        double r126519 = r126509 * r126518;
        return r126519;
}

Error

Bits error versus g

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.2

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

  3. Applied div-inv15.2

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around 0 34.6

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

  6. Simplified0.9

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{0.5}\right)}\]
  7. Using strategy rm

  8. Applied add-cbrt-cube1.0

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

  9. Simplified0.9

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

  10. Final simplification0.9

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

Reproduce

herbie shell --seed 2019209 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))