Average Error: 15.5 → 0.8
Time: 18.0s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{1}{a}} \cdot \left(\left(\sqrt[3]{0.5} \cdot \sqrt[3]{-1}\right) \cdot \sqrt[3]{-g}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{1}{a}} \cdot \left(\left(\sqrt[3]{0.5} \cdot \sqrt[3]{-1}\right) \cdot \sqrt[3]{-g}\right)
double f(double g, double a) {
        double r147238 = g;
        double r147239 = 2.0;
        double r147240 = a;
        double r147241 = r147239 * r147240;
        double r147242 = r147238 / r147241;
        double r147243 = cbrt(r147242);
        return r147243;
}
↓
double f(double g, double a) {
        double r147244 = 1.0;
        double r147245 = a;
        double r147246 = r147244 / r147245;
        double r147247 = cbrt(r147246);
        double r147248 = 0.5;
        double r147249 = cbrt(r147248);
        double r147250 = -1.0;
        double r147251 = cbrt(r147250);
        double r147252 = r147249 * r147251;
        double r147253 = g;
        double r147254 = -r147253;
        double r147255 = cbrt(r147254);
        double r147256 = r147252 * r147255;
        double r147257 = r147247 * r147256;
        return r147257;
}

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 15.5

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

  3. Applied div-inv15.5

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

  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 add-sqr-sqrt0.9

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

  7. Applied times-frac0.8

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

  8. Applied cbrt-prod0.8

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

  9. Applied associate-*r*0.8

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

  10. Simplified0.8

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

  11. Taylor expanded around -inf 34.4

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

  12. Simplified0.8

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

  13. Final simplification0.8

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

Reproduce

herbie shell --seed 2019304 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))