Average Error: 14.4 → 1.9
Time: 4.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\left(x \cdot \left|\frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\left(x \cdot \left|\frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r98828 = x;
        double r98829 = y;
        double r98830 = z;
        double r98831 = r98829 / r98830;
        double r98832 = t;
        double r98833 = r98831 * r98832;
        double r98834 = r98833 / r98832;
        double r98835 = r98828 * r98834;
        return r98835;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r98836 = x;
        double r98837 = y;
        double r98838 = cbrt(r98837);
        double r98839 = z;
        double r98840 = cbrt(r98839);
        double r98841 = r98838 / r98840;
        double r98842 = fabs(r98841);
        double r98843 = r98836 * r98842;
        double r98844 = r98838 * r98838;
        double r98845 = r98840 * r98840;
        double r98846 = r98844 / r98845;
        double r98847 = sqrt(r98846);
        double r98848 = r98843 * r98847;
        double r98849 = r98848 * r98841;
        return r98849;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

    \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

  2. Simplified6.2

    \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt7.0

    \[\leadsto x \cdot \frac{y}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

  5. Applied add-cube-cbrt7.2

    \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}\]

  6. Applied times-frac7.2

    \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)}\]

  7. Applied associate-*r*1.9

    \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt1.9

    \[\leadsto \left(x \cdot \color{blue}{\left(\sqrt{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \sqrt{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right)}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]

  10. Applied associate-*r*1.9

    \[\leadsto \color{blue}{\left(\left(x \cdot \sqrt{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right) \cdot \sqrt{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right)} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]

  11. Simplified1.9

    \[\leadsto \left(\color{blue}{\left(x \cdot \left|\frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right|\right)} \cdot \sqrt{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]

  12. Final simplification1.9

    \[\leadsto \left(\left(x \cdot \left|\frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]

Reproduce

herbie shell --seed 2019362 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))