Average Error: 14.1 → 2.0
Time: 4.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\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}}
double f(double x, double y, double z, double t) {
        double r119900 = x;
        double r119901 = y;
        double r119902 = z;
        double r119903 = r119901 / r119902;
        double r119904 = t;
        double r119905 = r119903 * r119904;
        double r119906 = r119905 / r119904;
        double r119907 = r119900 * r119906;
        return r119907;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r119908 = x;
        double r119909 = y;
        double r119910 = cbrt(r119909);
        double r119911 = r119910 * r119910;
        double r119912 = z;
        double r119913 = cbrt(r119912);
        double r119914 = r119913 * r119913;
        double r119915 = r119911 / r119914;
        double r119916 = r119908 * r119915;
        double r119917 = r119910 / r119913;
        double r119918 = r119916 * r119917;
        return r119918;
}

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 14.1

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

  2. Simplified5.8

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

  4. Applied add-cube-cbrt6.6

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

  5. Applied add-cube-cbrt6.8

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

  6. Applied times-frac6.8

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

  7. Applied associate-*r*2.0

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

  8. Final simplification2.0

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

Reproduce

herbie shell --seed 2020100 
(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)))