Average Error: 14.8 → 1.4
Time: 5.5s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\left(x \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\left(x \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r154790 = x;
        double r154791 = y;
        double r154792 = z;
        double r154793 = r154791 / r154792;
        double r154794 = t;
        double r154795 = r154793 * r154794;
        double r154796 = r154795 / r154794;
        double r154797 = r154790 * r154796;
        return r154797;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r154798 = x;
        double r154799 = y;
        double r154800 = cbrt(r154799);
        double r154801 = z;
        double r154802 = cbrt(r154801);
        double r154803 = r154800 / r154802;
        double r154804 = r154798 * r154803;
        double r154805 = r154804 * r154803;
        double r154806 = r154805 * r154803;
        return r154806;
}

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 14.8

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

  2. Simplified6.5

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

  4. Applied add-cube-cbrt7.2

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

  5. Applied add-cube-cbrt7.4

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

  6. Applied times-frac7.4

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

  7. Applied associate-*r*2.1

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

  9. Applied times-frac2.1

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

  10. Applied associate-*r*1.4

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

  11. Final simplification1.4

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

Reproduce

herbie shell --seed 2019322 
(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)))