Average Error: 14.4 → 1.4
Time: 4.2s
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 r130719 = x;
        double r130720 = y;
        double r130721 = z;
        double r130722 = r130720 / r130721;
        double r130723 = t;
        double r130724 = r130722 * r130723;
        double r130725 = r130724 / r130723;
        double r130726 = r130719 * r130725;
        return r130726;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r130727 = x;
        double r130728 = y;
        double r130729 = cbrt(r130728);
        double r130730 = z;
        double r130731 = cbrt(r130730);
        double r130732 = r130729 / r130731;
        double r130733 = r130727 * r130732;
        double r130734 = r130733 * r130732;
        double r130735 = r130734 * r130732;
        return r130735;
}

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. Simplified6.1

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

  4. Applied add-cube-cbrt6.9

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

  5. Applied add-cube-cbrt7.1

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

  6. Applied times-frac7.1

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

  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. Using strategy rm

  9. Applied times-frac2.0

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

  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 2020018 
(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)))