Average Error: 14.8 → 1.4
Time: 22.3s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot y\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot y\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r2686874 = x;
        double r2686875 = y;
        double r2686876 = z;
        double r2686877 = r2686875 / r2686876;
        double r2686878 = t;
        double r2686879 = r2686877 * r2686878;
        double r2686880 = r2686879 / r2686878;
        double r2686881 = r2686874 * r2686880;
        return r2686881;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r2686882 = x;
        double r2686883 = cbrt(r2686882);
        double r2686884 = z;
        double r2686885 = cbrt(r2686884);
        double r2686886 = r2686883 / r2686885;
        double r2686887 = y;
        double r2686888 = r2686886 * r2686887;
        double r2686889 = r2686888 * r2686886;
        double r2686890 = r2686889 * r2686886;
        return r2686890;
}

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. Simplified6.0

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

  4. Applied add-cube-cbrt6.8

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

  5. Applied add-cube-cbrt7.0

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

  6. Applied times-frac7.0

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

  7. Applied associate-*l*2.0

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

  9. Applied times-frac2.0

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

  10. Applied associate-*l*1.4

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

  11. Final simplification1.4

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

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))