Average Error: 14.4 → 1.4
Time: 4.5s
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 r174020 = x;
        double r174021 = y;
        double r174022 = z;
        double r174023 = r174021 / r174022;
        double r174024 = t;
        double r174025 = r174023 * r174024;
        double r174026 = r174025 / r174024;
        double r174027 = r174020 * r174026;
        return r174027;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r174028 = x;
        double r174029 = y;
        double r174030 = cbrt(r174029);
        double r174031 = z;
        double r174032 = cbrt(r174031);
        double r174033 = r174030 / r174032;
        double r174034 = r174028 * r174033;
        double r174035 = r174034 * r174033;
        double r174036 = r174035 * r174033;
        return r174036;
}

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 +o rules:numerics
(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)))