Average Error: 15.0 → 2.1
Time: 4.4s
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 r84029 = x;
        double r84030 = y;
        double r84031 = z;
        double r84032 = r84030 / r84031;
        double r84033 = t;
        double r84034 = r84032 * r84033;
        double r84035 = r84034 / r84033;
        double r84036 = r84029 * r84035;
        return r84036;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r84037 = x;
        double r84038 = y;
        double r84039 = cbrt(r84038);
        double r84040 = r84039 * r84039;
        double r84041 = z;
        double r84042 = cbrt(r84041);
        double r84043 = r84042 * r84042;
        double r84044 = r84040 / r84043;
        double r84045 = r84037 * r84044;
        double r84046 = r84039 / r84042;
        double r84047 = r84045 * r84046;
        return r84047;
}

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 15.0

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

  2. Simplified6.2

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

  4. Applied add-cube-cbrt7.0

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

  5. Applied add-cube-cbrt7.2

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

  6. Applied times-frac7.2

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

  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. Final simplification2.1

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

Reproduce

herbie shell --seed 2020027 +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)))