Average Error: 14.9 → 2.0
Time: 24.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot x\right)\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot x\right)
double f(double x, double y, double z, double t) {
        double r74100 = x;
        double r74101 = y;
        double r74102 = z;
        double r74103 = r74101 / r74102;
        double r74104 = t;
        double r74105 = r74103 * r74104;
        double r74106 = r74105 / r74104;
        double r74107 = r74100 * r74106;
        return r74107;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r74108 = y;
        double r74109 = cbrt(r74108);
        double r74110 = r74109 * r74109;
        double r74111 = z;
        double r74112 = cbrt(r74111);
        double r74113 = r74112 * r74112;
        double r74114 = r74110 / r74113;
        double r74115 = r74109 / r74112;
        double r74116 = x;
        double r74117 = r74115 * r74116;
        double r74118 = r74114 * r74117;
        return r74118;
}

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 14.9

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

  2. Simplified6.3

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

  4. Applied add-cube-cbrt7.1

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

  5. Applied add-cube-cbrt7.3

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

  6. Applied times-frac7.3

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

  7. Applied associate-*l*2.0

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

  8. Final simplification2.0

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

Reproduce

herbie shell --seed 2019323 +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)))