Average Error: 14.2 → 1.4
Time: 19.5s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot x\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot x\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r13565971 = x;
        double r13565972 = y;
        double r13565973 = z;
        double r13565974 = r13565972 / r13565973;
        double r13565975 = t;
        double r13565976 = r13565974 * r13565975;
        double r13565977 = r13565976 / r13565975;
        double r13565978 = r13565971 * r13565977;
        return r13565978;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r13565979 = y;
        double r13565980 = cbrt(r13565979);
        double r13565981 = z;
        double r13565982 = cbrt(r13565981);
        double r13565983 = r13565980 / r13565982;
        double r13565984 = x;
        double r13565985 = r13565983 * r13565984;
        double r13565986 = r13565983 * r13565985;
        double r13565987 = r13565986 * r13565983;
        return r13565987;
}

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 14.2

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

  2. Simplified6.0

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

  4. Applied add-cube-cbrt6.8

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

  5. Applied add-cube-cbrt6.9

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

  6. Applied times-frac6.9

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

  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

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

Reproduce

herbie shell --seed 2019107 +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)))