Average Error: 14.8 → 2.0
Time: 19.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(y \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(y \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r6247493 = x;
        double r6247494 = y;
        double r6247495 = z;
        double r6247496 = r6247494 / r6247495;
        double r6247497 = t;
        double r6247498 = r6247496 * r6247497;
        double r6247499 = r6247498 / r6247497;
        double r6247500 = r6247493 * r6247499;
        return r6247500;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r6247501 = y;
        double r6247502 = x;
        double r6247503 = cbrt(r6247502);
        double r6247504 = z;
        double r6247505 = cbrt(r6247504);
        double r6247506 = r6247503 / r6247505;
        double r6247507 = r6247506 * r6247506;
        double r6247508 = r6247501 * r6247507;
        double r6247509 = r6247508 * r6247506;
        return r6247509;
}

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. Simplified6.1

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

  4. Applied add-cube-cbrt6.9

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

  5. Applied add-cube-cbrt7.1

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

  6. Applied times-frac7.1

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

  7. Applied associate-*r*1.9

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

  8. Simplified2.0

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

  9. Final simplification2.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))