Average Error: 14.1 → 2.0
Time: 30.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot y\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot y\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r6441538 = x;
        double r6441539 = y;
        double r6441540 = z;
        double r6441541 = r6441539 / r6441540;
        double r6441542 = t;
        double r6441543 = r6441541 * r6441542;
        double r6441544 = r6441543 / r6441542;
        double r6441545 = r6441538 * r6441544;
        return r6441545;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r6441546 = x;
        double r6441547 = cbrt(r6441546);
        double r6441548 = z;
        double r6441549 = cbrt(r6441548);
        double r6441550 = r6441547 / r6441549;
        double r6441551 = y;
        double r6441552 = r6441550 * r6441551;
        double r6441553 = r6441547 * r6441547;
        double r6441554 = r6441549 * r6441549;
        double r6441555 = r6441553 / r6441554;
        double r6441556 = r6441552 * r6441555;
        return r6441556;
}

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 14.1

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

  2. Simplified6.0

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

  4. Applied add-cube-cbrt6.8

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

  5. Applied add-cube-cbrt7.0

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

  6. Applied times-frac7.0

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

  7. Applied associate-*l*2.0

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

  8. Final simplification2.0

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

Reproduce

herbie shell --seed 2019151 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))