Average Error: 14.8 → 1.4
Time: 21.9s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot y\right)\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot y\right)\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r4359667 = x;
        double r4359668 = y;
        double r4359669 = z;
        double r4359670 = r4359668 / r4359669;
        double r4359671 = t;
        double r4359672 = r4359670 * r4359671;
        double r4359673 = r4359672 / r4359671;
        double r4359674 = r4359667 * r4359673;
        return r4359674;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r4359675 = x;
        double r4359676 = cbrt(r4359675);
        double r4359677 = z;
        double r4359678 = cbrt(r4359677);
        double r4359679 = r4359676 / r4359678;
        double r4359680 = y;
        double r4359681 = r4359679 * r4359680;
        double r4359682 = r4359679 * r4359681;
        double r4359683 = r4359682 * r4359679;
        return r4359683;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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. Simplified1.4

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

  9. Final simplification1.4

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

Reproduce

herbie shell --seed 2019172 +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)))