Average Error: 1.6 → 0.7
Time: 5.9s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{x + 4}{y} - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{x + 4}{y} - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|
double f(double x, double y, double z) {
        double r44593 = x;
        double r44594 = 4.0;
        double r44595 = r44593 + r44594;
        double r44596 = y;
        double r44597 = r44595 / r44596;
        double r44598 = r44593 / r44596;
        double r44599 = z;
        double r44600 = r44598 * r44599;
        double r44601 = r44597 - r44600;
        double r44602 = fabs(r44601);
        return r44602;
}
↓
double f(double x, double y, double z) {
        double r44603 = x;
        double r44604 = 4.0;
        double r44605 = r44603 + r44604;
        double r44606 = y;
        double r44607 = r44605 / r44606;
        double r44608 = cbrt(r44603);
        double r44609 = r44608 * r44608;
        double r44610 = cbrt(r44606);
        double r44611 = r44610 * r44610;
        double r44612 = r44609 / r44611;
        double r44613 = r44608 / r44610;
        double r44614 = z;
        double r44615 = r44613 * r44614;
        double r44616 = r44612 * r44615;
        double r44617 = r44607 - r44616;
        double r44618 = fabs(r44617);
        return r44618;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.6

    \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.8

    \[\leadsto \left|\frac{x + 4}{y} - \frac{x}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}} \cdot z\right|\]

  4. Applied add-cube-cbrt1.9

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot z\right|\]

  5. Applied times-frac1.9

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)} \cdot z\right|\]

  6. Applied associate-*l*0.7

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)}\right|\]

  7. Final simplification0.7

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))