Average Error: 1.7 → 0.6
Time: 15.8s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{4 + x}{y} - \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right)\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{4 + x}{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 r1104704 = x;
        double r1104705 = 4.0;
        double r1104706 = r1104704 + r1104705;
        double r1104707 = y;
        double r1104708 = r1104706 / r1104707;
        double r1104709 = r1104704 / r1104707;
        double r1104710 = z;
        double r1104711 = r1104709 * r1104710;
        double r1104712 = r1104708 - r1104711;
        double r1104713 = fabs(r1104712);
        return r1104713;
}
↓
double f(double x, double y, double z) {
        double r1104714 = 4.0;
        double r1104715 = x;
        double r1104716 = r1104714 + r1104715;
        double r1104717 = y;
        double r1104718 = r1104716 / r1104717;
        double r1104719 = cbrt(r1104715);
        double r1104720 = r1104719 * r1104719;
        double r1104721 = cbrt(r1104717);
        double r1104722 = r1104721 * r1104721;
        double r1104723 = r1104720 / r1104722;
        double r1104724 = r1104719 / r1104721;
        double r1104725 = z;
        double r1104726 = r1104724 * r1104725;
        double r1104727 = r1104723 * r1104726;
        double r1104728 = r1104718 - r1104727;
        double r1104729 = fabs(r1104728);
        return r1104729;
}

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 1.7

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

  3. Applied add-cube-cbrt2.0

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

  4. Applied add-cube-cbrt2.0

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

  5. Applied times-frac2.0

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

  6. Applied associate-*l*0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))