Average Error: 1.7 → 1.9
Time: 14.9s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{4 + x}{y} - \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right)\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{4 + x}{y} - \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot z\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right)\right|
double f(double x, double y, double z) {
        double r742060 = x;
        double r742061 = 4.0;
        double r742062 = r742060 + r742061;
        double r742063 = y;
        double r742064 = r742062 / r742063;
        double r742065 = r742060 / r742063;
        double r742066 = z;
        double r742067 = r742065 * r742066;
        double r742068 = r742064 - r742067;
        double r742069 = fabs(r742068);
        return r742069;
}
↓
double f(double x, double y, double z) {
        double r742070 = 4.0;
        double r742071 = x;
        double r742072 = r742070 + r742071;
        double r742073 = y;
        double r742074 = r742072 / r742073;
        double r742075 = cbrt(r742071);
        double r742076 = cbrt(r742073);
        double r742077 = r742075 / r742076;
        double r742078 = z;
        double r742079 = r742077 * r742078;
        double r742080 = r742071 / r742073;
        double r742081 = cbrt(r742080);
        double r742082 = r742081 * r742081;
        double r742083 = r742079 * r742082;
        double r742084 = r742074 - r742083;
        double r742085 = fabs(r742084);
        return r742085;
}

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

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

  4. Applied associate-*l*2.0

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

  6. Applied cbrt-div1.9

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

  7. Final simplification1.9

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

Reproduce

herbie shell --seed 2019129 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))