Average Error: 1.7 → 1.9
Time: 18.1s
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 r772188 = x;
        double r772189 = 4.0;
        double r772190 = r772188 + r772189;
        double r772191 = y;
        double r772192 = r772190 / r772191;
        double r772193 = r772188 / r772191;
        double r772194 = z;
        double r772195 = r772193 * r772194;
        double r772196 = r772192 - r772195;
        double r772197 = fabs(r772196);
        return r772197;
}
↓
double f(double x, double y, double z) {
        double r772198 = 4.0;
        double r772199 = x;
        double r772200 = r772198 + r772199;
        double r772201 = y;
        double r772202 = r772200 / r772201;
        double r772203 = cbrt(r772199);
        double r772204 = cbrt(r772201);
        double r772205 = r772203 / r772204;
        double r772206 = z;
        double r772207 = r772205 * r772206;
        double r772208 = r772199 / r772201;
        double r772209 = cbrt(r772208);
        double r772210 = r772209 * r772209;
        double r772211 = r772207 * r772210;
        double r772212 = r772202 - r772211;
        double r772213 = fabs(r772212);
        return r772213;
}

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 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))