Average Error: 1.6 → 2.2
Time: 13.3s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{4 + x}{y} - \left(\frac{x}{\sqrt[3]{y}} \cdot z\right) \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{4 + x}{y} - \left(\frac{x}{\sqrt[3]{y}} \cdot z\right) \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right|
double f(double x, double y, double z) {
        double r2128311 = x;
        double r2128312 = 4.0;
        double r2128313 = r2128311 + r2128312;
        double r2128314 = y;
        double r2128315 = r2128313 / r2128314;
        double r2128316 = r2128311 / r2128314;
        double r2128317 = z;
        double r2128318 = r2128316 * r2128317;
        double r2128319 = r2128315 - r2128318;
        double r2128320 = fabs(r2128319);
        return r2128320;
}
↓
double f(double x, double y, double z) {
        double r2128321 = 4.0;
        double r2128322 = x;
        double r2128323 = r2128321 + r2128322;
        double r2128324 = y;
        double r2128325 = r2128323 / r2128324;
        double r2128326 = cbrt(r2128324);
        double r2128327 = r2128322 / r2128326;
        double r2128328 = z;
        double r2128329 = r2128327 * r2128328;
        double r2128330 = 1.0;
        double r2128331 = r2128326 * r2128326;
        double r2128332 = r2128330 / r2128331;
        double r2128333 = r2128329 * r2128332;
        double r2128334 = r2128325 - r2128333;
        double r2128335 = fabs(r2128334);
        return r2128335;
}

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-cbrt1.9

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

  4. Applied *-un-lft-identity1.9

    \[\leadsto \left|\frac{x + 4}{y} - \frac{\color{blue}{1 \cdot x}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot z\right|\]

  5. Applied times-frac1.9

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{x}{\sqrt[3]{y}}\right)} \cdot z\right|\]

  6. Applied associate-*l*2.2

    \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot z\right)}\right|\]

  7. Final simplification2.2

    \[\leadsto \left|\frac{4 + x}{y} - \left(\frac{x}{\sqrt[3]{y}} \cdot z\right) \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right|\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))