Average Error: 1.5 → 3.7
Time: 3.0s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|
double f(double x, double y, double z) {
        double r26771 = x;
        double r26772 = 4.0;
        double r26773 = r26771 + r26772;
        double r26774 = y;
        double r26775 = r26773 / r26774;
        double r26776 = r26771 / r26774;
        double r26777 = z;
        double r26778 = r26776 * r26777;
        double r26779 = r26775 - r26778;
        double r26780 = fabs(r26779);
        return r26780;
}
↓
double f(double x, double y, double z) {
        double r26781 = x;
        double r26782 = 4.0;
        double r26783 = r26781 + r26782;
        double r26784 = z;
        double r26785 = r26781 * r26784;
        double r26786 = r26783 - r26785;
        double r26787 = y;
        double r26788 = r26786 / r26787;
        double r26789 = fabs(r26788);
        return r26789;
}

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 1.5

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

  3. Applied associate-*l/3.7

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

  4. Applied sub-div3.7

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

  5. Final simplification3.7

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

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))