Average Error: 1.6 → 1.6
Time: 18.5s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\left(\frac{4}{y} + \frac{x}{y}\right) - z \cdot \frac{x}{y}\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\left(\frac{4}{y} + \frac{x}{y}\right) - z \cdot \frac{x}{y}\right|
double f(double x, double y, double z) {
        double r1810489 = x;
        double r1810490 = 4.0;
        double r1810491 = r1810489 + r1810490;
        double r1810492 = y;
        double r1810493 = r1810491 / r1810492;
        double r1810494 = r1810489 / r1810492;
        double r1810495 = z;
        double r1810496 = r1810494 * r1810495;
        double r1810497 = r1810493 - r1810496;
        double r1810498 = fabs(r1810497);
        return r1810498;
}
↓
double f(double x, double y, double z) {
        double r1810499 = 4.0;
        double r1810500 = y;
        double r1810501 = r1810499 / r1810500;
        double r1810502 = x;
        double r1810503 = r1810502 / r1810500;
        double r1810504 = r1810501 + r1810503;
        double r1810505 = z;
        double r1810506 = r1810505 * r1810503;
        double r1810507 = r1810504 - r1810506;
        double r1810508 = fabs(r1810507);
        return r1810508;
}

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. Taylor expanded around 0 1.6

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

  3. Simplified1.6

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

  4. Final simplification1.6

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))