Average Error: 1.7 → 1.7
Time: 3.1s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\left(4 \cdot \frac{1}{y} + \frac{x}{y}\right) - \frac{x}{y} \cdot z\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\left(4 \cdot \frac{1}{y} + \frac{x}{y}\right) - \frac{x}{y} \cdot z\right|
double f(double x, double y, double z) {
        double r27314 = x;
        double r27315 = 4.0;
        double r27316 = r27314 + r27315;
        double r27317 = y;
        double r27318 = r27316 / r27317;
        double r27319 = r27314 / r27317;
        double r27320 = z;
        double r27321 = r27319 * r27320;
        double r27322 = r27318 - r27321;
        double r27323 = fabs(r27322);
        return r27323;
}
↓
double f(double x, double y, double z) {
        double r27324 = 4.0;
        double r27325 = 1.0;
        double r27326 = y;
        double r27327 = r27325 / r27326;
        double r27328 = r27324 * r27327;
        double r27329 = x;
        double r27330 = r27329 / r27326;
        double r27331 = r27328 + r27330;
        double r27332 = z;
        double r27333 = r27330 * r27332;
        double r27334 = r27331 - r27333;
        double r27335 = fabs(r27334);
        return r27335;
}

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. Taylor expanded around 0 1.7

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

  3. Final simplification1.7

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))