Average Error: 1.7 → 1.7
Time: 3.6s
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 r27324 = x;
        double r27325 = 4.0;
        double r27326 = r27324 + r27325;
        double r27327 = y;
        double r27328 = r27326 / r27327;
        double r27329 = r27324 / r27327;
        double r27330 = z;
        double r27331 = r27329 * r27330;
        double r27332 = r27328 - r27331;
        double r27333 = fabs(r27332);
        return r27333;
}
↓
double f(double x, double y, double z) {
        double r27334 = 4.0;
        double r27335 = 1.0;
        double r27336 = y;
        double r27337 = r27335 / r27336;
        double r27338 = r27334 * r27337;
        double r27339 = x;
        double r27340 = r27339 / r27336;
        double r27341 = r27338 + r27340;
        double r27342 = z;
        double r27343 = r27340 * r27342;
        double r27344 = r27341 - r27343;
        double r27345 = fabs(r27344);
        return r27345;
}

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))))