Average Error: 1.8 → 1.8
Time: 14.4s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\left(x + 4\right) \cdot \frac{1}{y} - \frac{x}{y} \cdot z\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\left(x + 4\right) \cdot \frac{1}{y} - \frac{x}{y} \cdot z\right|
double f(double x, double y, double z) {
        double r43419 = x;
        double r43420 = 4.0;
        double r43421 = r43419 + r43420;
        double r43422 = y;
        double r43423 = r43421 / r43422;
        double r43424 = r43419 / r43422;
        double r43425 = z;
        double r43426 = r43424 * r43425;
        double r43427 = r43423 - r43426;
        double r43428 = fabs(r43427);
        return r43428;
}
↓
double f(double x, double y, double z) {
        double r43429 = x;
        double r43430 = 4.0;
        double r43431 = r43429 + r43430;
        double r43432 = 1.0;
        double r43433 = y;
        double r43434 = r43432 / r43433;
        double r43435 = r43431 * r43434;
        double r43436 = r43429 / r43433;
        double r43437 = z;
        double r43438 = r43436 * r43437;
        double r43439 = r43435 - r43438;
        double r43440 = fabs(r43439);
        return r43440;
}

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 1.8

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

  3. Applied div-inv1.8

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

  4. Final simplification1.8

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

Reproduce

herbie shell --seed 2019209 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))