Average Error: 1.7 → 1.7
Time: 12.7s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|
double f(double x, double y, double z) {
        double r1529054 = x;
        double r1529055 = 4.0;
        double r1529056 = r1529054 + r1529055;
        double r1529057 = y;
        double r1529058 = r1529056 / r1529057;
        double r1529059 = r1529054 / r1529057;
        double r1529060 = z;
        double r1529061 = r1529059 * r1529060;
        double r1529062 = r1529058 - r1529061;
        double r1529063 = fabs(r1529062);
        return r1529063;
}
↓
double f(double x, double y, double z) {
        double r1529064 = 4.0;
        double r1529065 = x;
        double r1529066 = r1529064 + r1529065;
        double r1529067 = y;
        double r1529068 = r1529066 / r1529067;
        double r1529069 = r1529065 / r1529067;
        double r1529070 = z;
        double r1529071 = r1529069 * r1529070;
        double r1529072 = r1529068 - r1529071;
        double r1529073 = fabs(r1529072);
        return r1529073;
}

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. Final simplification1.7

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))