Average Error: 1.7 → 1.7
Time: 12.9s
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 r1879964 = x;
        double r1879965 = 4.0;
        double r1879966 = r1879964 + r1879965;
        double r1879967 = y;
        double r1879968 = r1879966 / r1879967;
        double r1879969 = r1879964 / r1879967;
        double r1879970 = z;
        double r1879971 = r1879969 * r1879970;
        double r1879972 = r1879968 - r1879971;
        double r1879973 = fabs(r1879972);
        return r1879973;
}
↓
double f(double x, double y, double z) {
        double r1879974 = 4.0;
        double r1879975 = x;
        double r1879976 = r1879974 + r1879975;
        double r1879977 = y;
        double r1879978 = r1879976 / r1879977;
        double r1879979 = r1879975 / r1879977;
        double r1879980 = z;
        double r1879981 = r1879979 * r1879980;
        double r1879982 = r1879978 - r1879981;
        double r1879983 = fabs(r1879982);
        return r1879983;
}

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 2019169 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))