Average Error: 1.7 → 1.7
Time: 12.6s
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 r1066586 = x;
        double r1066587 = 4.0;
        double r1066588 = r1066586 + r1066587;
        double r1066589 = y;
        double r1066590 = r1066588 / r1066589;
        double r1066591 = r1066586 / r1066589;
        double r1066592 = z;
        double r1066593 = r1066591 * r1066592;
        double r1066594 = r1066590 - r1066593;
        double r1066595 = fabs(r1066594);
        return r1066595;
}
↓
double f(double x, double y, double z) {
        double r1066596 = 4.0;
        double r1066597 = x;
        double r1066598 = r1066596 + r1066597;
        double r1066599 = y;
        double r1066600 = r1066598 / r1066599;
        double r1066601 = r1066597 / r1066599;
        double r1066602 = z;
        double r1066603 = r1066601 * r1066602;
        double r1066604 = r1066600 - r1066603;
        double r1066605 = fabs(r1066604);
        return r1066605;
}

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))))