Average Error: 1.7 → 3.5
Time: 8.7s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|
double f(double x, double y, double z) {
        double r23144 = x;
        double r23145 = 4.0;
        double r23146 = r23144 + r23145;
        double r23147 = y;
        double r23148 = r23146 / r23147;
        double r23149 = r23144 / r23147;
        double r23150 = z;
        double r23151 = r23149 * r23150;
        double r23152 = r23148 - r23151;
        double r23153 = fabs(r23152);
        return r23153;
}
↓
double f(double x, double y, double z) {
        double r23154 = x;
        double r23155 = 4.0;
        double r23156 = r23154 + r23155;
        double r23157 = z;
        double r23158 = r23154 * r23157;
        double r23159 = r23156 - r23158;
        double r23160 = y;
        double r23161 = r23159 / r23160;
        double r23162 = fabs(r23161);
        return r23162;
}

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. Split input into 2 regimes

  2. if x < -2005867205.6988971 or 1.851374073176425e-34 < x

    1. Initial program 0.2

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

    3. Applied div-inv0.2

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

    4. Applied associate-*l*0.2

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

    5. Simplified0.2

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

    if -2005867205.6988971 < x < 1.851374073176425e-34

    1. Initial program 2.7

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

    3. Applied associate-*l/0.1

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

    4. Applied sub-div0.1

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.5

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))