Average Error: 1.5 → 3.6
Time: 9.0s
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 r35668 = x;
        double r35669 = 4.0;
        double r35670 = r35668 + r35669;
        double r35671 = y;
        double r35672 = r35670 / r35671;
        double r35673 = r35668 / r35671;
        double r35674 = z;
        double r35675 = r35673 * r35674;
        double r35676 = r35672 - r35675;
        double r35677 = fabs(r35676);
        return r35677;
}
↓
double f(double x, double y, double z) {
        double r35678 = x;
        double r35679 = 4.0;
        double r35680 = r35678 + r35679;
        double r35681 = z;
        double r35682 = r35678 * r35681;
        double r35683 = r35680 - r35682;
        double r35684 = y;
        double r35685 = r35683 / r35684;
        double r35686 = fabs(r35685);
        return r35686;
}

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 3 regimes

  2. if x < -1.1091102582946148e+97

    1. Initial program 0.1

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

    3. Applied clear-num0.3

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

    if -1.1091102582946148e+97 < x < 214190368136.35208

    1. Initial program 2.1

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

    3. Applied associate-*l/0.5

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

    4. Applied sub-div0.5

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

    if 214190368136.35208 < x

    1. Initial program 0.1

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    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. Simplified0.1

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

  4. Final simplification3.6

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))