Average Error: 1.7 → 3.6
Time: 4.8s
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 r19207 = x;
        double r19208 = 4.0;
        double r19209 = r19207 + r19208;
        double r19210 = y;
        double r19211 = r19209 / r19210;
        double r19212 = r19207 / r19210;
        double r19213 = z;
        double r19214 = r19212 * r19213;
        double r19215 = r19211 - r19214;
        double r19216 = fabs(r19215);
        return r19216;
}
↓
double f(double x, double y, double z) {
        double r19217 = x;
        double r19218 = 4.0;
        double r19219 = r19217 + r19218;
        double r19220 = z;
        double r19221 = r19217 * r19220;
        double r19222 = r19219 - r19221;
        double r19223 = y;
        double r19224 = r19222 / r19223;
        double r19225 = fabs(r19224);
        return r19225;
}

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 < -2.2956787801108007e-49 or 2.9212638165055445e+46 < x

    1. Initial program 0.2

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

    3. Applied clear-num0.3

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

    5. Applied div-inv0.4

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

    6. Applied associate-*l*0.5

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

    7. Simplified0.4

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

    if -2.2956787801108007e-49 < x < 2.9212638165055445e+46

    1. Initial program 2.8

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

    3. Applied associate-*l/0.2

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

    4. Applied sub-div0.2

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

  4. Final simplification3.6

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

Reproduce

herbie shell --seed 2019308 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))