Average Error: 1.7 → 1.7
Time: 21.5s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\left(\frac{4}{y} + \frac{x}{y}\right) - z \cdot \frac{x}{y}\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\left(\frac{4}{y} + \frac{x}{y}\right) - z \cdot \frac{x}{y}\right|
double f(double x, double y, double z) {
        double r663242 = x;
        double r663243 = 4.0;
        double r663244 = r663242 + r663243;
        double r663245 = y;
        double r663246 = r663244 / r663245;
        double r663247 = r663242 / r663245;
        double r663248 = z;
        double r663249 = r663247 * r663248;
        double r663250 = r663246 - r663249;
        double r663251 = fabs(r663250);
        return r663251;
}
↓
double f(double x, double y, double z) {
        double r663252 = 4.0;
        double r663253 = y;
        double r663254 = r663252 / r663253;
        double r663255 = x;
        double r663256 = r663255 / r663253;
        double r663257 = r663254 + r663256;
        double r663258 = z;
        double r663259 = r663258 * r663256;
        double r663260 = r663257 - r663259;
        double r663261 = fabs(r663260);
        return r663261;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Taylor expanded around 0 1.7

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

  3. Simplified1.7

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

  4. Final simplification1.7

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))