Average Error: 1.6 → 1.7
Time: 4.4s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{1}{\frac{y}{x + 4}} - \frac{x}{y} \cdot z\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{1}{\frac{y}{x + 4}} - \frac{x}{y} \cdot z\right|
double f(double x, double y, double z) {
        double r34187 = x;
        double r34188 = 4.0;
        double r34189 = r34187 + r34188;
        double r34190 = y;
        double r34191 = r34189 / r34190;
        double r34192 = r34187 / r34190;
        double r34193 = z;
        double r34194 = r34192 * r34193;
        double r34195 = r34191 - r34194;
        double r34196 = fabs(r34195);
        return r34196;
}
↓
double f(double x, double y, double z) {
        double r34197 = 1.0;
        double r34198 = y;
        double r34199 = x;
        double r34200 = 4.0;
        double r34201 = r34199 + r34200;
        double r34202 = r34198 / r34201;
        double r34203 = r34197 / r34202;
        double r34204 = r34199 / r34198;
        double r34205 = z;
        double r34206 = r34204 * r34205;
        double r34207 = r34203 - r34206;
        double r34208 = fabs(r34207);
        return r34208;
}

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 1.6

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

  3. Applied clear-num1.7

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

  4. Final simplification1.7

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))