Average Error: 1.7 → 1.7
Time: 3.6s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\left(4 \cdot \frac{1}{y} + \frac{x}{y}\right) - \frac{x}{y} \cdot z\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\left(4 \cdot \frac{1}{y} + \frac{x}{y}\right) - \frac{x}{y} \cdot z\right|
double f(double x, double y, double z) {
        double r29173 = x;
        double r29174 = 4.0;
        double r29175 = r29173 + r29174;
        double r29176 = y;
        double r29177 = r29175 / r29176;
        double r29178 = r29173 / r29176;
        double r29179 = z;
        double r29180 = r29178 * r29179;
        double r29181 = r29177 - r29180;
        double r29182 = fabs(r29181);
        return r29182;
}
↓
double f(double x, double y, double z) {
        double r29183 = 4.0;
        double r29184 = 1.0;
        double r29185 = y;
        double r29186 = r29184 / r29185;
        double r29187 = r29183 * r29186;
        double r29188 = x;
        double r29189 = r29188 / r29185;
        double r29190 = r29187 + r29189;
        double r29191 = z;
        double r29192 = r29189 * r29191;
        double r29193 = r29190 - r29192;
        double r29194 = fabs(r29193);
        return r29194;
}

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 1.7

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

  2. Taylor expanded around 0 1.7

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

  3. Final simplification1.7

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

Reproduce

herbie shell --seed 2019356 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))