Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[x + \frac{y - x}{z}\]
↓
\[\left(x + \frac{y}{z}\right) - \frac{x}{z}\]
x + \frac{y - x}{z}
↓
\left(x + \frac{y}{z}\right) - \frac{x}{z}
double f(double x, double y, double z) {
        double r9176 = x;
        double r9177 = y;
        double r9178 = r9177 - r9176;
        double r9179 = z;
        double r9180 = r9178 / r9179;
        double r9181 = r9176 + r9180;
        return r9181;
}
↓
double f(double x, double y, double z) {
        double r9182 = x;
        double r9183 = y;
        double r9184 = z;
        double r9185 = r9183 / r9184;
        double r9186 = r9182 + r9185;
        double r9187 = r9182 / r9184;
        double r9188 = r9186 - r9187;
        return r9188;
}

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 0.0

    \[x + \frac{y - x}{z}\]
  2. Using strategy rm

  3. Applied div-sub0.0

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

  4. Applied associate-+r-0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))