Average Error: 0.0 → 0.0
Time: 11.0s
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 r14189 = x;
        double r14190 = y;
        double r14191 = r14190 - r14189;
        double r14192 = z;
        double r14193 = r14191 / r14192;
        double r14194 = r14189 + r14193;
        return r14194;
}
↓
double f(double x, double y, double z) {
        double r14195 = x;
        double r14196 = y;
        double r14197 = z;
        double r14198 = r14196 / r14197;
        double r14199 = r14195 + r14198;
        double r14200 = r14195 / r14197;
        double r14201 = r14199 - r14200;
        return r14201;
}

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 2019198 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  (+ x (/ (- y x) z)))