Average Error: 0.0 → 0.0
Time: 7.9s
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 r12026 = x;
        double r12027 = y;
        double r12028 = r12027 - r12026;
        double r12029 = z;
        double r12030 = r12028 / r12029;
        double r12031 = r12026 + r12030;
        return r12031;
}
↓
double f(double x, double y, double z) {
        double r12032 = x;
        double r12033 = y;
        double r12034 = z;
        double r12035 = r12033 / r12034;
        double r12036 = r12032 + r12035;
        double r12037 = r12032 / r12034;
        double r12038 = r12036 - r12037;
        return r12038;
}

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 2019323 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))