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 r14328 = x;
        double r14329 = y;
        double r14330 = r14329 - r14328;
        double r14331 = z;
        double r14332 = r14330 / r14331;
        double r14333 = r14328 + r14332;
        return r14333;
}
↓
double f(double x, double y, double z) {
        double r14334 = x;
        double r14335 = y;
        double r14336 = z;
        double r14337 = r14335 / r14336;
        double r14338 = r14334 + r14337;
        double r14339 = r14334 / r14336;
        double r14340 = r14338 - r14339;
        return r14340;
}

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 2020062 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))