Average Error: 0.0 → 0.0
Time: 2.7s
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 r14332 = x;
        double r14333 = y;
        double r14334 = r14333 - r14332;
        double r14335 = z;
        double r14336 = r14334 / r14335;
        double r14337 = r14332 + r14336;
        return r14337;
}
↓
double f(double x, double y, double z) {
        double r14338 = x;
        double r14339 = y;
        double r14340 = z;
        double r14341 = r14339 / r14340;
        double r14342 = r14338 + r14341;
        double r14343 = r14338 / r14340;
        double r14344 = r14342 - r14343;
        return r14344;
}

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 2020060 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))