Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[x + \frac{y - x}{z}\]
↓
\[x + \left(\frac{y}{z} - \frac{x}{z}\right)\]
x + \frac{y - x}{z}
↓
x + \left(\frac{y}{z} - \frac{x}{z}\right)
double f(double x, double y, double z) {
        double r3283 = x;
        double r3284 = y;
        double r3285 = r3284 - r3283;
        double r3286 = z;
        double r3287 = r3285 / r3286;
        double r3288 = r3283 + r3287;
        return r3288;
}
↓
double f(double x, double y, double z) {
        double r3289 = x;
        double r3290 = y;
        double r3291 = z;
        double r3292 = r3290 / r3291;
        double r3293 = r3289 / r3291;
        double r3294 = r3292 - r3293;
        double r3295 = r3289 + r3294;
        return r3295;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))