Average Error: 0.0 → 0.0
Time: 5.7s
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 r3249 = x;
        double r3250 = y;
        double r3251 = r3250 - r3249;
        double r3252 = z;
        double r3253 = r3251 / r3252;
        double r3254 = r3249 + r3253;
        return r3254;
}
↓
double f(double x, double y, double z) {
        double r3255 = x;
        double r3256 = y;
        double r3257 = z;
        double r3258 = r3256 / r3257;
        double r3259 = r3255 + r3258;
        double r3260 = r3255 / r3257;
        double r3261 = r3259 - r3260;
        return r3261;
}

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 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))