Average Error: 0.0 → 0.0
Time: 1.3s
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 r3212 = x;
        double r3213 = y;
        double r3214 = r3213 - r3212;
        double r3215 = z;
        double r3216 = r3214 / r3215;
        double r3217 = r3212 + r3216;
        return r3217;
}
↓
double f(double x, double y, double z) {
        double r3218 = x;
        double r3219 = y;
        double r3220 = z;
        double r3221 = r3219 / r3220;
        double r3222 = r3218 + r3221;
        double r3223 = r3218 / r3220;
        double r3224 = r3222 - r3223;
        return r3224;
}

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 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))