Average Error: 0.0 → 0.0
Time: 6.9s
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 r10162 = x;
        double r10163 = y;
        double r10164 = r10163 - r10162;
        double r10165 = z;
        double r10166 = r10164 / r10165;
        double r10167 = r10162 + r10166;
        return r10167;
}
↓
double f(double x, double y, double z) {
        double r10168 = x;
        double r10169 = y;
        double r10170 = z;
        double r10171 = r10169 / r10170;
        double r10172 = r10168 / r10170;
        double r10173 = r10171 - r10172;
        double r10174 = r10168 + r10173;
        return r10174;
}

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 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)))