Average Error: 0.0 → 0.0
Time: 15.1s
Precision: 64
\[x + \frac{y - x}{z}\]
↓
\[\left(\frac{y}{z} + x\right) - \frac{x}{z}\]
x + \frac{y - x}{z}
↓
\left(\frac{y}{z} + x\right) - \frac{x}{z}
double f(double x, double y, double z) {
        double r483873 = x;
        double r483874 = y;
        double r483875 = r483874 - r483873;
        double r483876 = z;
        double r483877 = r483875 / r483876;
        double r483878 = r483873 + r483877;
        return r483878;
}
↓
double f(double x, double y, double z) {
        double r483879 = y;
        double r483880 = z;
        double r483881 = r483879 / r483880;
        double r483882 = x;
        double r483883 = r483881 + r483882;
        double r483884 = r483882 / r483880;
        double r483885 = r483883 - r483884;
        return r483885;
}

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

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  (+ x (/ (- y x) z)))