Average Error: 0.0 → 0.0
Time: 18.2s
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 r1102310 = x;
        double r1102311 = y;
        double r1102312 = r1102311 - r1102310;
        double r1102313 = z;
        double r1102314 = r1102312 / r1102313;
        double r1102315 = r1102310 + r1102314;
        return r1102315;
}
↓
double f(double x, double y, double z) {
        double r1102316 = y;
        double r1102317 = z;
        double r1102318 = r1102316 / r1102317;
        double r1102319 = x;
        double r1102320 = r1102318 + r1102319;
        double r1102321 = r1102319 / r1102317;
        double r1102322 = r1102320 - r1102321;
        return r1102322;
}

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 2019170 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  (+ x (/ (- y x) z)))