Average Error: 0.0 → 0.0
Time: 3.4s
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 r18405 = x;
        double r18406 = y;
        double r18407 = r18406 - r18405;
        double r18408 = z;
        double r18409 = r18407 / r18408;
        double r18410 = r18405 + r18409;
        return r18410;
}
↓
double f(double x, double y, double z) {
        double r18411 = x;
        double r18412 = y;
        double r18413 = z;
        double r18414 = r18412 / r18413;
        double r18415 = r18411 + r18414;
        double r18416 = r18411 / r18413;
        double r18417 = r18415 - r18416;
        return r18417;
}

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 2020025 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))