Average Error: 0.0 → 0.0
Time: 11.0s
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 r13431 = x;
        double r13432 = y;
        double r13433 = r13432 - r13431;
        double r13434 = z;
        double r13435 = r13433 / r13434;
        double r13436 = r13431 + r13435;
        return r13436;
}
↓
double f(double x, double y, double z) {
        double r13437 = x;
        double r13438 = y;
        double r13439 = z;
        double r13440 = r13438 / r13439;
        double r13441 = r13437 / r13439;
        double r13442 = r13440 - r13441;
        double r13443 = r13437 + r13442;
        return r13443;
}

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 2019325 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))