Average Error: 0.0 → 0.0
Time: 8.5s
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 r10485 = x;
        double r10486 = y;
        double r10487 = r10486 - r10485;
        double r10488 = z;
        double r10489 = r10487 / r10488;
        double r10490 = r10485 + r10489;
        return r10490;
}
↓
double f(double x, double y, double z) {
        double r10491 = x;
        double r10492 = y;
        double r10493 = z;
        double r10494 = r10492 / r10493;
        double r10495 = r10491 + r10494;
        double r10496 = r10491 / r10493;
        double r10497 = r10495 - r10496;
        return r10497;
}

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 2019322 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))