Average Error: 0.0 → 0.0
Time: 2.1s
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 r10529 = x;
        double r10530 = y;
        double r10531 = r10530 - r10529;
        double r10532 = z;
        double r10533 = r10531 / r10532;
        double r10534 = r10529 + r10533;
        return r10534;
}
↓
double f(double x, double y, double z) {
        double r10535 = x;
        double r10536 = y;
        double r10537 = z;
        double r10538 = r10536 / r10537;
        double r10539 = r10535 / r10537;
        double r10540 = r10538 - r10539;
        double r10541 = r10535 + r10540;
        return r10541;
}

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 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))