Average Error: 0.0 → 0.0
Time: 3.2s
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 r12840 = x;
        double r12841 = y;
        double r12842 = r12841 - r12840;
        double r12843 = z;
        double r12844 = r12842 / r12843;
        double r12845 = r12840 + r12844;
        return r12845;
}
↓
double f(double x, double y, double z) {
        double r12846 = x;
        double r12847 = y;
        double r12848 = z;
        double r12849 = r12847 / r12848;
        double r12850 = r12846 / r12848;
        double r12851 = r12849 - r12850;
        double r12852 = r12846 + r12851;
        return r12852;
}

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 2020002 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))