Average Error: 0.0 → 0.0
Time: 16.3s
Precision: 64
\[x + \frac{y - x}{z}\]
↓
\[\left(\frac{y}{z} + x\right) - \frac{x}{z}\]
x + \frac{y - x}{z}
↓
\left(\frac{y}{z} + x\right) - \frac{x}{z}
double f(double x, double y, double z) {
        double r524141 = x;
        double r524142 = y;
        double r524143 = r524142 - r524141;
        double r524144 = z;
        double r524145 = r524143 / r524144;
        double r524146 = r524141 + r524145;
        return r524146;
}
↓
double f(double x, double y, double z) {
        double r524147 = y;
        double r524148 = z;
        double r524149 = r524147 / r524148;
        double r524150 = x;
        double r524151 = r524149 + r524150;
        double r524152 = r524150 / r524148;
        double r524153 = r524151 - r524152;
        return r524153;
}

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

    \[\leadsto \left(\frac{y}{z} + x\right) - \frac{x}{z}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  (+ x (/ (- y x) z)))