Average Error: 0.0 → 0.0
Time: 1.3s
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 r7097 = x;
        double r7098 = y;
        double r7099 = r7098 - r7097;
        double r7100 = z;
        double r7101 = r7099 / r7100;
        double r7102 = r7097 + r7101;
        return r7102;
}
↓
double f(double x, double y, double z) {
        double r7103 = x;
        double r7104 = y;
        double r7105 = z;
        double r7106 = r7104 / r7105;
        double r7107 = r7103 + r7106;
        double r7108 = r7103 / r7105;
        double r7109 = r7107 - r7108;
        return r7109;
}

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