Average Error: 0.0 → 0.0
Time: 6.2s
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 r10103 = x;
        double r10104 = y;
        double r10105 = r10104 - r10103;
        double r10106 = z;
        double r10107 = r10105 / r10106;
        double r10108 = r10103 + r10107;
        return r10108;
}
↓
double f(double x, double y, double z) {
        double r10109 = x;
        double r10110 = y;
        double r10111 = z;
        double r10112 = r10110 / r10111;
        double r10113 = r10109 / r10111;
        double r10114 = r10112 - r10113;
        double r10115 = r10109 + r10114;
        return r10115;
}

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)))