Average Error: 0.0 → 0.0
Time: 1.3s
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 r6376 = x;
        double r6377 = y;
        double r6378 = r6377 - r6376;
        double r6379 = z;
        double r6380 = r6378 / r6379;
        double r6381 = r6376 + r6380;
        return r6381;
}
↓
double f(double x, double y, double z) {
        double r6382 = x;
        double r6383 = y;
        double r6384 = z;
        double r6385 = r6383 / r6384;
        double r6386 = r6382 / r6384;
        double r6387 = r6385 - r6386;
        double r6388 = r6382 + r6387;
        return r6388;
}

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 2020034 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))