Average Error: 0.0 → 0.0
Time: 2.6s
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 r14378 = x;
        double r14379 = y;
        double r14380 = r14379 - r14378;
        double r14381 = z;
        double r14382 = r14380 / r14381;
        double r14383 = r14378 + r14382;
        return r14383;
}
↓
double f(double x, double y, double z) {
        double r14384 = x;
        double r14385 = y;
        double r14386 = z;
        double r14387 = r14385 / r14386;
        double r14388 = r14384 + r14387;
        double r14389 = r14384 / r14386;
        double r14390 = r14388 - r14389;
        return r14390;
}

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 2020062 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))