Average Error: 0.0 → 0.0
Time: 11.5s
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 r16535 = x;
        double r16536 = y;
        double r16537 = r16536 - r16535;
        double r16538 = z;
        double r16539 = r16537 / r16538;
        double r16540 = r16535 + r16539;
        return r16540;
}
↓
double f(double x, double y, double z) {
        double r16541 = x;
        double r16542 = y;
        double r16543 = z;
        double r16544 = r16542 / r16543;
        double r16545 = r16541 + r16544;
        double r16546 = r16541 / r16543;
        double r16547 = r16545 - r16546;
        return r16547;
}

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 2019199 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  (+ x (/ (- y x) z)))