Average Error: 0.0 → 0.0
Time: 12.2s
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 r12566 = x;
        double r12567 = y;
        double r12568 = r12567 - r12566;
        double r12569 = z;
        double r12570 = r12568 / r12569;
        double r12571 = r12566 + r12570;
        return r12571;
}
↓
double f(double x, double y, double z) {
        double r12572 = x;
        double r12573 = y;
        double r12574 = z;
        double r12575 = r12573 / r12574;
        double r12576 = r12572 + r12575;
        double r12577 = r12572 / r12574;
        double r12578 = r12576 - r12577;
        return r12578;
}

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 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))