Average Error: 0.0 → 0.0
Time: 2.3s
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 r11201 = x;
        double r11202 = y;
        double r11203 = r11202 - r11201;
        double r11204 = z;
        double r11205 = r11203 / r11204;
        double r11206 = r11201 + r11205;
        return r11206;
}
↓
double f(double x, double y, double z) {
        double r11207 = x;
        double r11208 = y;
        double r11209 = z;
        double r11210 = r11208 / r11209;
        double r11211 = r11207 + r11210;
        double r11212 = r11207 / r11209;
        double r11213 = r11211 - r11212;
        return r11213;
}

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 2020100 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))