Average Error: 0.0 → 0.0
Time: 7.2s
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 r12955 = x;
        double r12956 = y;
        double r12957 = r12956 - r12955;
        double r12958 = z;
        double r12959 = r12957 / r12958;
        double r12960 = r12955 + r12959;
        return r12960;
}
↓
double f(double x, double y, double z) {
        double r12961 = x;
        double r12962 = y;
        double r12963 = z;
        double r12964 = r12962 / r12963;
        double r12965 = r12961 / r12963;
        double r12966 = r12964 - r12965;
        double r12967 = r12961 + r12966;
        return r12967;
}

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