Average Error: 0.0 → 0.0
Time: 3.5s
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 r13957 = x;
        double r13958 = y;
        double r13959 = r13958 - r13957;
        double r13960 = z;
        double r13961 = r13959 / r13960;
        double r13962 = r13957 + r13961;
        return r13962;
}
↓
double f(double x, double y, double z) {
        double r13963 = x;
        double r13964 = y;
        double r13965 = z;
        double r13966 = r13964 / r13965;
        double r13967 = r13963 / r13965;
        double r13968 = r13966 - r13967;
        double r13969 = r13963 + r13968;
        return r13969;
}

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 2019354 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))