Average Error: 0.0 → 0.0
Time: 1.4s
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 r4212 = x;
        double r4213 = y;
        double r4214 = r4213 - r4212;
        double r4215 = z;
        double r4216 = r4214 / r4215;
        double r4217 = r4212 + r4216;
        return r4217;
}
↓
double f(double x, double y, double z) {
        double r4218 = x;
        double r4219 = y;
        double r4220 = z;
        double r4221 = r4219 / r4220;
        double r4222 = r4218 / r4220;
        double r4223 = r4221 - r4222;
        double r4224 = r4218 + r4223;
        return r4224;
}

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 2020036 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))