Average Error: 0.0 → 0.0
Time: 11.0s
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 r12528 = x;
        double r12529 = y;
        double r12530 = r12529 - r12528;
        double r12531 = z;
        double r12532 = r12530 / r12531;
        double r12533 = r12528 + r12532;
        return r12533;
}
↓
double f(double x, double y, double z) {
        double r12534 = x;
        double r12535 = y;
        double r12536 = z;
        double r12537 = r12535 / r12536;
        double r12538 = r12534 + r12537;
        double r12539 = r12534 / r12536;
        double r12540 = r12538 - r12539;
        return r12540;
}

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)))