Average Error: 0.0 → 0.0
Time: 9.8s
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 r10429 = x;
        double r10430 = y;
        double r10431 = r10430 - r10429;
        double r10432 = z;
        double r10433 = r10431 / r10432;
        double r10434 = r10429 + r10433;
        return r10434;
}
↓
double f(double x, double y, double z) {
        double r10435 = x;
        double r10436 = y;
        double r10437 = z;
        double r10438 = r10436 / r10437;
        double r10439 = r10435 / r10437;
        double r10440 = r10438 - r10439;
        double r10441 = r10435 + r10440;
        return r10441;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\frac{y - x}{z} + x}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} + x\]

  5. Final simplification0.0

    \[\leadsto x + \left(\frac{y}{z} - \frac{x}{z}\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  (+ x (/ (- y x) z)))