Average Error: 0.1 → 0.1
Time: 16.5s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
double f(double x, double y, double z) {
        double r176350 = 1.0;
        double r176351 = 2.0;
        double r176352 = r176350 / r176351;
        double r176353 = x;
        double r176354 = y;
        double r176355 = z;
        double r176356 = sqrt(r176355);
        double r176357 = r176354 * r176356;
        double r176358 = r176353 + r176357;
        double r176359 = r176352 * r176358;
        return r176359;
}
↓
double f(double x, double y, double z) {
        double r176360 = 1.0;
        double r176361 = 2.0;
        double r176362 = r176360 / r176361;
        double r176363 = x;
        double r176364 = y;
        double r176365 = z;
        double r176366 = sqrt(r176365);
        double r176367 = r176364 * r176366;
        double r176368 = r176363 + r176367;
        double r176369 = r176362 * r176368;
        return r176369;
}

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 0.1

    \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.1

    \[\leadsto \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))