Average Error: 0.1 → 0.1
Time: 15.5s
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 r157365 = 1.0;
        double r157366 = 2.0;
        double r157367 = r157365 / r157366;
        double r157368 = x;
        double r157369 = y;
        double r157370 = z;
        double r157371 = sqrt(r157370);
        double r157372 = r157369 * r157371;
        double r157373 = r157368 + r157372;
        double r157374 = r157367 * r157373;
        return r157374;
}
↓
double f(double x, double y, double z) {
        double r157375 = 1.0;
        double r157376 = 2.0;
        double r157377 = r157375 / r157376;
        double r157378 = x;
        double r157379 = y;
        double r157380 = z;
        double r157381 = sqrt(r157380);
        double r157382 = r157379 * r157381;
        double r157383 = r157378 + r157382;
        double r157384 = r157377 * r157383;
        return r157384;
}

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 2019305 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))