Average Error: 0.1 → 0.1
Time: 16.2s
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 r173287 = 1.0;
        double r173288 = 2.0;
        double r173289 = r173287 / r173288;
        double r173290 = x;
        double r173291 = y;
        double r173292 = z;
        double r173293 = sqrt(r173292);
        double r173294 = r173291 * r173293;
        double r173295 = r173290 + r173294;
        double r173296 = r173289 * r173295;
        return r173296;
}
↓
double f(double x, double y, double z) {
        double r173297 = 1.0;
        double r173298 = 2.0;
        double r173299 = r173297 / r173298;
        double r173300 = x;
        double r173301 = y;
        double r173302 = z;
        double r173303 = sqrt(r173302);
        double r173304 = r173301 * r173303;
        double r173305 = r173300 + r173304;
        double r173306 = r173299 * r173305;
        return r173306;
}

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 2019326 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))