Average Error: 0.1 → 0.1
Time: 15.2s
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 r210986 = 1.0;
        double r210987 = 2.0;
        double r210988 = r210986 / r210987;
        double r210989 = x;
        double r210990 = y;
        double r210991 = z;
        double r210992 = sqrt(r210991);
        double r210993 = r210990 * r210992;
        double r210994 = r210989 + r210993;
        double r210995 = r210988 * r210994;
        return r210995;
}
↓
double f(double x, double y, double z) {
        double r210996 = 1.0;
        double r210997 = 2.0;
        double r210998 = r210996 / r210997;
        double r210999 = x;
        double r211000 = y;
        double r211001 = z;
        double r211002 = sqrt(r211001);
        double r211003 = r211000 * r211002;
        double r211004 = r210999 + r211003;
        double r211005 = r210998 * r211004;
        return r211005;
}

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