Average Error: 0.1 → 0.1
Time: 17.0s
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 r127028 = 1.0;
        double r127029 = 2.0;
        double r127030 = r127028 / r127029;
        double r127031 = x;
        double r127032 = y;
        double r127033 = z;
        double r127034 = sqrt(r127033);
        double r127035 = r127032 * r127034;
        double r127036 = r127031 + r127035;
        double r127037 = r127030 * r127036;
        return r127037;
}
↓
double f(double x, double y, double z) {
        double r127038 = 1.0;
        double r127039 = 2.0;
        double r127040 = r127038 / r127039;
        double r127041 = x;
        double r127042 = y;
        double r127043 = z;
        double r127044 = sqrt(r127043);
        double r127045 = r127042 * r127044;
        double r127046 = r127041 + r127045;
        double r127047 = r127040 * r127046;
        return r127047;
}

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 2019306 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))