Average Error: 0.1 → 0.1
Time: 16.1s
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 r205079 = 1.0;
        double r205080 = 2.0;
        double r205081 = r205079 / r205080;
        double r205082 = x;
        double r205083 = y;
        double r205084 = z;
        double r205085 = sqrt(r205084);
        double r205086 = r205083 * r205085;
        double r205087 = r205082 + r205086;
        double r205088 = r205081 * r205087;
        return r205088;
}
↓
double f(double x, double y, double z) {
        double r205089 = 1.0;
        double r205090 = 2.0;
        double r205091 = r205089 / r205090;
        double r205092 = x;
        double r205093 = y;
        double r205094 = z;
        double r205095 = sqrt(r205094);
        double r205096 = r205093 * r205095;
        double r205097 = r205092 + r205096;
        double r205098 = r205091 * r205097;
        return r205098;
}

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 2019303 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))