Average Error: 0.1 → 0.1
Time: 19.0s
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 r279026 = 1.0;
        double r279027 = 2.0;
        double r279028 = r279026 / r279027;
        double r279029 = x;
        double r279030 = y;
        double r279031 = z;
        double r279032 = sqrt(r279031);
        double r279033 = r279030 * r279032;
        double r279034 = r279029 + r279033;
        double r279035 = r279028 * r279034;
        return r279035;
}
↓
double f(double x, double y, double z) {
        double r279036 = 1.0;
        double r279037 = 2.0;
        double r279038 = r279036 / r279037;
        double r279039 = x;
        double r279040 = y;
        double r279041 = z;
        double r279042 = sqrt(r279041);
        double r279043 = r279040 * r279042;
        double r279044 = r279039 + r279043;
        double r279045 = r279038 * r279044;
        return r279045;
}

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)))))