Average Error: 0.1 → 0.1
Time: 9.2s
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 r157116 = 1.0;
        double r157117 = 2.0;
        double r157118 = r157116 / r157117;
        double r157119 = x;
        double r157120 = y;
        double r157121 = z;
        double r157122 = sqrt(r157121);
        double r157123 = r157120 * r157122;
        double r157124 = r157119 + r157123;
        double r157125 = r157118 * r157124;
        return r157125;
}
↓
double f(double x, double y, double z) {
        double r157126 = 1.0;
        double r157127 = 2.0;
        double r157128 = r157126 / r157127;
        double r157129 = x;
        double r157130 = y;
        double r157131 = z;
        double r157132 = sqrt(r157131);
        double r157133 = r157130 * r157132;
        double r157134 = r157129 + r157133;
        double r157135 = r157128 * r157134;
        return r157135;
}

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 2020045 +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)))))