Average Error: 0.2 → 0.2
Time: 4.5s
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 r205200 = 1.0;
        double r205201 = 2.0;
        double r205202 = r205200 / r205201;
        double r205203 = x;
        double r205204 = y;
        double r205205 = z;
        double r205206 = sqrt(r205205);
        double r205207 = r205204 * r205206;
        double r205208 = r205203 + r205207;
        double r205209 = r205202 * r205208;
        return r205209;
}
↓
double f(double x, double y, double z) {
        double r205210 = 1.0;
        double r205211 = 2.0;
        double r205212 = r205210 / r205211;
        double r205213 = x;
        double r205214 = y;
        double r205215 = z;
        double r205216 = sqrt(r205215);
        double r205217 = r205214 * r205216;
        double r205218 = r205213 + r205217;
        double r205219 = r205212 * r205218;
        return r205219;
}

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 0.2

    \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.2

    \[\leadsto \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))