Average Error: 0.1 → 0.1
Time: 4.9s
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 r276274 = 1.0;
        double r276275 = 2.0;
        double r276276 = r276274 / r276275;
        double r276277 = x;
        double r276278 = y;
        double r276279 = z;
        double r276280 = sqrt(r276279);
        double r276281 = r276278 * r276280;
        double r276282 = r276277 + r276281;
        double r276283 = r276276 * r276282;
        return r276283;
}
↓
double f(double x, double y, double z) {
        double r276284 = 1.0;
        double r276285 = 2.0;
        double r276286 = r276284 / r276285;
        double r276287 = x;
        double r276288 = y;
        double r276289 = z;
        double r276290 = sqrt(r276289);
        double r276291 = r276288 * r276290;
        double r276292 = r276287 + r276291;
        double r276293 = r276286 * r276292;
        return r276293;
}

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 2020025 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))