Average Error: 0.2 → 0.2
Time: 4.4s
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 r237289 = 1.0;
        double r237290 = 2.0;
        double r237291 = r237289 / r237290;
        double r237292 = x;
        double r237293 = y;
        double r237294 = z;
        double r237295 = sqrt(r237294);
        double r237296 = r237293 * r237295;
        double r237297 = r237292 + r237296;
        double r237298 = r237291 * r237297;
        return r237298;
}
↓
double f(double x, double y, double z) {
        double r237299 = 1.0;
        double r237300 = 2.0;
        double r237301 = r237299 / r237300;
        double r237302 = x;
        double r237303 = y;
        double r237304 = z;
        double r237305 = sqrt(r237304);
        double r237306 = r237303 * r237305;
        double r237307 = r237302 + r237306;
        double r237308 = r237301 * r237307;
        return r237308;
}

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 2020057 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))