Average Error: 0.1 → 0.1
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 r242272 = 1.0;
        double r242273 = 2.0;
        double r242274 = r242272 / r242273;
        double r242275 = x;
        double r242276 = y;
        double r242277 = z;
        double r242278 = sqrt(r242277);
        double r242279 = r242276 * r242278;
        double r242280 = r242275 + r242279;
        double r242281 = r242274 * r242280;
        return r242281;
}
↓
double f(double x, double y, double z) {
        double r242282 = 1.0;
        double r242283 = 2.0;
        double r242284 = r242282 / r242283;
        double r242285 = x;
        double r242286 = y;
        double r242287 = z;
        double r242288 = sqrt(r242287);
        double r242289 = r242286 * r242288;
        double r242290 = r242285 + r242289;
        double r242291 = r242284 * r242290;
        return r242291;
}

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 2020062 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))