Average Error: 0.1 → 0.1
Time: 18.3s
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 r157412 = 1.0;
        double r157413 = 2.0;
        double r157414 = r157412 / r157413;
        double r157415 = x;
        double r157416 = y;
        double r157417 = z;
        double r157418 = sqrt(r157417);
        double r157419 = r157416 * r157418;
        double r157420 = r157415 + r157419;
        double r157421 = r157414 * r157420;
        return r157421;
}
↓
double f(double x, double y, double z) {
        double r157422 = 1.0;
        double r157423 = 2.0;
        double r157424 = r157422 / r157423;
        double r157425 = x;
        double r157426 = y;
        double r157427 = z;
        double r157428 = sqrt(r157427);
        double r157429 = r157426 * r157428;
        double r157430 = r157425 + r157429;
        double r157431 = r157424 * r157430;
        return r157431;
}

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 2019323 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))