Average Error: 0.1 → 0.1
Time: 14.9s
Precision: 64
\[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)
double f(double x, double y, double z) {
        double r12413613 = 1.0;
        double r12413614 = 2.0;
        double r12413615 = r12413613 / r12413614;
        double r12413616 = x;
        double r12413617 = y;
        double r12413618 = z;
        double r12413619 = sqrt(r12413618);
        double r12413620 = r12413617 * r12413619;
        double r12413621 = r12413616 + r12413620;
        double r12413622 = r12413615 * r12413621;
        return r12413622;
}
↓
double f(double x, double y, double z) {
        double r12413623 = 1.0;
        double r12413624 = 2.0;
        double r12413625 = r12413623 / r12413624;
        double r12413626 = x;
        double r12413627 = z;
        double r12413628 = sqrt(r12413627);
        double r12413629 = y;
        double r12413630 = r12413628 * r12413629;
        double r12413631 = r12413626 + r12413630;
        double r12413632 = r12413625 * r12413631;
        return r12413632;
}

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

    \[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.1

    \[\leadsto \frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))