Average Error: 0.2 → 0.2
Time: 19.8s
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 r213602 = 1.0;
        double r213603 = 2.0;
        double r213604 = r213602 / r213603;
        double r213605 = x;
        double r213606 = y;
        double r213607 = z;
        double r213608 = sqrt(r213607);
        double r213609 = r213606 * r213608;
        double r213610 = r213605 + r213609;
        double r213611 = r213604 * r213610;
        return r213611;
}
↓
double f(double x, double y, double z) {
        double r213612 = 1.0;
        double r213613 = 2.0;
        double r213614 = r213612 / r213613;
        double r213615 = x;
        double r213616 = y;
        double r213617 = z;
        double r213618 = sqrt(r213617);
        double r213619 = r213616 * r213618;
        double r213620 = r213615 + r213619;
        double r213621 = r213614 * r213620;
        return r213621;
}

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 2019304 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))