Average Error: 0.2 → 0.2
Time: 7.5s
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 r200577 = 1.0;
        double r200578 = 2.0;
        double r200579 = r200577 / r200578;
        double r200580 = x;
        double r200581 = y;
        double r200582 = z;
        double r200583 = sqrt(r200582);
        double r200584 = r200581 * r200583;
        double r200585 = r200580 + r200584;
        double r200586 = r200579 * r200585;
        return r200586;
}
↓
double f(double x, double y, double z) {
        double r200587 = 1.0;
        double r200588 = 2.0;
        double r200589 = r200587 / r200588;
        double r200590 = x;
        double r200591 = y;
        double r200592 = z;
        double r200593 = sqrt(r200592);
        double r200594 = r200591 * r200593;
        double r200595 = r200590 + r200594;
        double r200596 = r200589 * r200595;
        return r200596;
}

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)))))