Average Error: 0.1 → 0.1
Time: 10.8s
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 r143535 = 1.0;
        double r143536 = 2.0;
        double r143537 = r143535 / r143536;
        double r143538 = x;
        double r143539 = y;
        double r143540 = z;
        double r143541 = sqrt(r143540);
        double r143542 = r143539 * r143541;
        double r143543 = r143538 + r143542;
        double r143544 = r143537 * r143543;
        return r143544;
}
↓
double f(double x, double y, double z) {
        double r143545 = 1.0;
        double r143546 = 2.0;
        double r143547 = r143545 / r143546;
        double r143548 = x;
        double r143549 = y;
        double r143550 = z;
        double r143551 = sqrt(r143550);
        double r143552 = r143549 * r143551;
        double r143553 = r143548 + r143552;
        double r143554 = r143547 * r143553;
        return r143554;
}

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 2019298 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))