Average Error: 0.1 → 0.1
Time: 4.1s
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 r260538 = 1.0;
        double r260539 = 2.0;
        double r260540 = r260538 / r260539;
        double r260541 = x;
        double r260542 = y;
        double r260543 = z;
        double r260544 = sqrt(r260543);
        double r260545 = r260542 * r260544;
        double r260546 = r260541 + r260545;
        double r260547 = r260540 * r260546;
        return r260547;
}
↓
double f(double x, double y, double z) {
        double r260548 = 1.0;
        double r260549 = 2.0;
        double r260550 = r260548 / r260549;
        double r260551 = x;
        double r260552 = y;
        double r260553 = z;
        double r260554 = sqrt(r260553);
        double r260555 = r260552 * r260554;
        double r260556 = r260551 + r260555;
        double r260557 = r260550 * r260556;
        return r260557;
}

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 2020060 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))