Average Error: 0.1 → 0.1
Time: 3.9s
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 r225570 = 1.0;
        double r225571 = 2.0;
        double r225572 = r225570 / r225571;
        double r225573 = x;
        double r225574 = y;
        double r225575 = z;
        double r225576 = sqrt(r225575);
        double r225577 = r225574 * r225576;
        double r225578 = r225573 + r225577;
        double r225579 = r225572 * r225578;
        return r225579;
}
↓
double f(double x, double y, double z) {
        double r225580 = 1.0;
        double r225581 = 2.0;
        double r225582 = r225580 / r225581;
        double r225583 = x;
        double r225584 = y;
        double r225585 = z;
        double r225586 = sqrt(r225585);
        double r225587 = r225584 * r225586;
        double r225588 = r225583 + r225587;
        double r225589 = r225582 * r225588;
        return r225589;
}

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)))))