Average Error: 0.1 → 0.1
Time: 4.3s
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 r241498 = 1.0;
        double r241499 = 2.0;
        double r241500 = r241498 / r241499;
        double r241501 = x;
        double r241502 = y;
        double r241503 = z;
        double r241504 = sqrt(r241503);
        double r241505 = r241502 * r241504;
        double r241506 = r241501 + r241505;
        double r241507 = r241500 * r241506;
        return r241507;
}
↓
double f(double x, double y, double z) {
        double r241508 = 1.0;
        double r241509 = 2.0;
        double r241510 = r241508 / r241509;
        double r241511 = x;
        double r241512 = y;
        double r241513 = z;
        double r241514 = sqrt(r241513);
        double r241515 = r241512 * r241514;
        double r241516 = r241511 + r241515;
        double r241517 = r241510 * r241516;
        return r241517;
}

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 2020081 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))