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 r293505 = 1.0;
        double r293506 = 2.0;
        double r293507 = r293505 / r293506;
        double r293508 = x;
        double r293509 = y;
        double r293510 = z;
        double r293511 = sqrt(r293510);
        double r293512 = r293509 * r293511;
        double r293513 = r293508 + r293512;
        double r293514 = r293507 * r293513;
        return r293514;
}
↓
double f(double x, double y, double z) {
        double r293515 = 1.0;
        double r293516 = 2.0;
        double r293517 = r293515 / r293516;
        double r293518 = x;
        double r293519 = y;
        double r293520 = z;
        double r293521 = sqrt(r293520);
        double r293522 = r293519 * r293521;
        double r293523 = r293518 + r293522;
        double r293524 = r293517 * r293523;
        return r293524;
}

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 2020027 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))