Average Error: 0.1 → 0.1
Time: 7.8s
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 r182593 = 1.0;
        double r182594 = 2.0;
        double r182595 = r182593 / r182594;
        double r182596 = x;
        double r182597 = y;
        double r182598 = z;
        double r182599 = sqrt(r182598);
        double r182600 = r182597 * r182599;
        double r182601 = r182596 + r182600;
        double r182602 = r182595 * r182601;
        return r182602;
}
↓
double f(double x, double y, double z) {
        double r182603 = 1.0;
        double r182604 = 2.0;
        double r182605 = r182603 / r182604;
        double r182606 = x;
        double r182607 = y;
        double r182608 = z;
        double r182609 = sqrt(r182608);
        double r182610 = r182607 * r182609;
        double r182611 = r182606 + r182610;
        double r182612 = r182605 * r182611;
        return r182612;
}

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 2019308 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))