Average Error: 0.1 → 0.1
Time: 14.6s
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 r179557 = 1.0;
        double r179558 = 2.0;
        double r179559 = r179557 / r179558;
        double r179560 = x;
        double r179561 = y;
        double r179562 = z;
        double r179563 = sqrt(r179562);
        double r179564 = r179561 * r179563;
        double r179565 = r179560 + r179564;
        double r179566 = r179559 * r179565;
        return r179566;
}
↓
double f(double x, double y, double z) {
        double r179567 = 1.0;
        double r179568 = 2.0;
        double r179569 = r179567 / r179568;
        double r179570 = x;
        double r179571 = y;
        double r179572 = z;
        double r179573 = sqrt(r179572);
        double r179574 = r179571 * r179573;
        double r179575 = r179570 + r179574;
        double r179576 = r179569 * r179575;
        return r179576;
}

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 2019212 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))