Average Error: 0.1 → 0.1
Time: 15.9s
Precision: 64
\[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)
double f(double x, double y, double z) {
        double r10864759 = 1.0;
        double r10864760 = 2.0;
        double r10864761 = r10864759 / r10864760;
        double r10864762 = x;
        double r10864763 = y;
        double r10864764 = z;
        double r10864765 = sqrt(r10864764);
        double r10864766 = r10864763 * r10864765;
        double r10864767 = r10864762 + r10864766;
        double r10864768 = r10864761 * r10864767;
        return r10864768;
}
↓
double f(double x, double y, double z) {
        double r10864769 = 1.0;
        double r10864770 = 2.0;
        double r10864771 = r10864769 / r10864770;
        double r10864772 = x;
        double r10864773 = z;
        double r10864774 = sqrt(r10864773);
        double r10864775 = y;
        double r10864776 = r10864774 * r10864775;
        double r10864777 = r10864772 + r10864776;
        double r10864778 = r10864771 * r10864777;
        return r10864778;
}

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

    \[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.1

    \[\leadsto \frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))