Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B

Average Error: 0.1 → 0.1

Time: 15.5s

Precision: 64

Math

\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

↓

\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

C

double f(double x, double y, double z) {
        double r131851 = 1.0;
        double r131852 = 2.0;
        double r131853 = r131851 / r131852;
        double r131854 = x;
        double r131855 = y;
        double r131856 = z;
        double r131857 = sqrt(r131856);
        double r131858 = r131855 * r131857;
        double r131859 = r131854 + r131858;
        double r131860 = r131853 * r131859;
        return r131860;
}

↓

double f(double x, double y, double z) {
        double r131861 = 1.0;
        double r131862 = 2.0;
        double r131863 = r131861 / r131862;
        double r131864 = x;
        double r131865 = y;
        double r131866 = z;
        double r131867 = sqrt(r131866);
        double r131868 = r131865 * r131867;
        double r131869 = r131864 + r131868;
        double r131870 = r131863 * r131869;
        return r131870;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.1

   \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
2. Using strategy rm

3. Applied *-un-lft-identity 0.1

   \[\leadsto \frac{1}{2} \cdot \left(x + \color{blue}{1 \cdot \left(y \cdot \sqrt{z}\right)}\right)\]

4. Final simplification 0.1

   \[\leadsto \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))