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

Average Error: 0.2 → 0.2

Time: 11.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r256856 = 1.0;
        double r256857 = 2.0;
        double r256858 = r256856 / r256857;
        double r256859 = x;
        double r256860 = y;
        double r256861 = z;
        double r256862 = sqrt(r256861);
        double r256863 = r256860 * r256862;
        double r256864 = r256859 + r256863;
        double r256865 = r256858 * r256864;
        return r256865;
}

↓

double f(double x, double y, double z) {
        double r256866 = 1.0;
        double r256867 = 2.0;
        double r256868 = r256866 / r256867;
        double r256869 = x;
        double r256870 = y;
        double r256871 = z;
        double r256872 = sqrt(r256871);
        double r256873 = r256870 * r256872;
        double r256874 = r256869 + r256873;
        double r256875 = r256868 * r256874;
        return r256875;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))