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

Average Error: 0.2 → 0.2

Time: 15.3s

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 r279939 = 1.0;
        double r279940 = 2.0;
        double r279941 = r279939 / r279940;
        double r279942 = x;
        double r279943 = y;
        double r279944 = z;
        double r279945 = sqrt(r279944);
        double r279946 = r279943 * r279945;
        double r279947 = r279942 + r279946;
        double r279948 = r279941 * r279947;
        return r279948;
}

↓

double f(double x, double y, double z) {
        double r279949 = 1.0;
        double r279950 = 2.0;
        double r279951 = r279949 / r279950;
        double r279952 = x;
        double r279953 = y;
        double r279954 = z;
        double r279955 = sqrt(r279954);
        double r279956 = r279953 * r279955;
        double r279957 = r279952 + r279956;
        double r279958 = r279951 * r279957;
        return r279958;
}

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 2020046 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))