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

Average Error: 0.2 → 0.2

Time: 11.1s

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 r261781 = 1.0;
        double r261782 = 2.0;
        double r261783 = r261781 / r261782;
        double r261784 = x;
        double r261785 = y;
        double r261786 = z;
        double r261787 = sqrt(r261786);
        double r261788 = r261785 * r261787;
        double r261789 = r261784 + r261788;
        double r261790 = r261783 * r261789;
        return r261790;
}

↓

double f(double x, double y, double z) {
        double r261791 = 1.0;
        double r261792 = 2.0;
        double r261793 = r261791 / r261792;
        double r261794 = x;
        double r261795 = y;
        double r261796 = z;
        double r261797 = sqrt(r261796);
        double r261798 = r261795 * r261797;
        double r261799 = r261794 + r261798;
        double r261800 = r261793 * r261799;
        return r261800;
}

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)))))