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

Average Error: 0.2 → 0.2

Time: 11.4s

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 r366152 = 1.0;
        double r366153 = 2.0;
        double r366154 = r366152 / r366153;
        double r366155 = x;
        double r366156 = y;
        double r366157 = z;
        double r366158 = sqrt(r366157);
        double r366159 = r366156 * r366158;
        double r366160 = r366155 + r366159;
        double r366161 = r366154 * r366160;
        return r366161;
}

↓

double f(double x, double y, double z) {
        double r366162 = 1.0;
        double r366163 = 2.0;
        double r366164 = r366162 / r366163;
        double r366165 = x;
        double r366166 = y;
        double r366167 = z;
        double r366168 = sqrt(r366167);
        double r366169 = r366166 * r366168;
        double r366170 = r366165 + r366169;
        double r366171 = r366164 * r366170;
        return r366171;
}

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 2020047 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))