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

Average Error: 0.1 → 0.1

Time: 10.1s

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 r215350 = 1.0;
        double r215351 = 2.0;
        double r215352 = r215350 / r215351;
        double r215353 = x;
        double r215354 = y;
        double r215355 = z;
        double r215356 = sqrt(r215355);
        double r215357 = r215354 * r215356;
        double r215358 = r215353 + r215357;
        double r215359 = r215352 * r215358;
        return r215359;
}

↓

double f(double x, double y, double z) {
        double r215360 = 1.0;
        double r215361 = 2.0;
        double r215362 = r215360 / r215361;
        double r215363 = x;
        double r215364 = y;
        double r215365 = z;
        double r215366 = sqrt(r215365);
        double r215367 = r215364 * r215366;
        double r215368 = r215363 + r215367;
        double r215369 = r215362 * r215368;
        return r215369;
}

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. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))