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 r305331 = 1.0;
        double r305332 = 2.0;
        double r305333 = r305331 / r305332;
        double r305334 = x;
        double r305335 = y;
        double r305336 = z;
        double r305337 = sqrt(r305336);
        double r305338 = r305335 * r305337;
        double r305339 = r305334 + r305338;
        double r305340 = r305333 * r305339;
        return r305340;
}

↓

double f(double x, double y, double z) {
        double r305341 = 1.0;
        double r305342 = 2.0;
        double r305343 = r305341 / r305342;
        double r305344 = x;
        double r305345 = y;
        double r305346 = z;
        double r305347 = sqrt(r305346);
        double r305348 = r305345 * r305347;
        double r305349 = r305344 + r305348;
        double r305350 = r305343 * r305349;
        return r305350;
}

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)))))