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

Average Error: 0.1 → 0.1

Time: 12.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\frac{1}{2} \cdot \mathsf{fma}\left(\sqrt{z}, y, x\right)\]

C

double f(double x, double y, double z) {
        double r271298 = 1.0;
        double r271299 = 2.0;
        double r271300 = r271298 / r271299;
        double r271301 = x;
        double r271302 = y;
        double r271303 = z;
        double r271304 = sqrt(r271303);
        double r271305 = r271302 * r271304;
        double r271306 = r271301 + r271305;
        double r271307 = r271300 * r271306;
        return r271307;
}

↓

double f(double x, double y, double z) {
        double r271308 = 1.0;
        double r271309 = 2.0;
        double r271310 = r271308 / r271309;
        double r271311 = z;
        double r271312 = sqrt(r271311);
        double r271313 = y;
        double r271314 = x;
        double r271315 = fma(r271312, r271313, r271314);
        double r271316 = r271310 * r271315;
        return r271316;
}

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. Simplified 0.1

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \mathsf{fma}\left(\sqrt{z}, y, x\right)}\]

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))