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

Average Error: 0.1 → 0.1

Time: 19.7s

Precision: 64

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 r198009 = 1.0;
        double r198010 = 2.0;
        double r198011 = r198009 / r198010;
        double r198012 = x;
        double r198013 = y;
        double r198014 = z;
        double r198015 = sqrt(r198014);
        double r198016 = r198013 * r198015;
        double r198017 = r198012 + r198016;
        double r198018 = r198011 * r198017;
        return r198018;
}

↓

double f(double x, double y, double z) {
        double r198019 = 1.0;
        double r198020 = 2.0;
        double r198021 = r198019 / r198020;
        double r198022 = z;
        double r198023 = sqrt(r198022);
        double r198024 = y;
        double r198025 = x;
        double r198026 = fma(r198023, r198024, r198025);
        double r198027 = r198021 * r198026;
        return r198027;
}

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 2019326 +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)))))