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

Average Error: 0.1 → 0.1

Time: 14.5s

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 r209646 = 1.0;
        double r209647 = 2.0;
        double r209648 = r209646 / r209647;
        double r209649 = x;
        double r209650 = y;
        double r209651 = z;
        double r209652 = sqrt(r209651);
        double r209653 = r209650 * r209652;
        double r209654 = r209649 + r209653;
        double r209655 = r209648 * r209654;
        return r209655;
}

↓

double f(double x, double y, double z) {
        double r209656 = 1.0;
        double r209657 = 2.0;
        double r209658 = r209656 / r209657;
        double r209659 = z;
        double r209660 = sqrt(r209659);
        double r209661 = y;
        double r209662 = x;
        double r209663 = fma(r209660, r209661, r209662);
        double r209664 = r209658 * r209663;
        return r209664;
}

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 2019305 +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)))))