Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

Average Error: 0.0 → 0

Time: 5.5s

Precision: 64

Math

\[\frac{x \cdot y}{2} - \frac{z}{8}\]

↓

\[\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)\]

C

double f(double x, double y, double z) {
        double r134447 = x;
        double r134448 = y;
        double r134449 = r134447 * r134448;
        double r134450 = 2.0;
        double r134451 = r134449 / r134450;
        double r134452 = z;
        double r134453 = 8.0;
        double r134454 = r134452 / r134453;
        double r134455 = r134451 - r134454;
        return r134455;
}

↓

double f(double x, double y, double z) {
        double r134456 = x;
        double r134457 = y;
        double r134458 = 2.0;
        double r134459 = r134457 / r134458;
        double r134460 = z;
        double r134461 = 8.0;
        double r134462 = r134460 / r134461;
        double r134463 = -r134462;
        double r134464 = fma(r134456, r134459, r134463);
        return r134464;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.0

   \[\frac{x \cdot y}{2} - \frac{z}{8}\]
2. Using strategy rm

3. Applied *-un-lft-identity 0.0

   \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2}} - \frac{z}{8}\]

4. Applied times-frac 0.0

   \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2}} - \frac{z}{8}\]

5. Applied fma-neg 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)}\]

6. Final simplification 0

   \[\leadsto \mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2) (/ z 8)))