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

Average Error: 0.0 → 0.0

Time: 2.0s

Precision: 64

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

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 r182970 = x;
        double r182971 = y;
        double r182972 = r182970 * r182971;
        double r182973 = 2.0;
        double r182974 = r182972 / r182973;
        double r182975 = z;
        double r182976 = 8.0;
        double r182977 = r182975 / r182976;
        double r182978 = r182974 - r182977;
        return r182978;
}

↓

double f(double x, double y, double z) {
        double r182979 = x;
        double r182980 = y;
        double r182981 = 2.0;
        double r182982 = r182980 / r182981;
        double r182983 = z;
        double r182984 = 8.0;
        double r182985 = r182983 / r182984;
        double r182986 = -r182985;
        double r182987 = fma(r182979, r182982, r182986);
        return r182987;
}

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 0.0

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

6. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019351 +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)))