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

Average Error: 0.0 → 0.0

Time: 1.4s

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 r294097 = x;
        double r294098 = y;
        double r294099 = r294097 * r294098;
        double r294100 = 2.0;
        double r294101 = r294099 / r294100;
        double r294102 = z;
        double r294103 = 8.0;
        double r294104 = r294102 / r294103;
        double r294105 = r294101 - r294104;
        return r294105;
}

↓

double f(double x, double y, double z) {
        double r294106 = x;
        double r294107 = y;
        double r294108 = 2.0;
        double r294109 = r294107 / r294108;
        double r294110 = z;
        double r294111 = 8.0;
        double r294112 = r294110 / r294111;
        double r294113 = -r294112;
        double r294114 = fma(r294106, r294109, r294113);
        return r294114;
}

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 2020046 +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)))