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

Average Error: 0.0 → 0.0

Time: 1.1s

Precision: 64

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

Math

\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

↓

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

C

double f(double x, double y, double z, double t) {
        double r843315 = 1.0;
        double r843316 = 8.0;
        double r843317 = r843315 / r843316;
        double r843318 = x;
        double r843319 = r843317 * r843318;
        double r843320 = y;
        double r843321 = z;
        double r843322 = r843320 * r843321;
        double r843323 = 2.0;
        double r843324 = r843322 / r843323;
        double r843325 = r843319 - r843324;
        double r843326 = t;
        double r843327 = r843325 + r843326;
        return r843327;
}

↓

double f(double x, double y, double z, double t) {
        double r843328 = y;
        double r843329 = -r843328;
        double r843330 = 2.0;
        double r843331 = r843329 / r843330;
        double r843332 = z;
        double r843333 = 1.0;
        double r843334 = 8.0;
        double r843335 = r843333 / r843334;
        double r843336 = x;
        double r843337 = t;
        double r843338 = fma(r843335, r843336, r843337);
        double r843339 = fma(r843331, r843332, r843338);
        return r843339;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y\]

Derivation

1. Initial program 0.0

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

2. Simplified 0.0

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (+ (/ x 8) t) (* (/ z 2) y))

  (+ (- (* (/ 1 8) x) (/ (* y z) 2)) t))