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

Average Error: 0.0 → 0.0

Time: 2.1s

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 r771467 = 1.0;
        double r771468 = 8.0;
        double r771469 = r771467 / r771468;
        double r771470 = x;
        double r771471 = r771469 * r771470;
        double r771472 = y;
        double r771473 = z;
        double r771474 = r771472 * r771473;
        double r771475 = 2.0;
        double r771476 = r771474 / r771475;
        double r771477 = r771471 - r771476;
        double r771478 = t;
        double r771479 = r771477 + r771478;
        return r771479;
}

↓

double f(double x, double y, double z, double t) {
        double r771480 = y;
        double r771481 = 2.0;
        double r771482 = r771480 / r771481;
        double r771483 = -r771482;
        double r771484 = z;
        double r771485 = 1.0;
        double r771486 = 8.0;
        double r771487 = r771485 / r771486;
        double r771488 = x;
        double r771489 = t;
        double r771490 = fma(r771487, r771488, r771489);
        double r771491 = fma(r771483, r771484, r771490);
        return r771491;
}

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 2020042 +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))