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

Average Error: 0.0 → 0.0

Time: 1.0s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r672352 = 1.0;
        double r672353 = 8.0;
        double r672354 = r672352 / r672353;
        double r672355 = x;
        double r672356 = r672354 * r672355;
        double r672357 = y;
        double r672358 = z;
        double r672359 = r672357 * r672358;
        double r672360 = 2.0;
        double r672361 = r672359 / r672360;
        double r672362 = r672356 - r672361;
        double r672363 = t;
        double r672364 = r672362 + r672363;
        return r672364;
}

↓

double f(double x, double y, double z, double t) {
        double r672365 = x;
        double r672366 = 8.0;
        double r672367 = r672365 / r672366;
        double r672368 = 1.0;
        double r672369 = y;
        double r672370 = 2.0;
        double r672371 = r672369 / r672370;
        double r672372 = -r672371;
        double r672373 = z;
        double r672374 = t;
        double r672375 = fma(r672372, r672373, r672374);
        double r672376 = fma(r672367, r672368, r672375);
        return r672376;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020081 +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))