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

Average Error: 0.0 → 0.0

Time: 7.0s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r27397432 = 1.0;
        double r27397433 = 8.0;
        double r27397434 = r27397432 / r27397433;
        double r27397435 = x;
        double r27397436 = r27397434 * r27397435;
        double r27397437 = y;
        double r27397438 = z;
        double r27397439 = r27397437 * r27397438;
        double r27397440 = 2.0;
        double r27397441 = r27397439 / r27397440;
        double r27397442 = r27397436 - r27397441;
        double r27397443 = t;
        double r27397444 = r27397442 + r27397443;
        return r27397444;
}

↓

double f(double x, double y, double z, double t) {
        double r27397445 = x;
        double r27397446 = 8.0;
        double r27397447 = r27397445 / r27397446;
        double r27397448 = 1.0;
        double r27397449 = t;
        double r27397450 = z;
        double r27397451 = y;
        double r27397452 = r27397450 * r27397451;
        double r27397453 = 2.0;
        double r27397454 = r27397452 / r27397453;
        double r27397455 = r27397449 - r27397454;
        double r27397456 = fma(r27397447, r27397448, r27397455);
        return r27397456;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))