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

Average Error: 0.0 → 0.0

Time: 916.0ms

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 r688358 = 1.0;
        double r688359 = 8.0;
        double r688360 = r688358 / r688359;
        double r688361 = x;
        double r688362 = r688360 * r688361;
        double r688363 = y;
        double r688364 = z;
        double r688365 = r688363 * r688364;
        double r688366 = 2.0;
        double r688367 = r688365 / r688366;
        double r688368 = r688362 - r688367;
        double r688369 = t;
        double r688370 = r688368 + r688369;
        return r688370;
}

↓

double f(double x, double y, double z, double t) {
        double r688371 = x;
        double r688372 = 8.0;
        double r688373 = r688371 / r688372;
        double r688374 = 1.0;
        double r688375 = y;
        double r688376 = 2.0;
        double r688377 = r688375 / r688376;
        double r688378 = -r688377;
        double r688379 = z;
        double r688380 = t;
        double r688381 = fma(r688378, r688379, r688380);
        double r688382 = fma(r688373, r688374, r688381);
        return r688382;
}

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 2020001 +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))