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

Average Error: 0.0 → 0.0

Time: 31.2s

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 r28347263 = 1.0;
        double r28347264 = 8.0;
        double r28347265 = r28347263 / r28347264;
        double r28347266 = x;
        double r28347267 = r28347265 * r28347266;
        double r28347268 = y;
        double r28347269 = z;
        double r28347270 = r28347268 * r28347269;
        double r28347271 = 2.0;
        double r28347272 = r28347270 / r28347271;
        double r28347273 = r28347267 - r28347272;
        double r28347274 = t;
        double r28347275 = r28347273 + r28347274;
        return r28347275;
}

↓

double f(double x, double y, double z, double t) {
        double r28347276 = x;
        double r28347277 = 8.0;
        double r28347278 = r28347276 / r28347277;
        double r28347279 = 1.0;
        double r28347280 = t;
        double r28347281 = z;
        double r28347282 = y;
        double r28347283 = r28347281 * r28347282;
        double r28347284 = 2.0;
        double r28347285 = r28347283 / r28347284;
        double r28347286 = r28347280 - r28347285;
        double r28347287 = fma(r28347278, r28347279, r28347286);
        return r28347287;
}

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 2019168 +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))