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

Average Error: 0.0 → 0.0

Time: 6.6s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r448272 = 1.0;
        double r448273 = 8.0;
        double r448274 = r448272 / r448273;
        double r448275 = x;
        double r448276 = r448274 * r448275;
        double r448277 = y;
        double r448278 = z;
        double r448279 = r448277 * r448278;
        double r448280 = 2.0;
        double r448281 = r448279 / r448280;
        double r448282 = r448276 - r448281;
        double r448283 = t;
        double r448284 = r448282 + r448283;
        return r448284;
}

↓

double f(double x, double y, double z, double t) {
        double r448285 = y;
        double r448286 = 2.0;
        double r448287 = r448285 / r448286;
        double r448288 = -r448287;
        double r448289 = z;
        double r448290 = x;
        double r448291 = 1.0;
        double r448292 = 8.0;
        double r448293 = r448291 / r448292;
        double r448294 = t;
        double r448295 = fma(r448290, r448293, r448294);
        double r448296 = fma(r448288, r448289, r448295);
        return r448296;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019208 +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))