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

Average Error: 0.0 → 0.0

Time: 7.4s

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 r30656294 = 1.0;
        double r30656295 = 8.0;
        double r30656296 = r30656294 / r30656295;
        double r30656297 = x;
        double r30656298 = r30656296 * r30656297;
        double r30656299 = y;
        double r30656300 = z;
        double r30656301 = r30656299 * r30656300;
        double r30656302 = 2.0;
        double r30656303 = r30656301 / r30656302;
        double r30656304 = r30656298 - r30656303;
        double r30656305 = t;
        double r30656306 = r30656304 + r30656305;
        return r30656306;
}

↓

double f(double x, double y, double z, double t) {
        double r30656307 = x;
        double r30656308 = 8.0;
        double r30656309 = r30656307 / r30656308;
        double r30656310 = 1.0;
        double r30656311 = t;
        double r30656312 = z;
        double r30656313 = y;
        double r30656314 = r30656312 * r30656313;
        double r30656315 = 2.0;
        double r30656316 = r30656314 / r30656315;
        double r30656317 = r30656311 - r30656316;
        double r30656318 = fma(r30656309, r30656310, r30656317);
        return r30656318;
}

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))