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

Average Error: 0.0 → 0.0

Time: 14.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r31300279 = 1.0;
        double r31300280 = 8.0;
        double r31300281 = r31300279 / r31300280;
        double r31300282 = x;
        double r31300283 = r31300281 * r31300282;
        double r31300284 = y;
        double r31300285 = z;
        double r31300286 = r31300284 * r31300285;
        double r31300287 = 2.0;
        double r31300288 = r31300286 / r31300287;
        double r31300289 = r31300283 - r31300288;
        double r31300290 = t;
        double r31300291 = r31300289 + r31300290;
        return r31300291;
}

↓

double f(double x, double y, double z, double t) {
        double r31300292 = x;
        double r31300293 = 8.0;
        double r31300294 = r31300292 / r31300293;
        double r31300295 = 1.0;
        double r31300296 = t;
        double r31300297 = fma(r31300294, r31300295, r31300296);
        double r31300298 = z;
        double r31300299 = y;
        double r31300300 = r31300298 * r31300299;
        double r31300301 = 2.0;
        double r31300302 = r31300300 / r31300301;
        double r31300303 = r31300297 - r31300302;
        return r31300303;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019174 +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))