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

Average Error: 0.0 → 0.0

Time: 781.0ms

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 r695342 = 1.0;
        double r695343 = 8.0;
        double r695344 = r695342 / r695343;
        double r695345 = x;
        double r695346 = r695344 * r695345;
        double r695347 = y;
        double r695348 = z;
        double r695349 = r695347 * r695348;
        double r695350 = 2.0;
        double r695351 = r695349 / r695350;
        double r695352 = r695346 - r695351;
        double r695353 = t;
        double r695354 = r695352 + r695353;
        return r695354;
}

↓

double f(double x, double y, double z, double t) {
        double r695355 = x;
        double r695356 = 8.0;
        double r695357 = r695355 / r695356;
        double r695358 = 1.0;
        double r695359 = y;
        double r695360 = 2.0;
        double r695361 = r695359 / r695360;
        double r695362 = -r695361;
        double r695363 = z;
        double r695364 = t;
        double r695365 = fma(r695362, r695363, r695364);
        double r695366 = fma(r695357, r695358, r695365);
        return r695366;
}

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 2020065 +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))