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

Average Error: 0.0 → 0.0

Time: 1.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r103240 = 1.0;
        double r103241 = 8.0;
        double r103242 = r103240 / r103241;
        double r103243 = x;
        double r103244 = r103242 * r103243;
        double r103245 = y;
        double r103246 = z;
        double r103247 = r103245 * r103246;
        double r103248 = 2.0;
        double r103249 = r103247 / r103248;
        double r103250 = r103244 - r103249;
        double r103251 = t;
        double r103252 = r103250 + r103251;
        return r103252;
}

↓

double f(double x, double y, double z, double t) {
        double r103253 = y;
        double r103254 = 2.0;
        double r103255 = r103253 / r103254;
        double r103256 = -r103255;
        double r103257 = z;
        double r103258 = 1.0;
        double r103259 = 8.0;
        double r103260 = r103258 / r103259;
        double r103261 = x;
        double r103262 = t;
        double r103263 = fma(r103260, r103261, r103262);
        double r103264 = fma(r103256, r103257, r103263);
        return r103264;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020045 +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))