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

Average Error: 0.0 → 0.0

Time: 2.5s

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 r452346 = 1.0;
        double r452347 = 8.0;
        double r452348 = r452346 / r452347;
        double r452349 = x;
        double r452350 = r452348 * r452349;
        double r452351 = y;
        double r452352 = z;
        double r452353 = r452351 * r452352;
        double r452354 = 2.0;
        double r452355 = r452353 / r452354;
        double r452356 = r452350 - r452355;
        double r452357 = t;
        double r452358 = r452356 + r452357;
        return r452358;
}

↓

double f(double x, double y, double z, double t) {
        double r452359 = y;
        double r452360 = 2.0;
        double r452361 = r452359 / r452360;
        double r452362 = -r452361;
        double r452363 = z;
        double r452364 = x;
        double r452365 = 1.0;
        double r452366 = 8.0;
        double r452367 = r452365 / r452366;
        double r452368 = t;
        double r452369 = fma(r452364, r452367, r452368);
        double r452370 = fma(r452362, r452363, r452369);
        return r452370;
}

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 2019322 +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))