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 r119513 = 1.0;
        double r119514 = 8.0;
        double r119515 = r119513 / r119514;
        double r119516 = x;
        double r119517 = r119515 * r119516;
        double r119518 = y;
        double r119519 = z;
        double r119520 = r119518 * r119519;
        double r119521 = 2.0;
        double r119522 = r119520 / r119521;
        double r119523 = r119517 - r119522;
        double r119524 = t;
        double r119525 = r119523 + r119524;
        return r119525;
}

↓

double f(double x, double y, double z, double t) {
        double r119526 = y;
        double r119527 = 2.0;
        double r119528 = r119526 / r119527;
        double r119529 = -r119528;
        double r119530 = z;
        double r119531 = 1.0;
        double r119532 = 8.0;
        double r119533 = r119531 / r119532;
        double r119534 = x;
        double r119535 = t;
        double r119536 = fma(r119533, r119534, r119535);
        double r119537 = fma(r119529, r119530, r119536);
        return r119537;
}

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))