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

Average Error: 0.0 → 0.0

Time: 1.4s

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 r641708 = 1.0;
        double r641709 = 8.0;
        double r641710 = r641708 / r641709;
        double r641711 = x;
        double r641712 = r641710 * r641711;
        double r641713 = y;
        double r641714 = z;
        double r641715 = r641713 * r641714;
        double r641716 = 2.0;
        double r641717 = r641715 / r641716;
        double r641718 = r641712 - r641717;
        double r641719 = t;
        double r641720 = r641718 + r641719;
        return r641720;
}

↓

double f(double x, double y, double z, double t) {
        double r641721 = x;
        double r641722 = 8.0;
        double r641723 = r641721 / r641722;
        double r641724 = 1.0;
        double r641725 = y;
        double r641726 = 2.0;
        double r641727 = r641725 / r641726;
        double r641728 = -r641727;
        double r641729 = z;
        double r641730 = t;
        double r641731 = fma(r641728, r641729, r641730);
        double r641732 = fma(r641723, r641724, r641731);
        return r641732;
}

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 2020039 +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))