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

Average Error: 0.0 → 0.0

Time: 1.9s

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 r724691 = 1.0;
        double r724692 = 8.0;
        double r724693 = r724691 / r724692;
        double r724694 = x;
        double r724695 = r724693 * r724694;
        double r724696 = y;
        double r724697 = z;
        double r724698 = r724696 * r724697;
        double r724699 = 2.0;
        double r724700 = r724698 / r724699;
        double r724701 = r724695 - r724700;
        double r724702 = t;
        double r724703 = r724701 + r724702;
        return r724703;
}

↓

double f(double x, double y, double z, double t) {
        double r724704 = x;
        double r724705 = 8.0;
        double r724706 = r724704 / r724705;
        double r724707 = 1.0;
        double r724708 = y;
        double r724709 = 2.0;
        double r724710 = r724708 / r724709;
        double r724711 = -r724710;
        double r724712 = z;
        double r724713 = t;
        double r724714 = fma(r724711, r724712, r724713);
        double r724715 = fma(r724706, r724707, r724714);
        return r724715;
}

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 2020046 +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))