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

Average Error: 0.0 → 0.0

Time: 12.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r31277558 = 1.0;
        double r31277559 = 8.0;
        double r31277560 = r31277558 / r31277559;
        double r31277561 = x;
        double r31277562 = r31277560 * r31277561;
        double r31277563 = y;
        double r31277564 = z;
        double r31277565 = r31277563 * r31277564;
        double r31277566 = 2.0;
        double r31277567 = r31277565 / r31277566;
        double r31277568 = r31277562 - r31277567;
        double r31277569 = t;
        double r31277570 = r31277568 + r31277569;
        return r31277570;
}

↓

double f(double x, double y, double z, double t) {
        double r31277571 = x;
        double r31277572 = 8.0;
        double r31277573 = r31277571 / r31277572;
        double r31277574 = 1.0;
        double r31277575 = t;
        double r31277576 = fma(r31277573, r31277574, r31277575);
        double r31277577 = z;
        double r31277578 = y;
        double r31277579 = r31277577 * r31277578;
        double r31277580 = 2.0;
        double r31277581 = r31277579 / r31277580;
        double r31277582 = r31277576 - r31277581;
        return r31277582;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))