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

Average Error: 0.0 → 0.0

Time: 7.3s

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 r33376628 = 1.0;
        double r33376629 = 8.0;
        double r33376630 = r33376628 / r33376629;
        double r33376631 = x;
        double r33376632 = r33376630 * r33376631;
        double r33376633 = y;
        double r33376634 = z;
        double r33376635 = r33376633 * r33376634;
        double r33376636 = 2.0;
        double r33376637 = r33376635 / r33376636;
        double r33376638 = r33376632 - r33376637;
        double r33376639 = t;
        double r33376640 = r33376638 + r33376639;
        return r33376640;
}

↓

double f(double x, double y, double z, double t) {
        double r33376641 = x;
        double r33376642 = 8.0;
        double r33376643 = r33376641 / r33376642;
        double r33376644 = 1.0;
        double r33376645 = t;
        double r33376646 = fma(r33376643, r33376644, r33376645);
        double r33376647 = z;
        double r33376648 = y;
        double r33376649 = r33376647 * r33376648;
        double r33376650 = 2.0;
        double r33376651 = r33376649 / r33376650;
        double r33376652 = r33376646 - r33376651;
        return r33376652;
}

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 2019192 +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))