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

Average Error: 0.0 → 0.0

Time: 12.7s

Precision: 64

Math

\[\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t\]

↓

\[\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)\]

C

double f(double x, double y, double z, double t) {
        double r32547843 = 1.0;
        double r32547844 = 8.0;
        double r32547845 = r32547843 / r32547844;
        double r32547846 = x;
        double r32547847 = r32547845 * r32547846;
        double r32547848 = y;
        double r32547849 = z;
        double r32547850 = r32547848 * r32547849;
        double r32547851 = 2.0;
        double r32547852 = r32547850 / r32547851;
        double r32547853 = r32547847 - r32547852;
        double r32547854 = t;
        double r32547855 = r32547853 + r32547854;
        return r32547855;
}

↓

double f(double x, double y, double z, double t) {
        double r32547856 = x;
        double r32547857 = 8.0;
        double r32547858 = r32547856 / r32547857;
        double r32547859 = 1.0;
        double r32547860 = t;
        double r32547861 = z;
        double r32547862 = y;
        double r32547863 = r32547861 * r32547862;
        double r32547864 = 2.0;
        double r32547865 = r32547863 / r32547864;
        double r32547866 = r32547860 - r32547865;
        double r32547867 = fma(r32547858, r32547859, r32547866);
        return r32547867;
}

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

\[\left(\frac{x}{8.0} + t\right) - \frac{z}{2.0} \cdot y\]

Derivation

1. Initial program 0.0

   \[\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)\]

Reproduce

herbie shell --seed 2019168 +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))