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

Average Error: 0.0 → 0.0

Time: 7.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r30038787 = 1.0;
        double r30038788 = 8.0;
        double r30038789 = r30038787 / r30038788;
        double r30038790 = x;
        double r30038791 = r30038789 * r30038790;
        double r30038792 = y;
        double r30038793 = z;
        double r30038794 = r30038792 * r30038793;
        double r30038795 = 2.0;
        double r30038796 = r30038794 / r30038795;
        double r30038797 = r30038791 - r30038796;
        double r30038798 = t;
        double r30038799 = r30038797 + r30038798;
        return r30038799;
}

↓

double f(double x, double y, double z, double t) {
        double r30038800 = x;
        double r30038801 = 8.0;
        double r30038802 = r30038800 / r30038801;
        double r30038803 = 1.0;
        double r30038804 = t;
        double r30038805 = z;
        double r30038806 = y;
        double r30038807 = r30038805 * r30038806;
        double r30038808 = 2.0;
        double r30038809 = r30038807 / r30038808;
        double r30038810 = r30038804 - r30038809;
        double r30038811 = fma(r30038802, r30038803, r30038810);
        return r30038811;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019169 +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))