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

Average Error: 0.0 → 0.0

Time: 856.0ms

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 r712892 = 1.0;
        double r712893 = 8.0;
        double r712894 = r712892 / r712893;
        double r712895 = x;
        double r712896 = r712894 * r712895;
        double r712897 = y;
        double r712898 = z;
        double r712899 = r712897 * r712898;
        double r712900 = 2.0;
        double r712901 = r712899 / r712900;
        double r712902 = r712896 - r712901;
        double r712903 = t;
        double r712904 = r712902 + r712903;
        return r712904;
}

↓

double f(double x, double y, double z, double t) {
        double r712905 = x;
        double r712906 = 8.0;
        double r712907 = r712905 / r712906;
        double r712908 = 1.0;
        double r712909 = y;
        double r712910 = 2.0;
        double r712911 = r712909 / r712910;
        double r712912 = -r712911;
        double r712913 = z;
        double r712914 = t;
        double r712915 = fma(r712912, r712913, r712914);
        double r712916 = fma(r712907, r712908, r712915);
        return r712916;
}

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 2020059 +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))