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

Average Error: 0.0 → 0.0

Time: 3.3s

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 r1436841 = 1.0;
        double r1436842 = 8.0;
        double r1436843 = r1436841 / r1436842;
        double r1436844 = x;
        double r1436845 = r1436843 * r1436844;
        double r1436846 = y;
        double r1436847 = z;
        double r1436848 = r1436846 * r1436847;
        double r1436849 = 2.0;
        double r1436850 = r1436848 / r1436849;
        double r1436851 = r1436845 - r1436850;
        double r1436852 = t;
        double r1436853 = r1436851 + r1436852;
        return r1436853;
}

↓

double f(double x, double y, double z, double t) {
        double r1436854 = x;
        double r1436855 = 8.0;
        double r1436856 = r1436854 / r1436855;
        double r1436857 = 1.0;
        double r1436858 = y;
        double r1436859 = 2.0;
        double r1436860 = r1436858 / r1436859;
        double r1436861 = -r1436860;
        double r1436862 = z;
        double r1436863 = t;
        double r1436864 = fma(r1436861, r1436862, r1436863);
        double r1436865 = fma(r1436856, r1436857, r1436864);
        return r1436865;
}

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 2020034 +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))