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

Average Error: 0.0 → 0

Time: 1.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r764923 = 1.0;
        double r764924 = 8.0;
        double r764925 = r764923 / r764924;
        double r764926 = x;
        double r764927 = r764925 * r764926;
        double r764928 = y;
        double r764929 = z;
        double r764930 = r764928 * r764929;
        double r764931 = 2.0;
        double r764932 = r764930 / r764931;
        double r764933 = r764927 - r764932;
        double r764934 = t;
        double r764935 = r764933 + r764934;
        return r764935;
}

↓

double f(double x, double y, double z, double t) {
        double r764936 = y;
        double r764937 = 2.0;
        double r764938 = r764936 / r764937;
        double r764939 = -r764938;
        double r764940 = z;
        double r764941 = 1.0;
        double r764942 = 8.0;
        double r764943 = r764941 / r764942;
        double r764944 = x;
        double r764945 = t;
        double r764946 = fma(r764943, r764944, r764945);
        double r764947 = fma(r764939, r764940, r764946);
        return r764947;
}

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

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

Derivation

1. Initial program 0.0

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

2. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2020043 +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))