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

Average Error: 0.1 → 0.1

Time: 5.3s

Precision: 64

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

Math

\[\frac{x \cdot y}{2} - \frac{z}{8}\]

↓

\[\frac{x \cdot y}{2} - \frac{z}{8}\]

C

double f(double x, double y, double z) {
        double r238763 = x;
        double r238764 = y;
        double r238765 = r238763 * r238764;
        double r238766 = 2.0;
        double r238767 = r238765 / r238766;
        double r238768 = z;
        double r238769 = 8.0;
        double r238770 = r238768 / r238769;
        double r238771 = r238767 - r238770;
        return r238771;
}

↓

double f(double x, double y, double z) {
        double r238772 = x;
        double r238773 = y;
        double r238774 = r238772 * r238773;
        double r238775 = 2.0;
        double r238776 = r238774 / r238775;
        double r238777 = z;
        double r238778 = 8.0;
        double r238779 = r238777 / r238778;
        double r238780 = r238776 - r238779;
        return r238780;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.1

   \[\frac{x \cdot y}{2} - \frac{z}{8}\]

2. Final simplification 0.1

   \[\leadsto \frac{x \cdot y}{2} - \frac{z}{8}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2) (/ z 8)))