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

Average Error: 0.1 → 0.1

Time: 5.1s

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 r243535 = x;
        double r243536 = y;
        double r243537 = r243535 * r243536;
        double r243538 = 2.0;
        double r243539 = r243537 / r243538;
        double r243540 = z;
        double r243541 = 8.0;
        double r243542 = r243540 / r243541;
        double r243543 = r243539 - r243542;
        return r243543;
}

↓

double f(double x, double y, double z) {
        double r243544 = x;
        double r243545 = y;
        double r243546 = r243544 * r243545;
        double r243547 = 2.0;
        double r243548 = r243546 / r243547;
        double r243549 = z;
        double r243550 = 8.0;
        double r243551 = r243549 / r243550;
        double r243552 = r243548 - r243551;
        return r243552;
}

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)))