Average Error: 0.0 → 0.0
Time: 848.0ms
Precision: binary64
\[\frac{x}{y \cdot 2} \]
↓
\[0.5 \cdot \frac{x}{y} \]
\frac{x}{y \cdot 2}
↓
0.5 \cdot \frac{x}{y}

(FPCore (x y) :precision binary64 (/ x (* y 2.0)))
↓
(FPCore (x y) :precision binary64 (* 0.5 (/ x y)))
double code(double x, double y) {
	return x / (y * 2.0);
}
↓
double code(double x, double y) {
	return 0.5 * (x / y);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{x}{y \cdot 2} \]

  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y}} \]

  3. Final simplification0.0

    \[\leadsto 0.5 \cdot \frac{x}{y} \]

Reproduce

herbie shell --seed 2021307 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, C"
  :precision binary64
  (/ x (* y 2.0)))