Average Error: 9.5 → 0.1
Time: 898.0ms
Precision: binary64
\[\frac{x \cdot y - x \cdot 255}{y}\]
↓
\[\frac{x}{\frac{y}{y - 255}}\]
\frac{x \cdot y - x \cdot 255}{y}
↓
\frac{x}{\frac{y}{y - 255}}
double code(double x, double y) {
	return ((double) (((double) (((double) (x * y)) - ((double) (x * 255.0)))) / y));
}
↓
double code(double x, double y) {
	return ((double) (x / ((double) (y / ((double) (y - 255.0))))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 9.5

    \[\frac{x \cdot y - x \cdot 255}{y}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - 255}}}\]

  3. Final simplification0.1

    \[\leadsto \frac{x}{\frac{y}{y - 255}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(/ (- (* x y) (* x 255)) y)"
  :precision binary64
  (/ (- (* x y) (* x 255.0)) y))