Average Error: 0.0 → 0.0
Time: 2.0s
Precision: binary64
\[\frac{x + y}{y + 1} \]
↓
\[\frac{x}{1 + y} + \frac{y}{1 + y} \]
\frac{x + y}{y + 1}
↓
\frac{x}{1 + y} + \frac{y}{1 + y}

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))
↓
(FPCore (x y) :precision binary64 (+ (/ x (+ 1.0 y)) (/ y (+ 1.0 y))))
double code(double x, double y) {
	return (x + y) / (y + 1.0);
}
↓
double code(double x, double y) {
	return (x / (1.0 + y)) + (y / (1.0 + 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

    \[\frac{x + y}{y + 1} \]

  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{\frac{x}{1 + y} + \frac{y}{1 + y}} \]

  3. Final simplification0.0

    \[\leadsto \frac{x}{1 + y} + \frac{y}{1 + y} \]

Reproduce

herbie shell --seed 2022067 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))