Average Error: 0.0 → 0.0
Time: 2.7s
Precision: binary64
\[\left(x + 1\right) \cdot y - x\]
↓
\[y + \left(y \cdot x - x\right)\]
\left(x + 1\right) \cdot y - x
↓
y + \left(y \cdot x - x\right)
(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))
↓
(FPCore (x y) :precision binary64 (+ y (- (* y x) x)))
double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}
↓
double code(double x, double y) {
	return y + ((y * x) - x);
}

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

    \[\left(x + 1\right) \cdot y - x\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(x \cdot y + y\right)} - x\]

  3. Simplified0.0

    \[\leadsto \color{blue}{\left(y + y \cdot x\right)} - x\]
  4. Using strategy rm

  5. Applied associate--l+_binary64_71760.0

    \[\leadsto \color{blue}{y + \left(y \cdot x - x\right)}\]

  6. Final simplification0.0

    \[\leadsto y + \left(y \cdot x - x\right)\]

Reproduce

herbie shell --seed 2021040 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))