Average Error: 0.0 → 0
Time: 487.0ms
Precision: 64
\[x \cdot 116 - 16\]
↓
\[\mathsf{fma}\left(116, x, -16\right)\]
x \cdot 116 - 16
↓
\mathsf{fma}\left(116, x, -16\right)
double code(double x) {
	return ((x * 116.0) - 16.0);
}
↓
double code(double x) {
	return fma(116.0, x, -16.0);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot 116 - 16\]
  2. Using strategy rm

  3. Applied *-commutative0.0

    \[\leadsto \color{blue}{116 \cdot x} - 16\]

  4. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(116, x, -16\right)}\]

  5. Final simplification0

    \[\leadsto \mathsf{fma}\left(116, x, -16\right)\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))