Average Error: 0.0 → 0.0
Time: 3.2s
Precision: binary64
Cost: 320
\[x \cdot 116 - 16\]
↓
\[x \cdot 116 + -16\]
x \cdot 116 - 16
↓
x \cdot 116 + -16
(FPCore (x) :precision binary64 (- (* x 116.0) 16.0))
↓
(FPCore (x) :precision binary64 (+ (* x 116.0) -16.0))
double code(double x) {
	return (x * 116.0) - 16.0;
}
↓
double code(double x) {
	return (x * 116.0) + -16.0;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error48.0
Cost13504
\[\sqrt{x \cdot 116 + -16} \cdot \sqrt{x \cdot 116 + -16}\]
Alternative 2
Error21.0
Cost13184
\[\sqrt[3]{{\left(x \cdot 116 + -16\right)}^{3}}\]
Alternative 3
Error48.0
Cost13184
\[{\left(\sqrt{x \cdot 116 + -16}\right)}^{2}\]
Alternative 4
Error15.8
Cost832
\[\frac{x \cdot \left(x \cdot 13456\right) + -256}{x \cdot 116 + 16}\]
Alternative 5
Error31.5
Cost192
\[x \cdot 116\]
Alternative 6
Error31.5
Cost64
\[-16\]
Alternative 7
Error62.5
Cost64
\[1\]
Alternative 8
Error62.3
Cost64
\[0\]
Alternative 9
Error58.0
Cost64
\[-1\]

Error

Derivation

  1. Initial program 0.0

    \[x \cdot 116 - 16\]

  2. Simplified0.0

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

  3. Final simplification0.0

    \[\leadsto x \cdot 116 + -16\]

Reproduce

herbie shell --seed 2021042 
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116.0) 16.0))