Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x - 0.5 \cdot {x}^{2}\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x - 0.5 \cdot {x}^{2}
(FPCore (x) :precision binary64 (* x (- 1.0 (* x 0.5))))
↓
(FPCore (x) :precision binary64 (- x (* 0.5 (pow x 2.0))))
double code(double x) {
	return x * (1.0 - (x * 0.5));
}
↓
double code(double x) {
	return x - (0.5 * pow(x, 2.0));
}

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

    \[x \cdot \left(1 - x \cdot 0.5\right)\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{x - 0.5 \cdot {x}^{2}}\]

  3. Final simplification0.0

    \[\leadsto x - 0.5 \cdot {x}^{2}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1.0 (* x 0.5))))