Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x + x \cdot \left(x \cdot -0.5\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x + x \cdot \left(x \cdot -0.5\right)
(FPCore (x) :precision binary64 (* x (- 1.0 (* x 0.5))))
↓
(FPCore (x) :precision binary64 (+ x (* x (* x -0.5))))
double code(double x) {
	return x * (1.0 - (x * 0.5));
}
↓
double code(double x) {
	return x + (x * (x * -0.5));
}

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. Using strategy rm

  3. Applied sub-neg_binary64_12200.0

    \[\leadsto x \cdot \color{blue}{\left(1 + \left(-x \cdot 0.5\right)\right)}\]

  4. Applied distribute-rgt-in_binary64_12590.0

    \[\leadsto \color{blue}{1 \cdot x + \left(-x \cdot 0.5\right) \cdot x}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{x} + \left(-x \cdot 0.5\right) \cdot x\]

  6. Simplified0.0

    \[\leadsto x + \color{blue}{x \cdot \left(x \cdot -0.5\right)}\]

  7. Final simplification0.0

    \[\leadsto x + x \cdot \left(x \cdot -0.5\right)\]

Reproduce

herbie shell --seed 2020231 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1.0 (* x 0.5))))