Average Error: 0.0 → 0.0
Time: 735.0ms
Precision: binary64
\[x \cdot \left(1 - x \cdot 0.5\right) \]
↓
\[x \cdot \mathsf{fma}\left(x, -0.5, 1\right) \]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x \cdot \mathsf{fma}\left(x, -0.5, 1\right)

(FPCore (x) :precision binary64 (* x (- 1.0 (* x 0.5))))
↓
(FPCore (x) :precision binary64 (* x (fma x -0.5 1.0)))
double code(double x) {
	return x * (1.0 - (x * 0.5));
}
↓
double code(double x) {
	return x * fma(x, -0.5, 1.0);
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

    \[\leadsto x \cdot \mathsf{fma}\left(x, -0.5, 1\right) \]

Reproduce

herbie shell --seed 2022067 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1.0 (* x 0.5))))