Average Error: 0.0 → 0
Time: 597.0ms
Precision: 64
\[\left(x \cdot x\right) \cdot 2 - 1\]
↓
\[\mathsf{fma}\left(x, x \cdot 2, -1\right)\]
\left(x \cdot x\right) \cdot 2 - 1
↓
\mathsf{fma}\left(x, x \cdot 2, -1\right)
double code(double x) {
	return (((x * x) * 2.0) - 1.0);
}
↓
double code(double x) {
	return fma(x, (x * 2.0), -1.0);
}

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

    \[\left(x \cdot x\right) \cdot 2 - 1\]
  2. Using strategy rm

  3. Applied associate-*l*0.0

    \[\leadsto \color{blue}{x \cdot \left(x \cdot 2\right)} - 1\]

  4. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x \cdot 2, -1\right)}\]

  5. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, x \cdot 2, -1\right)\]

Reproduce

herbie shell --seed 2020071 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2"
  :precision binary64
  (- (* (* x x) 2) 1))