Average Error: 0.0 → 0.0
Time: 2.9s
Precision: binary64
Cost: 448
\[\left(x \cdot x\right) \cdot 2 - 1\]
↓
\[-1 + 2 \cdot \left(x \cdot x\right)\]
\left(x \cdot x\right) \cdot 2 - 1
↓
-1 + 2 \cdot \left(x \cdot x\right)
(FPCore (x) :precision binary64 (- (* (* x x) 2.0) 1.0))
↓
(FPCore (x) :precision binary64 (+ -1.0 (* 2.0 (* x x))))
double code(double x) {
	return ((x * x) * 2.0) - 1.0;
}
↓
double code(double x) {
	return -1.0 + (2.0 * (x * x));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.9
Cost769
\[\begin{array}{l} \mathbf{if}\;x \cdot x \leq 0.5108774671848952:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot x\right)\\ \end{array}\]
Alternative 2
Error22.2
Cost64
\[-1\]
Alternative 3
Error62.2
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[\left(x \cdot x\right) \cdot 2 - 1\]

  2. Simplified0.0

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

  3. Final simplification0.0

    \[\leadsto -1 + 2 \cdot \left(x \cdot x\right)\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2"
  :precision binary64
  (- (* (* x x) 2.0) 1.0))