Average Error: 0 → 0
Time: 675.0ms
Precision: binary64
\[\left(x + x\right) - 1 \]
↓
\[\mathsf{fma}\left(x, 2, -1\right) \]
(FPCore (x) :precision binary64 (- (+ x x) 1.0))
↓
(FPCore (x) :precision binary64 (fma x 2.0 -1.0))
double code(double x) {
	return (x + x) - 1.0;
}
↓
double code(double x) {
	return fma(x, 2.0, -1.0);
}

function code(x)
	return Float64(Float64(x + x) - 1.0)
end
↓
function code(x)
	return fma(x, 2.0, -1.0)
end

code[x_] := N[(N[(x + x), $MachinePrecision] - 1.0), $MachinePrecision]
↓
code[x_] := N[(x * 2.0 + -1.0), $MachinePrecision]

\left(x + x\right) - 1
↓
\mathsf{fma}\left(x, 2, -1\right)

Error

Bits error versus x

Derivation

  1. Initial program 0

    \[\left(x + x\right) - 1 \]

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2022150 
(FPCore (x)
  :name "Data.Random.Distribution.Normal:doubleStdNormalZ from random-fu-0.2.6.2"
  :precision binary64
  (- (+ x x) 1.0))