Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[\left(x + 1\right) \cdot y - x \]
↓
\[\mathsf{fma}\left(x, y, y - x\right) \]
(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))
↓
(FPCore (x y) :precision binary64 (fma x y (- y x)))
double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}
↓
double code(double x, double y) {
	return fma(x, y, (y - x));
}

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

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

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

Error

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded in x around 0 0.0

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

  3. Taylor expanded in y around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022190 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))