Average Error: 0.0 → 0
Time: 1.2s
Precision: binary64
\[x \cdot y - x \]
↓
\[\mathsf{fma}\left(y, x, -x\right) \]
(FPCore (x y) :precision binary64 (- (* x y) x))
↓
(FPCore (x y) :precision binary64 (fma y x (- x)))
double code(double x, double y) {
	return (x * y) - x;
}
↓
double code(double x, double y) {
	return fma(y, x, -x);
}

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

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

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

Error

Derivation

  1. Initial program 0.0

    \[x \cdot y - x \]

  2. Taylor expanded in x around 0 0.0

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

  3. Simplified0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2022192 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))