Average Error: 0.0 → 0
Time: 1.6s
Precision: binary64
Cost: 6656
\[x \cdot y - x \]
↓
\[\mathsf{fma}\left(x, y, -x\right) \]
(FPCore (x y) :precision binary64 (- (* x y) x))
↓
(FPCore (x y) :precision binary64 (fma x y (- x)))
double code(double x, double y) {
	return (x * y) - x;
}
↓
double code(double x, double y) {
	return fma(x, y, -x);
}

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

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

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

Error

Derivation

  1. Initial program 0.0

    \[x \cdot y - x \]

  2. Simplified0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -x\right)} \]
    Proof
    (fma.f64 x y (neg.f64 x)): 0 points increase in error, 0 points decrease in error
    (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x y) x)): 0 points increase in error, 0 points decrease in error

  3. Final simplification0

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

Alternatives

Alternative 1
Error1.5
Cost456
\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 2
Error0.0
Cost320
\[x \cdot \left(y + -1\right) \]
Alternative 3
Error27.6
Cost128
\[-x \]

Error

Reproduce

herbie shell --seed 2022340 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))