Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1

Average Error: 0.01% → 0%

Time: 1.8s

Precision: binary64

Cost: 6656

Math

\[x \cdot y - x \]

↓

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

FPCore

(FPCore (x y) :precision binary64 (- (* x y) x))

↓

(FPCore (x y) :precision binary64 (fma x y (- x)))

C

double code(double x, double y) {
	return (x * y) - x;
}

↓

double code(double x, double y) {
	return fma(x, y, -x);
}

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.01

   \[x \cdot y - x \]

2. Simplified 0

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

   [Start] 0.01	\[ x \cdot y - x \]
   fma-neg [=>] 0	\[ \color{blue}{\mathsf{fma}\left(x, y, -x\right)} \]

3. Final simplification 0

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

Alternatives

Alternative 1
Error	2.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2
Error	0.01%
Cost	320

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

Alternative 3
Error	43.16%
Cost	128

\[-x \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))