Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[x \cdot y - x \]
↓
\[\left(y - 1\right) \cdot x \]
x \cdot y - x
↓
\left(y - 1\right) \cdot x

(FPCore (x y) :precision binary64 (- (* x y) x))
↓
(FPCore (x y) :precision binary64 (* (- y 1.0) x))
double code(double x, double y) {
	return (x * y) - x;
}
↓
double code(double x, double y) {
	return (y - 1.0) * x;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2022067 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))