Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[x \cdot y - x \]
↓
\[\left(y + -1\right) \cdot x \]
(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;
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) - x
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + (-1.0d0)) * x
end function

public static double code(double x, double y) {
	return (x * y) - x;
}
↓
public static double code(double x, double y) {
	return (y + -1.0) * x;
}

def code(x, y):
	return (x * y) - x
↓
def code(x, y):
	return (y + -1.0) * x

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

function tmp = code(x, y)
	tmp = (x * y) - x;
end
↓
function tmp = code(x, y)
	tmp = (y + -1.0) * x;
end

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

x \cdot y - x
↓
\left(y + -1\right) \cdot 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 2022160 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))