Average Error: 0.1 → 0.1
Time: 3.2s
Precision: binary64
\[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
↓
\[x \cdot y - y \cdot \left(x \cdot y\right) \]
(FPCore (x y) :precision binary64 (* (* x y) (- 1.0 y)))
↓
(FPCore (x y) :precision binary64 (- (* x y) (* y (* x y))))
double code(double x, double y) {
	return (x * y) * (1.0 - y);
}
↓
double code(double x, double y) {
	return (x * y) - (y * (x * y));
}

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

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

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

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

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

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

\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
x \cdot y - y \cdot \left(x \cdot y\right)

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 0.1

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

  2. Applied add-cube-cbrt_binary640.4

    \[\leadsto \left(x \cdot y\right) \cdot \left(1 - \color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}\right) \]

  3. Applied cancel-sign-sub-inv_binary640.4

    \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{\left(1 + \left(-\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} \]

  4. Applied distribute-rgt-in_binary640.4

    \[\leadsto \color{blue}{1 \cdot \left(x \cdot y\right) + \left(\left(-\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right) \cdot \left(x \cdot y\right)} \]

  5. Applied associate-*r*_binary640.4

    \[\leadsto 1 \cdot \left(x \cdot y\right) + \color{blue}{\left(\left(\left(-\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right) \cdot x\right) \cdot y} \]

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2022131 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1.0 y)))