Average Error: 0.2 → 0.2
Time: 1.0s
Precision: binary64
\[\left(x \cdot 3\right) \cdot x \]
↓
\[3 \cdot {x}^{2} \]
(FPCore (x) :precision binary64 (* (* x 3.0) x))
↓
(FPCore (x) :precision binary64 (* 3.0 (pow x 2.0)))
double code(double x) {
	return (x * 3.0) * x;
}
↓
double code(double x) {
	return 3.0 * pow(x, 2.0);
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * 3.0d0) * x
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * (x ** 2.0d0)
end function

public static double code(double x) {
	return (x * 3.0) * x;
}
↓
public static double code(double x) {
	return 3.0 * Math.pow(x, 2.0);
}

def code(x):
	return (x * 3.0) * x
↓
def code(x):
	return 3.0 * math.pow(x, 2.0)

function code(x)
	return Float64(Float64(x * 3.0) * x)
end
↓
function code(x)
	return Float64(3.0 * (x ^ 2.0))
end

function tmp = code(x)
	tmp = (x * 3.0) * x;
end
↓
function tmp = code(x)
	tmp = 3.0 * (x ^ 2.0);
end

code[x_] := N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision]
↓
code[x_] := N[(3.0 * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]

\left(x \cdot 3\right) \cdot x
↓
3 \cdot {x}^{2}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(x \cdot 3\right) \cdot x \]

  2. Taylor expanded in x around 0 0.2

    \[\leadsto \color{blue}{3 \cdot {x}^{2}} \]

  3. Final simplification0.2

    \[\leadsto 3 \cdot {x}^{2} \]

Reproduce

herbie shell --seed 2022159 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))