?

Average Error: 0.1 → 0.1
Time: 11.1s
Precision: binary64
Cost: 19968

?

\[0 \leq x \land x \leq 100\]
\[\sqrt{3 \cdot x - {x}^{2}} + \sqrt{8 \cdot {x}^{3}} \]
↓
\[\sqrt{3 \cdot x - x \cdot x} + \sqrt{8 \cdot {x}^{3}} \]
(FPCore (x)
 :precision binary64
 (+ (sqrt (- (* 3.0 x) (pow x 2.0))) (sqrt (* 8.0 (pow x 3.0)))))
↓
(FPCore (x)
 :precision binary64
 (+ (sqrt (- (* 3.0 x) (* x x))) (sqrt (* 8.0 (pow x 3.0)))))
double code(double x) {
	return sqrt(((3.0 * x) - pow(x, 2.0))) + sqrt((8.0 * pow(x, 3.0)));
}
↓
double code(double x) {
	return sqrt(((3.0 * x) - (x * x))) + sqrt((8.0 * pow(x, 3.0)));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt(((3.0d0 * x) - (x ** 2.0d0))) + sqrt((8.0d0 * (x ** 3.0d0)))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt(((3.0d0 * x) - (x * x))) + sqrt((8.0d0 * (x ** 3.0d0)))
end function

public static double code(double x) {
	return Math.sqrt(((3.0 * x) - Math.pow(x, 2.0))) + Math.sqrt((8.0 * Math.pow(x, 3.0)));
}
↓
public static double code(double x) {
	return Math.sqrt(((3.0 * x) - (x * x))) + Math.sqrt((8.0 * Math.pow(x, 3.0)));
}

def code(x):
	return math.sqrt(((3.0 * x) - math.pow(x, 2.0))) + math.sqrt((8.0 * math.pow(x, 3.0)))
↓
def code(x):
	return math.sqrt(((3.0 * x) - (x * x))) + math.sqrt((8.0 * math.pow(x, 3.0)))

function code(x)
	return Float64(sqrt(Float64(Float64(3.0 * x) - (x ^ 2.0))) + sqrt(Float64(8.0 * (x ^ 3.0))))
end
↓
function code(x)
	return Float64(sqrt(Float64(Float64(3.0 * x) - Float64(x * x))) + sqrt(Float64(8.0 * (x ^ 3.0))))
end

function tmp = code(x)
	tmp = sqrt(((3.0 * x) - (x ^ 2.0))) + sqrt((8.0 * (x ^ 3.0)));
end
↓
function tmp = code(x)
	tmp = sqrt(((3.0 * x) - (x * x))) + sqrt((8.0 * (x ^ 3.0)));
end

code[x_] := N[(N[Sqrt[N[(N[(3.0 * x), $MachinePrecision] - N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[Sqrt[N[(8.0 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[Sqrt[N[(N[(3.0 * x), $MachinePrecision] - N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[Sqrt[N[(8.0 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

\sqrt{3 \cdot x - {x}^{2}} + \sqrt{8 \cdot {x}^{3}}
↓
\sqrt{3 \cdot x - x \cdot x} + \sqrt{8 \cdot {x}^{3}}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.1

    \[\sqrt{3 \cdot x - {x}^{2}} + \sqrt{8 \cdot {x}^{3}} \]

  2. Simplified0.1

    \[\leadsto \color{blue}{\sqrt{3 \cdot x - x \cdot x} + \sqrt{8 \cdot {x}^{3}}} \]
    Proof

    [Start]0.1

    \[ \sqrt{3 \cdot x - {x}^{2}} + \sqrt{8 \cdot {x}^{3}} \]

    unpow2 [=>]0.1

    \[ \sqrt{3 \cdot x - \color{blue}{x \cdot x}} + \sqrt{8 \cdot {x}^{3}} \]

  3. Final simplification0.1

    \[\leadsto \sqrt{3 \cdot x - x \cdot x} + \sqrt{8 \cdot {x}^{3}} \]

Alternatives

Alternative 1
Error0.1
Cost19840
\[\sqrt{8 \cdot {x}^{3}} + \sqrt{x \cdot \left(3 - x\right)} \]
Alternative 2
Error1.3
Cost19712
\[\sqrt{8 \cdot {x}^{3}} + \sqrt{3 \cdot x} \]

Error

Reproduce?

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(3*x - x^2) + sqrt(8*x^3)"
  :precision binary64
  :pre (and (<= 0.0 x) (<= x 100.0))
  (+ (sqrt (- (* 3.0 x) (pow x 2.0))) (sqrt (* 8.0 (pow x 3.0)))))