?

Average Error: 0.6 → 0.3
Time: 16.4s
Precision: binary64
Cost: 832

?

\[2.04 \leq x \land x \leq 2.66\]
\[\frac{\left(4 \cdot x\right) \cdot x}{1 + \frac{x}{1.11} \cdot \frac{x}{1.11}} \]
\[\frac{x \cdot \left(4 \cdot x\right)}{1 + \frac{x \cdot x}{1.2321000000000002}} \]
(FPCore (x)
 :precision binary64
 (/ (* (* 4.0 x) x) (+ 1.0 (* (/ x 1.11) (/ x 1.11)))))
(FPCore (x)
 :precision binary64
 (/ (* x (* 4.0 x)) (+ 1.0 (/ (* x x) 1.2321000000000002))))
double code(double x) {
	return ((4.0 * x) * x) / (1.0 + ((x / 1.11) * (x / 1.11)));
}
double code(double x) {
	return (x * (4.0 * x)) / (1.0 + ((x * x) / 1.2321000000000002));
}
real(8) function code(x)
    real(8), intent (in) :: x
    code = ((4.0d0 * x) * x) / (1.0d0 + ((x / 1.11d0) * (x / 1.11d0)))
end function
real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * (4.0d0 * x)) / (1.0d0 + ((x * x) / 1.2321000000000002d0))
end function
public static double code(double x) {
	return ((4.0 * x) * x) / (1.0 + ((x / 1.11) * (x / 1.11)));
}
public static double code(double x) {
	return (x * (4.0 * x)) / (1.0 + ((x * x) / 1.2321000000000002));
}
def code(x):
	return ((4.0 * x) * x) / (1.0 + ((x / 1.11) * (x / 1.11)))
def code(x):
	return (x * (4.0 * x)) / (1.0 + ((x * x) / 1.2321000000000002))
function code(x)
	return Float64(Float64(Float64(4.0 * x) * x) / Float64(1.0 + Float64(Float64(x / 1.11) * Float64(x / 1.11))))
end
function code(x)
	return Float64(Float64(x * Float64(4.0 * x)) / Float64(1.0 + Float64(Float64(x * x) / 1.2321000000000002)))
end
function tmp = code(x)
	tmp = ((4.0 * x) * x) / (1.0 + ((x / 1.11) * (x / 1.11)));
end
function tmp = code(x)
	tmp = (x * (4.0 * x)) / (1.0 + ((x * x) / 1.2321000000000002));
end
code[x_] := N[(N[(N[(4.0 * x), $MachinePrecision] * x), $MachinePrecision] / N[(1.0 + N[(N[(x / 1.11), $MachinePrecision] * N[(x / 1.11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
code[x_] := N[(N[(x * N[(4.0 * x), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(x * x), $MachinePrecision] / 1.2321000000000002), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\frac{\left(4 \cdot x\right) \cdot x}{1 + \frac{x}{1.11} \cdot \frac{x}{1.11}}
\frac{x \cdot \left(4 \cdot x\right)}{1 + \frac{x \cdot x}{1.2321000000000002}}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.6

    \[\frac{\left(4 \cdot x\right) \cdot x}{1 + \frac{x}{1.11} \cdot \frac{x}{1.11}} \]
  2. Applied egg-rr0.3

    \[\leadsto \frac{\left(4 \cdot x\right) \cdot x}{1 + \color{blue}{\frac{x \cdot x}{1.2321000000000002}}} \]
  3. Final simplification0.3

    \[\leadsto \frac{x \cdot \left(4 \cdot x\right)}{1 + \frac{x \cdot x}{1.2321000000000002}} \]

Alternatives

Alternative 1
Error0.3
Cost832
\[\frac{x \cdot \left(4 \cdot x\right)}{1 + \left(x \cdot x\right) \cdot 0.8116224332440547} \]
Alternative 2
Error0.4
Cost704
\[\frac{4 \cdot x}{x \cdot 0.8116224332440547 + \frac{1}{x}} \]
Alternative 3
Error48.4
Cost448
\[4.928400000000001 + \frac{-6.072281640000002}{x \cdot x} \]
Alternative 4
Error48.4
Cost448
\[4.928400000000001 + \frac{\frac{-6.072281640000002}{x}}{x} \]
Alternative 5
Error49.9
Cost64
\[4.928400000000001 \]

Error

Reproduce?

herbie shell --seed 1 
(FPCore (x)
  :name "((4.0 * x) * x) / (1.0 + ((x / 1.11) * (x / 1.11)))"
  :precision binary64
  :pre (and (<= 2.04 x) (<= x 2.66))
  (/ (* (* 4.0 x) x) (+ 1.0 (* (/ x 1.11) (/ x 1.11)))))