Average Error: 0.0 → 0.0
Time: 7.3s
Precision: binary64
Cost: 7936
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \]
↓
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + \frac{x \cdot \left(0.9846394441 - {\left(x \cdot 0.04481\right)}^{2}\right)}{0.99229 + x \cdot -0.04481}} \]
(FPCore (x)
 :precision binary64
 (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))
↓
(FPCore (x)
 :precision binary64
 (-
  x
  (/
   (+ 2.30753 (* x 0.27061))
   (+
    1.0
    (/
     (* x (- 0.9846394441 (pow (* x 0.04481) 2.0)))
     (+ 0.99229 (* x -0.04481)))))))
double code(double x) {
	return x - ((2.30753 + (x * 0.27061)) / (1.0 + ((0.99229 + (x * 0.04481)) * x)));
}
↓
double code(double x) {
	return x - ((2.30753 + (x * 0.27061)) / (1.0 + ((x * (0.9846394441 - pow((x * 0.04481), 2.0))) / (0.99229 + (x * -0.04481)))));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = x - ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + ((0.99229d0 + (x * 0.04481d0)) * x)))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = x - ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + ((x * (0.9846394441d0 - ((x * 0.04481d0) ** 2.0d0))) / (0.99229d0 + (x * (-0.04481d0))))))
end function

public static double code(double x) {
	return x - ((2.30753 + (x * 0.27061)) / (1.0 + ((0.99229 + (x * 0.04481)) * x)));
}
↓
public static double code(double x) {
	return x - ((2.30753 + (x * 0.27061)) / (1.0 + ((x * (0.9846394441 - Math.pow((x * 0.04481), 2.0))) / (0.99229 + (x * -0.04481)))));
}

def code(x):
	return x - ((2.30753 + (x * 0.27061)) / (1.0 + ((0.99229 + (x * 0.04481)) * x)))
↓
def code(x):
	return x - ((2.30753 + (x * 0.27061)) / (1.0 + ((x * (0.9846394441 - math.pow((x * 0.04481), 2.0))) / (0.99229 + (x * -0.04481)))))

function code(x)
	return Float64(x - Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(Float64(0.99229 + Float64(x * 0.04481)) * x))))
end
↓
function code(x)
	return Float64(x - Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(Float64(x * Float64(0.9846394441 - (Float64(x * 0.04481) ^ 2.0))) / Float64(0.99229 + Float64(x * -0.04481))))))
end

function tmp = code(x)
	tmp = x - ((2.30753 + (x * 0.27061)) / (1.0 + ((0.99229 + (x * 0.04481)) * x)));
end
↓
function tmp = code(x)
	tmp = x - ((2.30753 + (x * 0.27061)) / (1.0 + ((x * (0.9846394441 - ((x * 0.04481) ^ 2.0))) / (0.99229 + (x * -0.04481)))));
end

code[x_] := N[(x - N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(0.99229 + N[(x * 0.04481), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(x - N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(x * N[(0.9846394441 - N[Power[N[(x * 0.04481), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.99229 + N[(x * -0.04481), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}
↓
x - \frac{2.30753 + x \cdot 0.27061}{1 + \frac{x \cdot \left(0.9846394441 - {\left(x \cdot 0.04481\right)}^{2}\right)}{0.99229 + x \cdot -0.04481}}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \]

  2. Applied egg-rr0.0

    \[\leadsto x - \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\frac{\left(0.9846394441 - {\left(x \cdot 0.04481\right)}^{2}\right) \cdot x}{0.99229 + -0.04481 \cdot x}}} \]

  3. Final simplification0.0

    \[\leadsto x - \frac{2.30753 + x \cdot 0.27061}{1 + \frac{x \cdot \left(0.9846394441 - {\left(x \cdot 0.04481\right)}^{2}\right)}{0.99229 + x \cdot -0.04481}} \]

Alternatives

Alternative 1
Error0.0
Cost1088
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} \]
Alternative 2
Error0.7
Cost584
\[\begin{array}{l} t_0 := x - \frac{6.039053782637804}{x}\\ \mathbf{if}\;x \leq -2644.5854058498144:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.3917278794254961:\\ \;\;\;\;x \cdot 3.0191289437 + -2.30753\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error1.0
Cost576
\[x - \frac{2.30753}{1 + x \cdot 0.99229} \]
Alternative 4
Error1.1
Cost328
\[\begin{array}{l} \mathbf{if}\;x \leq -2644.5854058498144:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.3917278794254961:\\ \;\;\;\;-2.30753\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 5
Error1.4
Cost192
\[x + -2.30753 \]
Alternative 6
Error31.7
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022308 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))