Average Error: 0.0 → 0.0
Time: 7.5s
Precision: binary64
Cost: 1344
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \]
↓
\[x - \frac{2.30753 + \left(\left(x \cdot 0.27061 + 1\right) + -1\right)}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} \]
(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) -1.0))
   (+ 1.0 (* x (+ 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) + -1.0)) / (1.0 + (x * (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) + (-1.0d0))) / (1.0d0 + (x * (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) + -1.0)) / (1.0 + (x * (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) + -1.0)) / (1.0 + (x * (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(Float64(Float64(x * 0.27061) + 1.0) + -1.0)) / Float64(1.0 + Float64(x * 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) + -1.0)) / (1.0 + (x * (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[(N[(N[(x * 0.27061), $MachinePrecision] + 1.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x * 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 + \left(\left(x \cdot 0.27061 + 1\right) + -1\right)}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}

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-rr15.9

    \[\leadsto x - \frac{2.30753 + \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot 0.27061\right)} - 1\right)}}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \]

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Alternatives

Alternative 1
Error0.0
Cost1088
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} \]
Alternative 2
Error0.9
Cost832
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot 0.99229} \]
Alternative 3
Error1.1
Cost328
\[\begin{array}{l} \mathbf{if}\;x \leq -1.05:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2:\\ \;\;\;\;-2.30753\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 4
Error1.4
Cost192
\[x + -2.30753 \]
Alternative 5
Error31.2
Cost64
\[-2.30753 \]

Error

Reproduce

herbie shell --seed 2022329 
(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)))))