Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Fortran

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

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Fortran

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

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + \left(-1 + \left(x \cdot 0.99229 + \left(1 + 0.04481 \cdot {x}^{2}\right)\right)\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (-
  (/
   (+ 2.30753 (* x 0.27061))
   (+ 1.0 (+ -1.0 (+ (* x 0.99229) (+ 1.0 (* 0.04481 (pow x 2.0)))))))
  x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (-1.0 + ((x * 0.99229) + (1.0 + (0.04481 * pow(x, 2.0))))))) - x;
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Step-by-step derivation

   1. expm1-log1p-u 100.0%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)\right)}} - x \]

   2. expm1-udef 100.0%

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

   3. log1p-udef 100.0%

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

   4. add-exp-log 100.0%

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

   5. flip-+ 77.7%

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

   6. div-inv 77.7%

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

   7. fma-neg 77.7%

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

3. Applied egg-rr 77.7%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\mathsf{fma}\left(1 - {\left(x \cdot \mathsf{fma}\left(x, 0.04481, 0.99229\right)\right)}^{2}, \frac{1}{1 - x \cdot \mathsf{fma}\left(x, 0.04481, 0.99229\right)}, -1\right)}} - x \]
4. Step-by-step derivation

   1. fma-udef 77.7%

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

   2. +-commutative 77.7%

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

   3. associate-*r/ 77.7%

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

   4. *-rgt-identity 77.7%

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

5. Simplified 77.7%

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

6. Taylor expanded in x around 0 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Fortran

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

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 3: 98.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot 0.99229} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x 0.99229))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * 0.99229))) - x;
}

Fortran

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

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * 0.99229))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * 0.99229))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(x * 0.99229))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + (x * 0.99229))) - x;
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 99.3%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{0.99229 \cdot x}} - x \]
3. Step-by-step derivation

   1. *-commutative 99.3%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{x \cdot 0.99229}} - x \]

4. Simplified 99.3%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{x \cdot 0.99229}} - x \]

5. Final simplification 99.3%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot 0.99229} - x \]

Alternative 4: 98.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.15:\\ \;\;\;\;2.30753\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -3.6) (- x) (if (<= x 1.15) 2.30753 (- x))))

C

double code(double x) {
	double tmp;
	if (x <= -3.6) {
		tmp = -x;
	} else if (x <= 1.15) {
		tmp = 2.30753;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-3.6d0)) then
        tmp = -x
    else if (x <= 1.15d0) then
        tmp = 2.30753d0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -3.6) {
		tmp = -x;
	} else if (x <= 1.15) {
		tmp = 2.30753;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -3.6:
		tmp = -x
	elif x <= 1.15:
		tmp = 2.30753
	else:
		tmp = -x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -3.6)
		tmp = Float64(-x);
	elseif (x <= 1.15)
		tmp = 2.30753;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -3.6)
		tmp = -x;
	elseif (x <= 1.15)
		tmp = 2.30753;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -3.6], (-x), If[LessEqual[x, 1.15], 2.30753, (-x)]]

Derivation

1. Split input into 2 regimes

2. if x < -3.60000000000000009 or 1.1499999999999999 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.8%

      \[\leadsto \color{blue}{2.30753} - x \]

   3. Taylor expanded in x around inf 99.5%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   4. Step-by-step derivation

      1. neg-mul-1 99.5%

         \[\leadsto \color{blue}{-x} \]

   5. Simplified 99.5%

      \[\leadsto \color{blue}{-x} \]

   if -3.60000000000000009 < x < 1.1499999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.5%

      \[\leadsto \color{blue}{\left(2.30753 + -2.0191289437 \cdot x\right)} - x \]
   3. Step-by-step derivation

      1. associate--l+ 99.5%

         \[\leadsto \color{blue}{2.30753 + \left(-2.0191289437 \cdot x - x\right)} \]

      2. +-commutative 99.5%

         \[\leadsto \color{blue}{\left(-2.0191289437 \cdot x - x\right) + 2.30753} \]

      3. *-un-lft-identity 99.5%

         \[\leadsto \left(-2.0191289437 \cdot x - \color{blue}{1 \cdot x}\right) + 2.30753 \]

      4. distribute-rgt-out-- 99.5%

         \[\leadsto \color{blue}{x \cdot \left(-2.0191289437 - 1\right)} + 2.30753 \]

      5. metadata-eval 99.5%

         \[\leadsto x \cdot \color{blue}{-3.0191289437} + 2.30753 \]

   4. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{x \cdot -3.0191289437 + 2.30753} \]

   5. Taylor expanded in x around 0 98.9%

      \[\leadsto \color{blue}{2.30753} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.15:\\ \;\;\;\;2.30753\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 5: 97.9% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ 2.30753 - x \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 2.30753 x))

C

double code(double x) {
	return 2.30753 - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 2.30753d0 - x
end function

Java

public static double code(double x) {
	return 2.30753 - x;
}

Python

def code(x):
	return 2.30753 - x

Julia

function code(x)
	return Float64(2.30753 - x)
end

MATLAB

function tmp = code(x)
	tmp = 2.30753 - x;
end

Wolfram

code[x_] := N[(2.30753 - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 98.8%

   \[\leadsto \color{blue}{2.30753} - x \]

3. Final simplification 98.8%

   \[\leadsto 2.30753 - x \]

Alternative 6: 50.6% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 2.30753 \end{array} \]

FPCore

(FPCore (x) :precision binary64 2.30753)

C

double code(double x) {
	return 2.30753;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 2.30753d0
end function

Java

public static double code(double x) {
	return 2.30753;
}

Python

def code(x):
	return 2.30753

Julia

function code(x)
	return 2.30753
end

MATLAB

function tmp = code(x)
	tmp = 2.30753;
end

Wolfram

code[x_] := 2.30753

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 59.9%

   \[\leadsto \color{blue}{\left(2.30753 + -2.0191289437 \cdot x\right)} - x \]
3. Step-by-step derivation

   1. associate--l+ 59.9%

      \[\leadsto \color{blue}{2.30753 + \left(-2.0191289437 \cdot x - x\right)} \]

   2. +-commutative 59.9%

      \[\leadsto \color{blue}{\left(-2.0191289437 \cdot x - x\right) + 2.30753} \]

   3. *-un-lft-identity 59.9%

      \[\leadsto \left(-2.0191289437 \cdot x - \color{blue}{1 \cdot x}\right) + 2.30753 \]

   4. distribute-rgt-out-- 59.9%

      \[\leadsto \color{blue}{x \cdot \left(-2.0191289437 - 1\right)} + 2.30753 \]

   5. metadata-eval 59.9%

      \[\leadsto x \cdot \color{blue}{-3.0191289437} + 2.30753 \]

4. Applied egg-rr 59.9%

   \[\leadsto \color{blue}{x \cdot -3.0191289437 + 2.30753} \]

5. Taylor expanded in x around 0 52.7%

   \[\leadsto \color{blue}{2.30753} \]

6. Final simplification 52.7%

   \[\leadsto 2.30753 \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))