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

Percentage Accurate: 99.9% → 99.9%

Time: 6.5s

Alternatives: 7

Speedup: 1.0×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(0.253 + x \cdot 0.12\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))

C

double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (0.253d0 + (x * 0.12d0)))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Python

def code(x):
	return 1.0 - (x * (0.253 + (x * 0.12)))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (0.253 + (x * 0.12)));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(0.253 + x \cdot 0.12\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))

C

double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (0.253d0 + (x * 0.12d0)))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Python

def code(x):
	return 1.0 - (x * (0.253 + (x * 0.12)))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (0.253 + (x * 0.12)));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ 1 + x \cdot \frac{x \cdot -0.0144 + \frac{0.064009}{x}}{\frac{-0.253}{x} - -0.12} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (+ 1.0 (* x (/ (+ (* x -0.0144) (/ 0.064009 x)) (- (/ -0.253 x) -0.12)))))

C

double code(double x) {
	return 1.0 + (x * (((x * -0.0144) + (0.064009 / x)) / ((-0.253 / x) - -0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 + (x * (((x * (-0.0144d0)) + (0.064009d0 / x)) / (((-0.253d0) / x) - (-0.12d0))))
end function

Java

public static double code(double x) {
	return 1.0 + (x * (((x * -0.0144) + (0.064009 / x)) / ((-0.253 / x) - -0.12)));
}

Python

def code(x):
	return 1.0 + (x * (((x * -0.0144) + (0.064009 / x)) / ((-0.253 / x) - -0.12)))

Julia

function code(x)
	return Float64(1.0 + Float64(x * Float64(Float64(Float64(x * -0.0144) + Float64(0.064009 / x)) / Float64(Float64(-0.253 / x) - -0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 + (x * (((x * -0.0144) + (0.064009 / x)) / ((-0.253 / x) - -0.12)));
end

Wolfram

code[x_] := N[(1.0 + N[(x * N[(N[(N[(x * -0.0144), $MachinePrecision] + N[(0.064009 / x), $MachinePrecision]), $MachinePrecision] / N[(N[(-0.253 / x), $MachinePrecision] - -0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 99.9%

   \[\leadsto 1 - x \cdot \color{blue}{\left(x \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
4. Step-by-step derivation

   1. *-un-lft-identity 99.9%

      \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\left(1 \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)}\right) \]

   2. un-div-inv 99.9%

      \[\leadsto 1 - x \cdot \left(x \cdot \left(1 \cdot \left(0.12 + \color{blue}{\frac{0.253}{x}}\right)\right)\right) \]

5. Applied egg-rr 99.9%

   \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\left(1 \cdot \left(0.12 + \frac{0.253}{x}\right)\right)}\right) \]
6. Step-by-step derivation

   1. *-lft-identity 99.9%

      \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\left(0.12 + \frac{0.253}{x}\right)}\right) \]

   2. +-commutative 99.9%

      \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\left(\frac{0.253}{x} + 0.12\right)}\right) \]

7. Simplified 99.9%

   \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\left(\frac{0.253}{x} + 0.12\right)}\right) \]
8. Step-by-step derivation

   1. flip-+ 72.4%

      \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\frac{\frac{0.253}{x} \cdot \frac{0.253}{x} - 0.12 \cdot 0.12}{\frac{0.253}{x} - 0.12}}\right) \]

   2. associate-*r/ 72.4%

      \[\leadsto 1 - x \cdot \color{blue}{\frac{x \cdot \left(\frac{0.253}{x} \cdot \frac{0.253}{x} - 0.12 \cdot 0.12\right)}{\frac{0.253}{x} - 0.12}} \]

   3. sub-neg 72.4%

      \[\leadsto 1 - x \cdot \frac{x \cdot \color{blue}{\left(\frac{0.253}{x} \cdot \frac{0.253}{x} + \left(-0.12 \cdot 0.12\right)\right)}}{\frac{0.253}{x} - 0.12} \]

   4. frac-times 72.4%

      \[\leadsto 1 - x \cdot \frac{x \cdot \left(\color{blue}{\frac{0.253 \cdot 0.253}{x \cdot x}} + \left(-0.12 \cdot 0.12\right)\right)}{\frac{0.253}{x} - 0.12} \]

   5. metadata-eval 72.4%

      \[\leadsto 1 - x \cdot \frac{x \cdot \left(\frac{\color{blue}{0.064009}}{x \cdot x} + \left(-0.12 \cdot 0.12\right)\right)}{\frac{0.253}{x} - 0.12} \]

   6. pow2 72.4%

      \[\leadsto 1 - x \cdot \frac{x \cdot \left(\frac{0.064009}{\color{blue}{{x}^{2}}} + \left(-0.12 \cdot 0.12\right)\right)}{\frac{0.253}{x} - 0.12} \]

   7. metadata-eval 72.4%

      \[\leadsto 1 - x \cdot \frac{x \cdot \left(\frac{0.064009}{{x}^{2}} + \left(-\color{blue}{0.0144}\right)\right)}{\frac{0.253}{x} - 0.12} \]

   8. metadata-eval 72.4%

      \[\leadsto 1 - x \cdot \frac{x \cdot \left(\frac{0.064009}{{x}^{2}} + \color{blue}{-0.0144}\right)}{\frac{0.253}{x} - 0.12} \]

   9. sub-neg 72.4%

      \[\leadsto 1 - x \cdot \frac{x \cdot \left(\frac{0.064009}{{x}^{2}} + -0.0144\right)}{\color{blue}{\frac{0.253}{x} + \left(-0.12\right)}} \]

   10. metadata-eval 72.4%

       \[\leadsto 1 - x \cdot \frac{x \cdot \left(\frac{0.064009}{{x}^{2}} + -0.0144\right)}{\frac{0.253}{x} + \color{blue}{-0.12}} \]

9. Applied egg-rr 72.4%

   \[\leadsto 1 - x \cdot \color{blue}{\frac{x \cdot \left(\frac{0.064009}{{x}^{2}} + -0.0144\right)}{\frac{0.253}{x} + -0.12}} \]

11. Simplified 99.9%

    \[\leadsto 1 - x \cdot \color{blue}{\frac{x \cdot -0.0144 + \frac{0.064009}{x}}{-0.12 - \frac{-0.253}{x}}} \]

12. Final simplification 99.9%

    \[\leadsto 1 + x \cdot \frac{x \cdot -0.0144 + \frac{0.064009}{x}}{\frac{-0.253}{x} - -0.12} \]
13. Add Preprocessing

Alternative 2: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;-0.12 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;1 - x \cdot 0.253\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -4.2) (not (<= x 2.0))) (* -0.12 (* x x)) (- 1.0 (* x 0.253))))

C

double code(double x) {
	double tmp;
	if ((x <= -4.2) || !(x <= 2.0)) {
		tmp = -0.12 * (x * x);
	} else {
		tmp = 1.0 - (x * 0.253);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-4.2d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = (-0.12d0) * (x * x)
    else
        tmp = 1.0d0 - (x * 0.253d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -4.2) || !(x <= 2.0)) {
		tmp = -0.12 * (x * x);
	} else {
		tmp = 1.0 - (x * 0.253);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -4.2) or not (x <= 2.0):
		tmp = -0.12 * (x * x)
	else:
		tmp = 1.0 - (x * 0.253)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -4.2) || !(x <= 2.0))
		tmp = Float64(-0.12 * Float64(x * x));
	else
		tmp = Float64(1.0 - Float64(x * 0.253));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -4.2) || ~((x <= 2.0)))
		tmp = -0.12 * (x * x);
	else
		tmp = 1.0 - (x * 0.253);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -4.2], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(-0.12 * N[(x * x), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x * 0.253), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.20000000000000018 or 2 < x

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.8%

      \[\leadsto \color{blue}{-0.12 \cdot {x}^{2}} \]
   4. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \color{blue}{{x}^{2} \cdot -0.12} \]

   5. Simplified 98.8%

      \[\leadsto \color{blue}{{x}^{2} \cdot -0.12} \]
   6. Step-by-step derivation

      1. unpow2 98.8%

         \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot -0.12 \]

   7. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot -0.12 \]

   if -4.20000000000000018 < x < 2

   1. Initial program 100.0%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.1%

      \[\leadsto 1 - \color{blue}{0.253 \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative 99.1%

         \[\leadsto 1 - \color{blue}{x \cdot 0.253} \]

   5. Simplified 99.1%

      \[\leadsto 1 - \color{blue}{x \cdot 0.253} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;-0.12 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;1 - x \cdot 0.253\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;-0.12 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -4.2) (not (<= x 2.0))) (* -0.12 (* x x)) 1.0))

C

double code(double x) {
	double tmp;
	if ((x <= -4.2) || !(x <= 2.0)) {
		tmp = -0.12 * (x * x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-4.2d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = (-0.12d0) * (x * x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -4.2) || !(x <= 2.0)) {
		tmp = -0.12 * (x * x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -4.2) or not (x <= 2.0):
		tmp = -0.12 * (x * x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -4.2) || !(x <= 2.0))
		tmp = Float64(-0.12 * Float64(x * x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -4.2) || ~((x <= 2.0)))
		tmp = -0.12 * (x * x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -4.2], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(-0.12 * N[(x * x), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -4.20000000000000018 or 2 < x

   1. Initial program 99.8%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.8%

      \[\leadsto \color{blue}{-0.12 \cdot {x}^{2}} \]
   4. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \color{blue}{{x}^{2} \cdot -0.12} \]

   5. Simplified 98.8%

      \[\leadsto \color{blue}{{x}^{2} \cdot -0.12} \]
   6. Step-by-step derivation

      1. unpow2 98.8%

         \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot -0.12 \]

   7. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot -0.12 \]

   if -4.20000000000000018 < x < 2

   1. Initial program 100.0%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;-0.12 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(x \cdot \left(\frac{0.253}{x} + 0.12\right)\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (* x (+ (/ 0.253 x) 0.12)))))

C

double code(double x) {
	return 1.0 - (x * (x * ((0.253 / x) + 0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (x * ((0.253d0 / x) + 0.12d0)))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (x * ((0.253 / x) + 0.12)));
}

Python

def code(x):
	return 1.0 - (x * (x * ((0.253 / x) + 0.12)))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(x * Float64(Float64(0.253 / x) + 0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (x * ((0.253 / x) + 0.12)));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(x * N[(N[(0.253 / x), $MachinePrecision] + 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 99.9%

   \[\leadsto 1 - x \cdot \color{blue}{\left(x \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]
4. Step-by-step derivation

   1. *-un-lft-identity 99.9%

      \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\left(1 \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)}\right) \]

   2. un-div-inv 99.9%

      \[\leadsto 1 - x \cdot \left(x \cdot \left(1 \cdot \left(0.12 + \color{blue}{\frac{0.253}{x}}\right)\right)\right) \]

5. Applied egg-rr 99.9%

   \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\left(1 \cdot \left(0.12 + \frac{0.253}{x}\right)\right)}\right) \]
6. Step-by-step derivation

   1. *-lft-identity 99.9%

      \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\left(0.12 + \frac{0.253}{x}\right)}\right) \]

   2. +-commutative 99.9%

      \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\left(\frac{0.253}{x} + 0.12\right)}\right) \]

7. Simplified 99.9%

   \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{\left(\frac{0.253}{x} + 0.12\right)}\right) \]
8. Add Preprocessing

Alternative 5: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(0.253 + x \cdot 0.12\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))

C

double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (0.253d0 + (x * 0.12d0)))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Python

def code(x):
	return 1.0 - (x * (0.253 + (x * 0.12)))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (0.253 + (x * 0.12)));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 6: 97.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(x \cdot 0.12\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (* x 0.12))))

C

double code(double x) {
	return 1.0 - (x * (x * 0.12));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (x * 0.12d0))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (x * 0.12));
}

Python

def code(x):
	return 1.0 - (x * (x * 0.12))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(x * 0.12)))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (x * 0.12));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 99.9%

   \[\leadsto 1 - x \cdot \color{blue}{\left(x \cdot \left(0.12 + 0.253 \cdot \frac{1}{x}\right)\right)} \]

4. Taylor expanded in x around inf 98.0%

   \[\leadsto 1 - x \cdot \left(x \cdot \color{blue}{0.12}\right) \]
5. Add Preprocessing

Alternative 7: 49.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 1.0)

C

double code(double x) {
	return 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0
end function

Java

public static double code(double x) {
	return 1.0;
}

Python

def code(x):
	return 1.0

Julia

function code(x)
	return 1.0
end

MATLAB

function tmp = code(x)
	tmp = 1.0;
end

Wolfram

code[x_] := 1.0

Derivation

1. Initial program 99.9%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 52.5%

   \[\leadsto \color{blue}{1} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024163 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))