Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

Alternatives: 5

Speedup: 1.0×

• 23.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot x\right) \cdot 2 - 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (* (* x x) 2.0) 1.0))

C

double code(double x) {
	return ((x * x) * 2.0) - 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((x * x) * 2.0d0) - 1.0d0
end function

Java

public static double code(double x) {
	return ((x * x) * 2.0) - 1.0;
}

Python

def code(x):
	return ((x * x) * 2.0) - 1.0

Julia

function code(x)
	return Float64(Float64(Float64(x * x) * 2.0) - 1.0)
end

MATLAB

function tmp = code(x)
	tmp = ((x * x) * 2.0) - 1.0;
end

Wolfram

code[x_] := N[(N[(N[(x * x), $MachinePrecision] * 2.0), $MachinePrecision] - 1.0), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot x\right) \cdot 2 - 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (* (* x x) 2.0) 1.0))

C

double code(double x) {
	return ((x * x) * 2.0) - 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((x * x) * 2.0d0) - 1.0d0
end function

Java

public static double code(double x) {
	return ((x * x) * 2.0) - 1.0;
}

Python

def code(x):
	return ((x * x) * 2.0) - 1.0

Julia

function code(x)
	return Float64(Float64(Float64(x * x) * 2.0) - 1.0)
end

MATLAB

function tmp = code(x)
	tmp = ((x * x) * 2.0) - 1.0;
end

Wolfram

code[x_] := N[(N[(N[(x * x), $MachinePrecision] * 2.0), $MachinePrecision] - 1.0), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot x\right) \cdot 2 - 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (* (* x x) 2.0) 1.0))

C

double code(double x) {
	return ((x * x) * 2.0) - 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((x * x) * 2.0d0) - 1.0d0
end function

Java

public static double code(double x) {
	return ((x * x) * 2.0) - 1.0;
}

Python

def code(x):
	return ((x * x) * 2.0) - 1.0

Julia

function code(x)
	return Float64(Float64(Float64(x * x) * 2.0) - 1.0)
end

MATLAB

function tmp = code(x)
	tmp = ((x * x) * 2.0) - 1.0;
end

Wolfram

code[x_] := N[(N[(N[(x * x), $MachinePrecision] * 2.0), $MachinePrecision] - 1.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

Alternative 2: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 5 \cdot 10^{-15}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= (* x x) 5e-15) -1.0 (* 2.0 (* x x))))

C

double code(double x) {
	double tmp;
	if ((x * x) <= 5e-15) {
		tmp = -1.0;
	} else {
		tmp = 2.0 * (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x * x) <= 5d-15) then
        tmp = -1.0d0
    else
        tmp = 2.0d0 * (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x * x) <= 5e-15) {
		tmp = -1.0;
	} else {
		tmp = 2.0 * (x * x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x * x) <= 5e-15:
		tmp = -1.0
	else:
		tmp = 2.0 * (x * x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(x * x) <= 5e-15)
		tmp = -1.0;
	else
		tmp = Float64(2.0 * Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x * x) <= 5e-15)
		tmp = -1.0;
	else
		tmp = 2.0 * (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(x * x), $MachinePrecision], 5e-15], -1.0, N[(2.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 4.99999999999999999e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 4.99999999999999999e-15 < (*.f64 x x)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.7:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 0.7) -1.0 (* 2.0 x)))

C

double code(double x) {
	double tmp;
	if (x <= 0.7) {
		tmp = -1.0;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 0.7d0) then
        tmp = -1.0d0
    else
        tmp = 2.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.7) {
		tmp = -1.0;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.7:
		tmp = -1.0
	else:
		tmp = 2.0 * x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.7)
		tmp = -1.0;
	else
		tmp = Float64(2.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.7)
		tmp = -1.0;
	else
		tmp = 2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.7], -1.0, N[(2.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.69999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 0.69999999999999996 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.7:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 0.7) -1.0 2.0))

C

double code(double x) {
	double tmp;
	if (x <= 0.7) {
		tmp = -1.0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 0.7d0) then
        tmp = -1.0d0
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.7) {
		tmp = -1.0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.7:
		tmp = -1.0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.7)
		tmp = -1.0;
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.7)
		tmp = -1.0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.7], -1.0, 2.0]

Derivation

1. Split input into 2 regimes

2. if x < 0.69999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 0.69999999999999996 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 50.5% accurate, 7.0× 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 100.0%

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

3. Taylor expanded in x around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (x)
  :name "Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2"
  :precision binary64
  (- (* (* x x) 2.0) 1.0))