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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 7

Speedup: N/A×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))

C

double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * (y - 1.0d0)) - (y * 0.5d0)) + 0.918938533204673d0
end function

Java

public static double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}

Python

def code(x, y):
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673

Julia

function code(x, y)
	return Float64(Float64(Float64(x * Float64(y - 1.0)) - Float64(y * 0.5)) + 0.918938533204673)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
end

Wolfram

code[x_, y_] := N[(N[(N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] - N[(y * 0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))

C

double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * (y - 1.0d0)) - (y * 0.5d0)) + 0.918938533204673d0
end function

Java

public static double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}

Python

def code(x, y):
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673

Julia

function code(x, y)
	return Float64(Float64(Float64(x * Float64(y - 1.0)) - Float64(y * 0.5)) + 0.918938533204673)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
end

Wolfram

code[x_, y_] := N[(N[(N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] - N[(y * 0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(y \cdot \left(-0.5 + x\right) - x\right) + 0.918938533204673 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (- (* y (+ -0.5 x)) x) 0.918938533204673))

C

double code(double x, double y) {
	return ((y * (-0.5 + x)) - x) + 0.918938533204673;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((y * ((-0.5d0) + x)) - x) + 0.918938533204673d0
end function

Java

public static double code(double x, double y) {
	return ((y * (-0.5 + x)) - x) + 0.918938533204673;
}

Python

def code(x, y):
	return ((y * (-0.5 + x)) - x) + 0.918938533204673

Julia

function code(x, y)
	return Float64(Float64(Float64(y * Float64(-0.5 + x)) - x) + 0.918938533204673)
end

MATLAB

function tmp = code(x, y)
	tmp = ((y * (-0.5 + x)) - x) + 0.918938533204673;
end

Wolfram

code[x_, y_] := N[(N[(N[(y * N[(-0.5 + x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.918938533204673), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
2. Add Preprocessing

3. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{\left(-0.5 \cdot y + x \cdot \left(y - 1\right)\right)} + 0.918938533204673 \]
4. Step-by-step derivation

   1. sub-neg 100.0%

      \[\leadsto \left(-0.5 \cdot y + x \cdot \color{blue}{\left(y + \left(-1\right)\right)}\right) + 0.918938533204673 \]

   2. metadata-eval 100.0%

      \[\leadsto \left(-0.5 \cdot y + x \cdot \left(y + \color{blue}{-1}\right)\right) + 0.918938533204673 \]

   3. *-commutative 100.0%

      \[\leadsto \left(\color{blue}{y \cdot -0.5} + x \cdot \left(y + -1\right)\right) + 0.918938533204673 \]

   4. distribute-rgt-in 100.0%

      \[\leadsto \left(y \cdot -0.5 + \color{blue}{\left(y \cdot x + -1 \cdot x\right)}\right) + 0.918938533204673 \]

   5. associate-+r+ 100.0%

      \[\leadsto \color{blue}{\left(\left(y \cdot -0.5 + y \cdot x\right) + -1 \cdot x\right)} + 0.918938533204673 \]

   6. *-commutative 100.0%

      \[\leadsto \left(\left(y \cdot -0.5 + \color{blue}{x \cdot y}\right) + -1 \cdot x\right) + 0.918938533204673 \]

   7. mul-1-neg 100.0%

      \[\leadsto \left(\left(y \cdot -0.5 + x \cdot y\right) + \color{blue}{\left(-x\right)}\right) + 0.918938533204673 \]

   8. unsub-neg 100.0%

      \[\leadsto \color{blue}{\left(\left(y \cdot -0.5 + x \cdot y\right) - x\right)} + 0.918938533204673 \]

   9. *-commutative 100.0%

      \[\leadsto \left(\left(y \cdot -0.5 + \color{blue}{y \cdot x}\right) - x\right) + 0.918938533204673 \]

   10. distribute-lft-out 100.0%

       \[\leadsto \left(\color{blue}{y \cdot \left(-0.5 + x\right)} - x\right) + 0.918938533204673 \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\left(y \cdot \left(-0.5 + x\right) - x\right)} + 0.918938533204673 \]

6. Final simplification 100.0%

   \[\leadsto \left(y \cdot \left(-0.5 + x\right) - x\right) + 0.918938533204673 \]
7. Add Preprocessing

Alternative 2: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-10} \lor \neg \left(x \leq 7.5 \cdot 10^{-12}\right):\\ \;\;\;\;0.918938533204673 + x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 + y \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.4e-10) (not (<= x 7.5e-12)))
   (+ 0.918938533204673 (* x (+ y -1.0)))
   (+ 0.918938533204673 (* y -0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.4e-10) || !(x <= 7.5e-12)) {
		tmp = 0.918938533204673 + (x * (y + -1.0));
	} else {
		tmp = 0.918938533204673 + (y * -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-3.4d-10)) .or. (.not. (x <= 7.5d-12))) then
        tmp = 0.918938533204673d0 + (x * (y + (-1.0d0)))
    else
        tmp = 0.918938533204673d0 + (y * (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -3.4e-10) || !(x <= 7.5e-12)) {
		tmp = 0.918938533204673 + (x * (y + -1.0));
	} else {
		tmp = 0.918938533204673 + (y * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.4e-10) or not (x <= 7.5e-12):
		tmp = 0.918938533204673 + (x * (y + -1.0))
	else:
		tmp = 0.918938533204673 + (y * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.4e-10) || !(x <= 7.5e-12))
		tmp = Float64(0.918938533204673 + Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(0.918938533204673 + Float64(y * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.4e-10) || ~((x <= 7.5e-12)))
		tmp = 0.918938533204673 + (x * (y + -1.0));
	else
		tmp = 0.918938533204673 + (y * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.4e-10], N[Not[LessEqual[x, 7.5e-12]], $MachinePrecision]], N[(0.918938533204673 + N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.40000000000000015e-10 or 7.5e-12 < x

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} + 0.918938533204673 \]

   if -3.40000000000000015e-10 < x < 7.5e-12

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{-0.5 \cdot y} + 0.918938533204673 \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-10} \lor \neg \left(x \leq 7.5 \cdot 10^{-12}\right):\\ \;\;\;\;0.918938533204673 + x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 + y \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-5} \lor \neg \left(y \leq 5.5 \cdot 10^{-8}\right):\\ \;\;\;\;0.918938533204673 + y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 + x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.02e-5) (not (<= y 5.5e-8)))
   (+ 0.918938533204673 (* y (- x 0.5)))
   (+ 0.918938533204673 (* x (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.02e-5) || !(y <= 5.5e-8)) {
		tmp = 0.918938533204673 + (y * (x - 0.5));
	} else {
		tmp = 0.918938533204673 + (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.02d-5)) .or. (.not. (y <= 5.5d-8))) then
        tmp = 0.918938533204673d0 + (y * (x - 0.5d0))
    else
        tmp = 0.918938533204673d0 + (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.02e-5) || !(y <= 5.5e-8)) {
		tmp = 0.918938533204673 + (y * (x - 0.5));
	} else {
		tmp = 0.918938533204673 + (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.02e-5) or not (y <= 5.5e-8):
		tmp = 0.918938533204673 + (y * (x - 0.5))
	else:
		tmp = 0.918938533204673 + (x * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.02e-5) || !(y <= 5.5e-8))
		tmp = Float64(0.918938533204673 + Float64(y * Float64(x - 0.5)));
	else
		tmp = Float64(0.918938533204673 + Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.02e-5) || ~((y <= 5.5e-8)))
		tmp = 0.918938533204673 + (y * (x - 0.5));
	else
		tmp = 0.918938533204673 + (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.02e-5], N[Not[LessEqual[y, 5.5e-8]], $MachinePrecision]], N[(0.918938533204673 + N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 + N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0200000000000001e-5 or 5.5000000000000003e-8 < y

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.6%

      \[\leadsto \color{blue}{y \cdot \left(x - 0.5\right)} + 0.918938533204673 \]

   if -1.0200000000000001e-5 < y < 5.5000000000000003e-8

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.7%

      \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} + 0.918938533204673 \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-5} \lor \neg \left(y \leq 5.5 \cdot 10^{-8}\right):\\ \;\;\;\;0.918938533204673 + y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 + x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -14500000000 \lor \neg \left(y \leq 0.025\right):\\ \;\;\;\;0.918938533204673 + y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 + \left(y \cdot -0.5 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -14500000000.0) (not (<= y 0.025)))
   (+ 0.918938533204673 (* y (- x 0.5)))
   (+ 0.918938533204673 (- (* y -0.5) x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -14500000000.0) || !(y <= 0.025)) {
		tmp = 0.918938533204673 + (y * (x - 0.5));
	} else {
		tmp = 0.918938533204673 + ((y * -0.5) - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-14500000000.0d0)) .or. (.not. (y <= 0.025d0))) then
        tmp = 0.918938533204673d0 + (y * (x - 0.5d0))
    else
        tmp = 0.918938533204673d0 + ((y * (-0.5d0)) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -14500000000.0) || !(y <= 0.025)) {
		tmp = 0.918938533204673 + (y * (x - 0.5));
	} else {
		tmp = 0.918938533204673 + ((y * -0.5) - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -14500000000.0) or not (y <= 0.025):
		tmp = 0.918938533204673 + (y * (x - 0.5))
	else:
		tmp = 0.918938533204673 + ((y * -0.5) - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -14500000000.0) || !(y <= 0.025))
		tmp = Float64(0.918938533204673 + Float64(y * Float64(x - 0.5)));
	else
		tmp = Float64(0.918938533204673 + Float64(Float64(y * -0.5) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -14500000000.0) || ~((y <= 0.025)))
		tmp = 0.918938533204673 + (y * (x - 0.5));
	else
		tmp = 0.918938533204673 + ((y * -0.5) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -14500000000.0], N[Not[LessEqual[y, 0.025]], $MachinePrecision]], N[(0.918938533204673 + N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 + N[(N[(y * -0.5), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e10 or 0.025000000000000001 < y

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.8%

      \[\leadsto \color{blue}{y \cdot \left(x - 0.5\right)} + 0.918938533204673 \]

   if -1.45e10 < y < 0.025000000000000001

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\left(-0.5 \cdot y + x \cdot \left(y - 1\right)\right)} + 0.918938533204673 \]
   4. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \left(-0.5 \cdot y + x \cdot \color{blue}{\left(y + \left(-1\right)\right)}\right) + 0.918938533204673 \]

      2. metadata-eval 100.0%

         \[\leadsto \left(-0.5 \cdot y + x \cdot \left(y + \color{blue}{-1}\right)\right) + 0.918938533204673 \]

      3. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{y \cdot -0.5} + x \cdot \left(y + -1\right)\right) + 0.918938533204673 \]

      4. distribute-rgt-in 100.0%

         \[\leadsto \left(y \cdot -0.5 + \color{blue}{\left(y \cdot x + -1 \cdot x\right)}\right) + 0.918938533204673 \]

      5. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(y \cdot -0.5 + y \cdot x\right) + -1 \cdot x\right)} + 0.918938533204673 \]

      6. *-commutative 100.0%

         \[\leadsto \left(\left(y \cdot -0.5 + \color{blue}{x \cdot y}\right) + -1 \cdot x\right) + 0.918938533204673 \]

      7. mul-1-neg 100.0%

         \[\leadsto \left(\left(y \cdot -0.5 + x \cdot y\right) + \color{blue}{\left(-x\right)}\right) + 0.918938533204673 \]

      8. unsub-neg 100.0%

         \[\leadsto \color{blue}{\left(\left(y \cdot -0.5 + x \cdot y\right) - x\right)} + 0.918938533204673 \]

      9. *-commutative 100.0%

         \[\leadsto \left(\left(y \cdot -0.5 + \color{blue}{y \cdot x}\right) - x\right) + 0.918938533204673 \]

      10. distribute-lft-out 100.0%

          \[\leadsto \left(\color{blue}{y \cdot \left(-0.5 + x\right)} - x\right) + 0.918938533204673 \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y \cdot \left(-0.5 + x\right) - x\right)} + 0.918938533204673 \]

   6. Taylor expanded in x around 0 99.7%

      \[\leadsto \left(\color{blue}{-0.5 \cdot y} - x\right) + 0.918938533204673 \]
   7. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \left(\color{blue}{y \cdot -0.5} - x\right) + 0.918938533204673 \]

   8. Simplified 99.7%

      \[\leadsto \left(\color{blue}{y \cdot -0.5} - x\right) + 0.918938533204673 \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -14500000000 \lor \neg \left(y \leq 0.025\right):\\ \;\;\;\;0.918938533204673 + y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 + \left(y \cdot -0.5 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-5} \lor \neg \left(y \leq 1.4 \cdot 10^{-8}\right):\\ \;\;\;\;0.918938533204673 + y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.45e-5) (not (<= y 1.4e-8)))
   (+ 0.918938533204673 (* y -0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.45e-5) || !(y <= 1.4e-8)) {
		tmp = 0.918938533204673 + (y * -0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.45d-5)) .or. (.not. (y <= 1.4d-8))) then
        tmp = 0.918938533204673d0 + (y * (-0.5d0))
    else
        tmp = 0.918938533204673d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.45e-5) || !(y <= 1.4e-8)) {
		tmp = 0.918938533204673 + (y * -0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.45e-5) or not (y <= 1.4e-8):
		tmp = 0.918938533204673 + (y * -0.5)
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.45e-5) || !(y <= 1.4e-8))
		tmp = Float64(0.918938533204673 + Float64(y * -0.5));
	else
		tmp = Float64(0.918938533204673 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.45e-5) || ~((y <= 1.4e-8)))
		tmp = 0.918938533204673 + (y * -0.5);
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.45e-5], N[Not[LessEqual[y, 1.4e-8]], $MachinePrecision]], N[(0.918938533204673 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e-5 or 1.4e-8 < y

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 61.7%

      \[\leadsto \color{blue}{-0.5 \cdot y} + 0.918938533204673 \]

   if -1.45e-5 < y < 1.4e-8

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.7%

      \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} + 0.918938533204673 \]

   4. Taylor expanded in y around 0 99.4%

      \[\leadsto \color{blue}{0.918938533204673 + -1 \cdot x} \]
   5. Step-by-step derivation

      1. neg-mul-1 99.4%

         \[\leadsto 0.918938533204673 + \color{blue}{\left(-x\right)} \]

      2. unsub-neg 99.4%

         \[\leadsto \color{blue}{0.918938533204673 - x} \]

   6. Simplified 99.4%

      \[\leadsto \color{blue}{0.918938533204673 - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-5} \lor \neg \left(y \leq 1.4 \cdot 10^{-8}\right):\\ \;\;\;\;0.918938533204673 + y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ 0.918938533204673 - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 0.918938533204673 x))

C

double code(double x, double y) {
	return 0.918938533204673 - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.918938533204673d0 - x
end function

Java

public static double code(double x, double y) {
	return 0.918938533204673 - x;
}

Python

def code(x, y):
	return 0.918938533204673 - x

Julia

function code(x, y)
	return Float64(0.918938533204673 - x)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.918938533204673 - x;
end

Wolfram

code[x_, y_] := N[(0.918938533204673 - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
2. Add Preprocessing

3. Taylor expanded in x around inf 70.7%

   \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} + 0.918938533204673 \]

4. Taylor expanded in y around 0 52.0%

   \[\leadsto \color{blue}{0.918938533204673 + -1 \cdot x} \]
5. Step-by-step derivation

   1. neg-mul-1 52.0%

      \[\leadsto 0.918938533204673 + \color{blue}{\left(-x\right)} \]

   2. unsub-neg 52.0%

      \[\leadsto \color{blue}{0.918938533204673 - x} \]

6. Simplified 52.0%

   \[\leadsto \color{blue}{0.918938533204673 - x} \]

7. Final simplification 52.0%

   \[\leadsto 0.918938533204673 - x \]
8. Add Preprocessing

Alternative 7: 25.7% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 0.918938533204673 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.918938533204673)

C

double code(double x, double y) {
	return 0.918938533204673;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.918938533204673d0
end function

Java

public static double code(double x, double y) {
	return 0.918938533204673;
}

Python

def code(x, y):
	return 0.918938533204673

Julia

function code(x, y)
	return 0.918938533204673
end

MATLAB

function tmp = code(x, y)
	tmp = 0.918938533204673;
end

Wolfram

code[x_, y_] := 0.918938533204673

Derivation

1. Initial program 100.0%

   \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
2. Add Preprocessing

3. Taylor expanded in x around inf 70.7%

   \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} + 0.918938533204673 \]

4. Taylor expanded in x around 0 23.3%

   \[\leadsto \color{blue}{0.918938533204673} \]

5. Final simplification 23.3%

   \[\leadsto 0.918938533204673 \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))