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

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 5

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
2. Step-by-step derivation

   1. associate-+l- 100.0%

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

   2. sub-neg 100.0%

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

   3. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around 0 100.0%

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

   1. sub-neg 100.0%

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

   2. sub-neg 100.0%

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

   3. metadata-eval 100.0%

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

   4. associate-+r+ 100.0%

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

   5. distribute-rgt-in 100.0%

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

   6. neg-mul-1 100.0%

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

   7. *-commutative 100.0%

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

   8. +-commutative 100.0%

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

   9. associate-+l+ 100.0%

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

   10. sub-neg 100.0%

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

   11. distribute-rgt-out-- 100.0%

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

   12. +-commutative 100.0%

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

   13. unsub-neg 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 2: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+260}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{+234}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+48}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+14}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.1:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+53}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.4e+260)
   (* y -0.5)
   (if (<= y -2.95e+234)
     (* y x)
     (if (<= y -7.6e+48)
       (* y -0.5)
       (if (<= y -2.45e+14)
         (* y x)
         (if (<= y 1.1)
           (- 0.918938533204673 x)
           (if (<= y 1.08e+53) (* y x) (* y -0.5))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.4e+260) {
		tmp = y * -0.5;
	} else if (y <= -2.95e+234) {
		tmp = y * x;
	} else if (y <= -7.6e+48) {
		tmp = y * -0.5;
	} else if (y <= -2.45e+14) {
		tmp = y * x;
	} else if (y <= 1.1) {
		tmp = 0.918938533204673 - x;
	} else if (y <= 1.08e+53) {
		tmp = y * x;
	} else {
		tmp = 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 (y <= (-3.4d+260)) then
        tmp = y * (-0.5d0)
    else if (y <= (-2.95d+234)) then
        tmp = y * x
    else if (y <= (-7.6d+48)) then
        tmp = y * (-0.5d0)
    else if (y <= (-2.45d+14)) then
        tmp = y * x
    else if (y <= 1.1d0) then
        tmp = 0.918938533204673d0 - x
    else if (y <= 1.08d+53) then
        tmp = y * x
    else
        tmp = y * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.4e+260) {
		tmp = y * -0.5;
	} else if (y <= -2.95e+234) {
		tmp = y * x;
	} else if (y <= -7.6e+48) {
		tmp = y * -0.5;
	} else if (y <= -2.45e+14) {
		tmp = y * x;
	} else if (y <= 1.1) {
		tmp = 0.918938533204673 - x;
	} else if (y <= 1.08e+53) {
		tmp = y * x;
	} else {
		tmp = y * -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.4e+260:
		tmp = y * -0.5
	elif y <= -2.95e+234:
		tmp = y * x
	elif y <= -7.6e+48:
		tmp = y * -0.5
	elif y <= -2.45e+14:
		tmp = y * x
	elif y <= 1.1:
		tmp = 0.918938533204673 - x
	elif y <= 1.08e+53:
		tmp = y * x
	else:
		tmp = y * -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.4e+260)
		tmp = Float64(y * -0.5);
	elseif (y <= -2.95e+234)
		tmp = Float64(y * x);
	elseif (y <= -7.6e+48)
		tmp = Float64(y * -0.5);
	elseif (y <= -2.45e+14)
		tmp = Float64(y * x);
	elseif (y <= 1.1)
		tmp = Float64(0.918938533204673 - x);
	elseif (y <= 1.08e+53)
		tmp = Float64(y * x);
	else
		tmp = Float64(y * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.4e+260)
		tmp = y * -0.5;
	elseif (y <= -2.95e+234)
		tmp = y * x;
	elseif (y <= -7.6e+48)
		tmp = y * -0.5;
	elseif (y <= -2.45e+14)
		tmp = y * x;
	elseif (y <= 1.1)
		tmp = 0.918938533204673 - x;
	elseif (y <= 1.08e+53)
		tmp = y * x;
	else
		tmp = y * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.4e+260], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -2.95e+234], N[(y * x), $MachinePrecision], If[LessEqual[y, -7.6e+48], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -2.45e+14], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.1], N[(0.918938533204673 - x), $MachinePrecision], If[LessEqual[y, 1.08e+53], N[(y * x), $MachinePrecision], N[(y * -0.5), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3999999999999998e260 or -2.95e234 < y < -7.60000000000000001e48 or 1.08e53 < y

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   6. Taylor expanded in x around 0 66.7%

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

   if -3.3999999999999998e260 < y < -2.95e234 or -7.60000000000000001e48 < y < -2.45e14 or 1.1000000000000001 < y < 1.08e53

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 97.5%

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

   6. Taylor expanded in x around inf 82.0%

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

      1. *-commutative 82.0%

         \[\leadsto \color{blue}{y \cdot x} \]

   8. Simplified 82.0%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -2.45e14 < y < 1.1000000000000001

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 95.9%

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

      1. neg-mul-1 95.9%

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

      2. unsub-neg 95.9%

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

   7. Simplified 95.9%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+260}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{+234}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+48}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+14}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.1:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+53}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \lor \neg \left(y \leq 1.3\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4) (not (<= y 1.3)))
   (* y (- x 0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4) || !(y <= 1.3)) {
		tmp = y * (x - 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 <= (-1.4d0)) .or. (.not. (y <= 1.3d0))) then
        tmp = y * (x - 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 <= -1.4) || !(y <= 1.3)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.4) or not (y <= 1.3):
		tmp = y * (x - 0.5)
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.4) || !(y <= 1.3))
		tmp = Float64(y * Float64(x - 0.5));
	else
		tmp = Float64(0.918938533204673 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.4) || ~((y <= 1.3)))
		tmp = y * (x - 0.5);
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.4], N[Not[LessEqual[y, 1.3]], $MachinePrecision]], N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3999999999999999 or 1.30000000000000004 < y

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.2%

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

   if -1.3999999999999999 < y < 1.30000000000000004

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.3%

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

      1. neg-mul-1 97.3%

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

      2. unsub-neg 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \lor \neg \left(y \leq 1.3\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.5 \lor \neg \left(x \leq 9.4 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.5) (not (<= x 9.4e-7))) (* y x) (* y -0.5)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.5) || !(x <= 9.4e-7)) {
		tmp = y * x;
	} else {
		tmp = 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 <= (-0.5d0)) .or. (.not. (x <= 9.4d-7))) then
        tmp = y * x
    else
        tmp = y * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.5) || !(x <= 9.4e-7)) {
		tmp = y * x;
	} else {
		tmp = y * -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.5) or not (x <= 9.4e-7):
		tmp = y * x
	else:
		tmp = y * -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.5) || !(x <= 9.4e-7))
		tmp = Float64(y * x);
	else
		tmp = Float64(y * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.5) || ~((x <= 9.4e-7)))
		tmp = y * x;
	else
		tmp = y * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.5], N[Not[LessEqual[x, 9.4e-7]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(y * -0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.5 or 9.4e-7 < x

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 48.5%

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

   6. Taylor expanded in x around inf 47.9%

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

      1. *-commutative 47.9%

         \[\leadsto \color{blue}{y \cdot x} \]

   8. Simplified 47.9%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -0.5 < x < 9.4e-7

   1. Initial program 100.0%

      \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 58.5%

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

   6. Taylor expanded in x around 0 58.4%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.5 \lor \neg \left(x \leq 9.4 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 26.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ y \cdot -0.5 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
2. Step-by-step derivation

   1. associate-+l- 100.0%

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

   2. sub-neg 100.0%

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

   3. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around inf 53.7%

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

6. Taylor expanded in x around 0 31.5%

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

7. Final simplification 31.5%

   \[\leadsto y \cdot -0.5 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(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))