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

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

Alternatives: 11

Speedup: 1.0×

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. distribute-rgt-in 100.0%

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

   2. *-commutative 100.0%

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

   3. mul-1-neg 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) - y \cdot 0.5\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+203}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.85:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.8:\\ \;\;\;\;\left(--0.918938533204673\right) - x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+190} \lor \neg \left(y \leq 5.6 \cdot 10^{+274}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (- x) (* y 0.5))))
   (if (<= y -1.3e+203)
     (* x y)
     (if (<= y -1.85)
       t_0
       (if (<= y 1.8)
         (- (- -0.918938533204673) x)
         (if (or (<= y 2.3e+190) (not (<= y 5.6e+274))) t_0 (* x y)))))))

C

double code(double x, double y) {
	double t_0 = -x - (y * 0.5);
	double tmp;
	if (y <= -1.3e+203) {
		tmp = x * y;
	} else if (y <= -1.85) {
		tmp = t_0;
	} else if (y <= 1.8) {
		tmp = -(-0.918938533204673) - x;
	} else if ((y <= 2.3e+190) || !(y <= 5.6e+274)) {
		tmp = t_0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -x - (y * 0.5d0)
    if (y <= (-1.3d+203)) then
        tmp = x * y
    else if (y <= (-1.85d0)) then
        tmp = t_0
    else if (y <= 1.8d0) then
        tmp = -(-0.918938533204673d0) - x
    else if ((y <= 2.3d+190) .or. (.not. (y <= 5.6d+274))) then
        tmp = t_0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -x - (y * 0.5);
	double tmp;
	if (y <= -1.3e+203) {
		tmp = x * y;
	} else if (y <= -1.85) {
		tmp = t_0;
	} else if (y <= 1.8) {
		tmp = -(-0.918938533204673) - x;
	} else if ((y <= 2.3e+190) || !(y <= 5.6e+274)) {
		tmp = t_0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -x - (y * 0.5)
	tmp = 0
	if y <= -1.3e+203:
		tmp = x * y
	elif y <= -1.85:
		tmp = t_0
	elif y <= 1.8:
		tmp = -(-0.918938533204673) - x
	elif (y <= 2.3e+190) or not (y <= 5.6e+274):
		tmp = t_0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(-x) - Float64(y * 0.5))
	tmp = 0.0
	if (y <= -1.3e+203)
		tmp = Float64(x * y);
	elseif (y <= -1.85)
		tmp = t_0;
	elseif (y <= 1.8)
		tmp = Float64(Float64(-(-0.918938533204673)) - x);
	elseif ((y <= 2.3e+190) || !(y <= 5.6e+274))
		tmp = t_0;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -x - (y * 0.5);
	tmp = 0.0;
	if (y <= -1.3e+203)
		tmp = x * y;
	elseif (y <= -1.85)
		tmp = t_0;
	elseif (y <= 1.8)
		tmp = -(-0.918938533204673) - x;
	elseif ((y <= 2.3e+190) || ~((y <= 5.6e+274)))
		tmp = t_0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[((-x) - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+203], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.85], t$95$0, If[LessEqual[y, 1.8], N[((--0.918938533204673) - x), $MachinePrecision], If[Or[LessEqual[y, 2.3e+190], N[Not[LessEqual[y, 5.6e+274]], $MachinePrecision]], t$95$0, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e203 or 2.3e190 < y < 5.60000000000000017e274

   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 70.0%

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

   6. Taylor expanded in y around inf 70.0%

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

   7. Taylor expanded in x around inf 70.0%

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

   if -1.2999999999999999e203 < y < -1.8500000000000001 or 1.80000000000000004 < y < 2.3e190 or 5.60000000000000017e274 < 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 0 57.7%

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

      1. neg-mul-1 57.7%

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

   7. Simplified 57.7%

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

   8. Taylor expanded in y around inf 56.7%

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

      1. *-commutative 56.7%

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

   10. Simplified 56.7%

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

   if -1.8500000000000001 < y < 1.80000000000000004

   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 99.2%

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

      1. neg-mul-1 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in y around 0 97.3%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+203}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.85:\\ \;\;\;\;\left(-x\right) - y \cdot 0.5\\ \mathbf{elif}\;y \leq 1.8:\\ \;\;\;\;\left(--0.918938533204673\right) - x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+190} \lor \neg \left(y \leq 5.6 \cdot 10^{+274}\right):\\ \;\;\;\;\left(-x\right) - y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \lor \neg \left(y \leq 1.8\right):\\ \;\;\;\;x \cdot y - y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\left(--0.918938533204673\right) - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.65) (not (<= y 1.8)))
   (- (* x y) (* y 0.5))
   (- (- -0.918938533204673) x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.65) || !(y <= 1.8)) {
		tmp = (x * y) - (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 <= (-1.65d0)) .or. (.not. (y <= 1.8d0))) then
        tmp = (x * y) - (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 <= -1.65) || !(y <= 1.8)) {
		tmp = (x * y) - (y * 0.5);
	} else {
		tmp = -(-0.918938533204673) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.65) or not (y <= 1.8):
		tmp = (x * y) - (y * 0.5)
	else:
		tmp = -(-0.918938533204673) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.65) || !(y <= 1.8))
		tmp = Float64(Float64(x * y) - Float64(y * 0.5));
	else
		tmp = Float64(Float64(-(-0.918938533204673)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.65) || ~((y <= 1.8)))
		tmp = (x * y) - (y * 0.5);
	else
		tmp = -(-0.918938533204673) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.65], N[Not[LessEqual[y, 1.8]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(y * 0.5), $MachinePrecision]), $MachinePrecision], N[((--0.918938533204673) - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6499999999999999 or 1.80000000000000004 < 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%

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

      1. *-commutative 51.1%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in y around inf 96.8%

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

   if -1.6499999999999999 < y < 1.80000000000000004

   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 99.2%

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

      1. neg-mul-1 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in y around 0 97.3%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \lor \neg \left(y \leq 1.8\right):\\ \;\;\;\;x \cdot y - y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\left(--0.918938533204673\right) - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -850000000000 \lor \neg \left(y \leq 4000000\right):\\ \;\;\;\;x \cdot y - y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right) - -0.918938533204673\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -850000000000.0) (not (<= y 4000000.0)))
   (- (* x y) (* y 0.5))
   (- (* x (+ y -1.0)) -0.918938533204673)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -850000000000.0) || !(y <= 4000000.0)) {
		tmp = (x * y) - (y * 0.5);
	} else {
		tmp = (x * (y + -1.0)) - -0.918938533204673;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-850000000000.0d0)) .or. (.not. (y <= 4000000.0d0))) then
        tmp = (x * y) - (y * 0.5d0)
    else
        tmp = (x * (y + (-1.0d0))) - (-0.918938533204673d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -850000000000.0) || !(y <= 4000000.0)) {
		tmp = (x * y) - (y * 0.5);
	} else {
		tmp = (x * (y + -1.0)) - -0.918938533204673;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -850000000000.0) or not (y <= 4000000.0):
		tmp = (x * y) - (y * 0.5)
	else:
		tmp = (x * (y + -1.0)) - -0.918938533204673
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -850000000000.0) || !(y <= 4000000.0))
		tmp = Float64(Float64(x * y) - Float64(y * 0.5));
	else
		tmp = Float64(Float64(x * Float64(y + -1.0)) - -0.918938533204673);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -850000000000.0) || ~((y <= 4000000.0)))
		tmp = (x * y) - (y * 0.5);
	else
		tmp = (x * (y + -1.0)) - -0.918938533204673;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -850000000000.0], N[Not[LessEqual[y, 4000000.0]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(y * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] - -0.918938533204673), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5e11 or 4e6 < 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 99.8%

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

      1. *-commutative 53.0%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 99.8%

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

   if -8.5e11 < y < 4e6

   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 97.4%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -850000000000 \lor \neg \left(y \leq 4000000\right):\\ \;\;\;\;x \cdot y - y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right) - -0.918938533204673\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+18} \lor \neg \left(x \leq 8 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot \left(y + -1\right) - -0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 - y \cdot 0.5\right) - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.08e+18) (not (<= x 8e-41)))
   (- (* x (+ y -1.0)) -0.918938533204673)
   (- (- 0.918938533204673 (* y 0.5)) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.08e+18) || !(x <= 8e-41)) {
		tmp = (x * (y + -1.0)) - -0.918938533204673;
	} 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 ((x <= (-1.08d+18)) .or. (.not. (x <= 8d-41))) then
        tmp = (x * (y + (-1.0d0))) - (-0.918938533204673d0)
    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 ((x <= -1.08e+18) || !(x <= 8e-41)) {
		tmp = (x * (y + -1.0)) - -0.918938533204673;
	} else {
		tmp = (0.918938533204673 - (y * 0.5)) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.08e+18) or not (x <= 8e-41):
		tmp = (x * (y + -1.0)) - -0.918938533204673
	else:
		tmp = (0.918938533204673 - (y * 0.5)) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.08e+18) || !(x <= 8e-41))
		tmp = Float64(Float64(x * Float64(y + -1.0)) - -0.918938533204673);
	else
		tmp = Float64(Float64(0.918938533204673 - Float64(y * 0.5)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.08e+18) || ~((x <= 8e-41)))
		tmp = (x * (y + -1.0)) - -0.918938533204673;
	else
		tmp = (0.918938533204673 - (y * 0.5)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.08e+18], N[Not[LessEqual[x, 8e-41]], $MachinePrecision]], N[(N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] - -0.918938533204673), $MachinePrecision], N[(N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.08e18 or 8.00000000000000005e-41 < 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 0 100.0%

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

   if -1.08e18 < x < 8.00000000000000005e-41

   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 99.5%

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

      1. neg-mul-1 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+18} \lor \neg \left(x \leq 8 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot \left(y + -1\right) - -0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 - y \cdot 0.5\right) - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+18} \lor \neg \left(x \leq 8 \cdot 10^{-41}\right):\\ \;\;\;\;\left(x \cdot y - x\right) - -0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 - y \cdot 0.5\right) - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.08e+18) (not (<= x 8e-41)))
   (- (- (* x y) x) -0.918938533204673)
   (- (- 0.918938533204673 (* y 0.5)) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.08e+18) || !(x <= 8e-41)) {
		tmp = ((x * y) - x) - -0.918938533204673;
	} 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 ((x <= (-1.08d+18)) .or. (.not. (x <= 8d-41))) then
        tmp = ((x * y) - x) - (-0.918938533204673d0)
    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 ((x <= -1.08e+18) || !(x <= 8e-41)) {
		tmp = ((x * y) - x) - -0.918938533204673;
	} else {
		tmp = (0.918938533204673 - (y * 0.5)) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.08e+18) or not (x <= 8e-41):
		tmp = ((x * y) - x) - -0.918938533204673
	else:
		tmp = (0.918938533204673 - (y * 0.5)) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.08e+18) || !(x <= 8e-41))
		tmp = Float64(Float64(Float64(x * y) - x) - -0.918938533204673);
	else
		tmp = Float64(Float64(0.918938533204673 - Float64(y * 0.5)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.08e+18) || ~((x <= 8e-41)))
		tmp = ((x * y) - x) - -0.918938533204673;
	else
		tmp = (0.918938533204673 - (y * 0.5)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.08e+18], N[Not[LessEqual[x, 8e-41]], $MachinePrecision]], N[(N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision] - -0.918938533204673), $MachinePrecision], N[(N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.08e18 or 8.00000000000000005e-41 < 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. Step-by-step derivation

      1. distribute-rgt-in 100.0%

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

      2. *-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

   if -1.08e18 < x < 8.00000000000000005e-41

   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 99.5%

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

      1. neg-mul-1 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+18} \lor \neg \left(x \leq 8 \cdot 10^{-41}\right):\\ \;\;\;\;\left(x \cdot y - x\right) - -0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 - y \cdot 0.5\right) - x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.92 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(--0.918938533204673\right) - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.92) (not (<= y 1.0))) (* x y) (- (- -0.918938533204673) x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.92) || !(y <= 1.0)) {
		tmp = x * y;
	} 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 <= (-1.92d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * y
    else
        tmp = -(-0.918938533204673d0) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.92) || !(y <= 1.0)) {
		tmp = x * y;
	} else {
		tmp = -(-0.918938533204673) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.92) or not (y <= 1.0):
		tmp = x * y
	else:
		tmp = -(-0.918938533204673) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.92) || !(y <= 1.0))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(-(-0.918938533204673)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.92) || ~((y <= 1.0)))
		tmp = x * y;
	else
		tmp = -(-0.918938533204673) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.92], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[((--0.918938533204673) - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9199999999999999 or 1 < 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 0 51.8%

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

   6. Taylor expanded in y around inf 49.4%

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

   7. Taylor expanded in x around inf 49.1%

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

   if -1.9199999999999999 < y < 1

   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 99.2%

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

      1. neg-mul-1 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in y around 0 97.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.92 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(--0.918938533204673\right) - x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65:\\ \;\;\;\;x \cdot y - -0.918938533204673\\ \mathbf{elif}\;y \leq 1.6:\\ \;\;\;\;\left(--0.918938533204673\right) - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.65)
   (- (* x y) -0.918938533204673)
   (if (<= y 1.6) (- (- -0.918938533204673) x) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.65) {
		tmp = (x * y) - -0.918938533204673;
	} else if (y <= 1.6) {
		tmp = -(-0.918938533204673) - x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.65d0)) then
        tmp = (x * y) - (-0.918938533204673d0)
    else if (y <= 1.6d0) then
        tmp = -(-0.918938533204673d0) - x
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.65) {
		tmp = (x * y) - -0.918938533204673;
	} else if (y <= 1.6) {
		tmp = -(-0.918938533204673) - x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.65:
		tmp = (x * y) - -0.918938533204673
	elif y <= 1.6:
		tmp = -(-0.918938533204673) - x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.65)
		tmp = Float64(Float64(x * y) - -0.918938533204673);
	elseif (y <= 1.6)
		tmp = Float64(Float64(-(-0.918938533204673)) - x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.65)
		tmp = (x * y) - -0.918938533204673;
	elseif (y <= 1.6)
		tmp = -(-0.918938533204673) - x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.65], N[(N[(x * y), $MachinePrecision] - -0.918938533204673), $MachinePrecision], If[LessEqual[y, 1.6], N[((--0.918938533204673) - x), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999

   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 55.3%

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

   6. Taylor expanded in y around inf 52.1%

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

   if -1.6499999999999999 < y < 1.6000000000000001

   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 99.2%

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

      1. neg-mul-1 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in y around 0 97.3%

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

   if 1.6000000000000001 < 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 0 48.5%

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

   6. Taylor expanded in y around inf 46.7%

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

   7. Taylor expanded in x around inf 47.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65:\\ \;\;\;\;x \cdot y - -0.918938533204673\\ \mathbf{elif}\;y \leq 1.6:\\ \;\;\;\;\left(--0.918938533204673\right) - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+18} \lor \neg \left(x \leq 0.92\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.08e+18) (not (<= x 0.92))) (* x y) 0.918938533204673))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.08e+18) || !(x <= 0.92)) {
		tmp = x * y;
	} else {
		tmp = 0.918938533204673;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.08d+18)) .or. (.not. (x <= 0.92d0))) then
        tmp = x * y
    else
        tmp = 0.918938533204673d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.08e+18) || !(x <= 0.92)) {
		tmp = x * y;
	} else {
		tmp = 0.918938533204673;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.08e+18) or not (x <= 0.92):
		tmp = x * y
	else:
		tmp = 0.918938533204673
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.08e+18) || !(x <= 0.92))
		tmp = Float64(x * y);
	else
		tmp = 0.918938533204673;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.08e+18) || ~((x <= 0.92)))
		tmp = x * y;
	else
		tmp = 0.918938533204673;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.08e+18], N[Not[LessEqual[x, 0.92]], $MachinePrecision]], N[(x * y), $MachinePrecision], 0.918938533204673]

Derivation

1. Split input into 2 regimes

2. if x < -1.08e18 or 0.92000000000000004 < 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 0 100.0%

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

   6. Taylor expanded in y around inf 48.8%

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

   7. Taylor expanded in x around inf 48.9%

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

   if -1.08e18 < x < 0.92000000000000004

   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 55.3%

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

   6. Taylor expanded in y around inf 51.2%

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

   7. Taylor expanded in x around 0 50.9%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+18} \lor \neg \left(x \leq 0.92\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(0.918938533204673 + N[(N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $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. Final simplification 100.0%

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

Alternative 11: 26.4% 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. 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 76.4%

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

6. Taylor expanded in y around inf 50.1%

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

7. Taylor expanded in x around 0 28.0%

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

8. Final simplification 28.0%

   \[\leadsto 0.918938533204673 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(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))