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

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

Alternatives: 9

Speedup: 1.2×

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(N[(y * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision] - x), $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. distribute-rgt-in 100.0%

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

   4. metadata-eval 100.0%

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

   5. neg-mul-1 100.0%

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

   6. unsub-neg 100.0%

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

   7. associate--l- 100.0%

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

   8. +-commutative 100.0%

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

   9. associate--r+ 100.0%

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

   10. associate--r- 100.0%

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

   11. distribute-lft-out-- 100.0%

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

   12. sub-neg 100.0%

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

   13. +-commutative 100.0%

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

   14. fma-def 100.0%

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

   15. +-commutative 100.0%

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

   16. metadata-eval 100.0%

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

3. Simplified 100.0%

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

   1. fma-udef 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

   \[\leadsto \left(y \cdot \left(x + -0.5\right) + 0.918938533204673\right) - x \]

Alternative 2: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-88}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-193}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-267}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-237}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-121}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   (* y x)
   (if (<= y -1.8e-88)
     (- x)
     (if (<= y -8.4e-193)
       0.918938533204673
       (if (<= y -4.2e-267)
         (- x)
         (if (<= y 9.6e-237)
           0.918938533204673
           (if (<= y 6.6e-121)
             (- x)
             (if (<= y 1.0) 0.918938533204673 (* y x)))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= -1.8e-88) {
		tmp = -x;
	} else if (y <= -8.4e-193) {
		tmp = 0.918938533204673;
	} else if (y <= -4.2e-267) {
		tmp = -x;
	} else if (y <= 9.6e-237) {
		tmp = 0.918938533204673;
	} else if (y <= 6.6e-121) {
		tmp = -x;
	} else if (y <= 1.0) {
		tmp = 0.918938533204673;
	} else {
		tmp = y * 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 <= (-1.0d0)) then
        tmp = y * x
    else if (y <= (-1.8d-88)) then
        tmp = -x
    else if (y <= (-8.4d-193)) then
        tmp = 0.918938533204673d0
    else if (y <= (-4.2d-267)) then
        tmp = -x
    else if (y <= 9.6d-237) then
        tmp = 0.918938533204673d0
    else if (y <= 6.6d-121) then
        tmp = -x
    else if (y <= 1.0d0) then
        tmp = 0.918938533204673d0
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= -1.8e-88) {
		tmp = -x;
	} else if (y <= -8.4e-193) {
		tmp = 0.918938533204673;
	} else if (y <= -4.2e-267) {
		tmp = -x;
	} else if (y <= 9.6e-237) {
		tmp = 0.918938533204673;
	} else if (y <= 6.6e-121) {
		tmp = -x;
	} else if (y <= 1.0) {
		tmp = 0.918938533204673;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = y * x
	elif y <= -1.8e-88:
		tmp = -x
	elif y <= -8.4e-193:
		tmp = 0.918938533204673
	elif y <= -4.2e-267:
		tmp = -x
	elif y <= 9.6e-237:
		tmp = 0.918938533204673
	elif y <= 6.6e-121:
		tmp = -x
	elif y <= 1.0:
		tmp = 0.918938533204673
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(y * x);
	elseif (y <= -1.8e-88)
		tmp = Float64(-x);
	elseif (y <= -8.4e-193)
		tmp = 0.918938533204673;
	elseif (y <= -4.2e-267)
		tmp = Float64(-x);
	elseif (y <= 9.6e-237)
		tmp = 0.918938533204673;
	elseif (y <= 6.6e-121)
		tmp = Float64(-x);
	elseif (y <= 1.0)
		tmp = 0.918938533204673;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = y * x;
	elseif (y <= -1.8e-88)
		tmp = -x;
	elseif (y <= -8.4e-193)
		tmp = 0.918938533204673;
	elseif (y <= -4.2e-267)
		tmp = -x;
	elseif (y <= 9.6e-237)
		tmp = 0.918938533204673;
	elseif (y <= 6.6e-121)
		tmp = -x;
	elseif (y <= 1.0)
		tmp = 0.918938533204673;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.8e-88], (-x), If[LessEqual[y, -8.4e-193], 0.918938533204673, If[LessEqual[y, -4.2e-267], (-x), If[LessEqual[y, 9.6e-237], 0.918938533204673, If[LessEqual[y, 6.6e-121], (-x), If[LessEqual[y, 1.0], 0.918938533204673, N[(y * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 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. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

      7. associate--l- 100.0%

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

      8. +-commutative 100.0%

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

      9. associate--r+ 100.0%

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

      10. associate--r- 100.0%

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

      11. distribute-lft-out-- 100.0%

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

      12. sub-neg 100.0%

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

      13. +-commutative 100.0%

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

      14. fma-def 100.0%

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

      15. +-commutative 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 56.2%

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

      1. *-commutative 56.2%

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

   8. Simplified 56.2%

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

   9. Taylor expanded in y around inf 56.1%

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

   10. Taylor expanded in y around inf 55.2%

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

   if -1 < y < -1.8e-88 or -8.3999999999999997e-193 < y < -4.2000000000000003e-267 or 9.5999999999999999e-237 < y < 6.6000000000000002e-121

   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. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

      7. associate--l- 100.0%

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

      8. +-commutative 100.0%

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

      9. associate--r+ 100.0%

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

      10. associate--r- 100.0%

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

      11. distribute-lft-out-- 100.0%

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

      12. sub-neg 100.0%

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

      13. +-commutative 100.0%

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

      14. fma-def 100.0%

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

      15. +-commutative 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 98.1%

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

      1. *-commutative 98.1%

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

   8. Simplified 98.1%

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

   9. Taylor expanded in y around inf 69.9%

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

   10. Taylor expanded in y around 0 67.3%

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

       1. neg-mul-1 67.3%

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

   12. Simplified 67.3%

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

   if -1.8e-88 < y < -8.3999999999999997e-193 or -4.2000000000000003e-267 < y < 9.5999999999999999e-237 or 6.6000000000000002e-121 < 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. Taylor expanded in y around inf 73.7%

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

   5. Taylor expanded in y around 0 71.6%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-88}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-193}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-267}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-237}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-121}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-8} \lor \neg \left(x \leq 7900\right):\\ \;\;\;\;\left(0.918938533204673 + y \cdot x\right) - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + \left(0.918938533204673 - y \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.8e-8) (not (<= x 7900.0)))
   (- (+ 0.918938533204673 (* y x)) x)
   (+ (* y x) (- 0.918938533204673 (* y 0.5)))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.8e-8) || !(x <= 7900.0)) {
		tmp = (0.918938533204673 + (y * x)) - x;
	} else {
		tmp = (y * x) + (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 <= (-5.8d-8)) .or. (.not. (x <= 7900.0d0))) then
        tmp = (0.918938533204673d0 + (y * x)) - x
    else
        tmp = (y * x) + (0.918938533204673d0 - (y * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -5.8e-8) || !(x <= 7900.0)) {
		tmp = (0.918938533204673 + (y * x)) - x;
	} else {
		tmp = (y * x) + (0.918938533204673 - (y * 0.5));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.8e-8) or not (x <= 7900.0):
		tmp = (0.918938533204673 + (y * x)) - x
	else:
		tmp = (y * x) + (0.918938533204673 - (y * 0.5))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.8e-8) || !(x <= 7900.0))
		tmp = Float64(Float64(0.918938533204673 + Float64(y * x)) - x);
	else
		tmp = Float64(Float64(y * x) + Float64(0.918938533204673 - Float64(y * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5.8e-8) || ~((x <= 7900.0)))
		tmp = (0.918938533204673 + (y * x)) - x;
	else
		tmp = (y * x) + (0.918938533204673 - (y * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.8e-8], N[Not[LessEqual[x, 7900.0]], $MachinePrecision]], N[(N[(0.918938533204673 + N[(y * x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] + N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8000000000000003e-8 or 7900 < 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. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

      7. associate--l- 100.0%

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

      8. +-commutative 100.0%

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

      9. associate--r+ 100.0%

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

      10. associate--r- 100.0%

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

      11. distribute-lft-out-- 100.0%

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

      12. sub-neg 100.0%

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

      13. +-commutative 100.0%

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

      14. fma-def 100.0%

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

      15. +-commutative 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -5.8000000000000003e-8 < x < 7900

   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. Taylor expanded in y around inf 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-8} \lor \neg \left(x \leq 7900\right):\\ \;\;\;\;\left(0.918938533204673 + y \cdot x\right) - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + \left(0.918938533204673 - y \cdot 0.5\right)\\ \end{array} \]

Alternative 4: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-8} \lor \neg \left(x \leq 3.05 \cdot 10^{-5}\right):\\ \;\;\;\;\left(0.918938533204673 + y \cdot x\right) - x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.1e-8) (not (<= x 3.05e-5)))
   (- (+ 0.918938533204673 (* y x)) x)
   (- 0.918938533204673 (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.1e-8) || !(x <= 3.05e-5)) {
		tmp = (0.918938533204673 + (y * x)) - x;
	} 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 <= (-4.1d-8)) .or. (.not. (x <= 3.05d-5))) then
        tmp = (0.918938533204673d0 + (y * x)) - x
    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 <= -4.1e-8) || !(x <= 3.05e-5)) {
		tmp = (0.918938533204673 + (y * x)) - x;
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.1e-8) or not (x <= 3.05e-5):
		tmp = (0.918938533204673 + (y * x)) - x
	else:
		tmp = 0.918938533204673 - (y * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.1e-8) || !(x <= 3.05e-5))
		tmp = Float64(Float64(0.918938533204673 + Float64(y * x)) - x);
	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 <= -4.1e-8) || ~((x <= 3.05e-5)))
		tmp = (0.918938533204673 + (y * x)) - x;
	else
		tmp = 0.918938533204673 - (y * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.1e-8], N[Not[LessEqual[x, 3.05e-5]], $MachinePrecision]], N[(N[(0.918938533204673 + N[(y * x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.10000000000000032e-8 or 3.04999999999999994e-5 < 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. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

      7. associate--l- 100.0%

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

      8. +-commutative 100.0%

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

      9. associate--r+ 100.0%

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

      10. associate--r- 100.0%

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

      11. distribute-lft-out-- 100.0%

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

      12. sub-neg 100.0%

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

      13. +-commutative 100.0%

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

      14. fma-def 100.0%

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

      15. +-commutative 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -4.10000000000000032e-8 < x < 3.04999999999999994e-5

   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. Taylor expanded in x around 0 99.2%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-8} \lor \neg \left(x \leq 3.05 \cdot 10^{-5}\right):\\ \;\;\;\;\left(0.918938533204673 + y \cdot x\right) - x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \]

Alternative 5: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \lor \neg \left(y \leq 1.15\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4) (not (<= y 1.15)))
   (* y (- x 0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4) || !(y <= 1.15)) {
		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 <= 1.15d0))) 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 <= 1.15)) {
		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 <= 1.15):
		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 <= 1.15))
		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 <= 1.15)))
		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, 1.15]], $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 1.1499999999999999 < 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. Taylor expanded in y around inf 97.9%

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

   if -1.3999999999999999 < y < 1.1499999999999999

   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. Taylor expanded in y around 0 96.3%

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

      1. neg-mul-1 96.3%

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

      2. unsub-neg 96.3%

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

   6. Simplified 96.3%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \lor \neg \left(y \leq 1.15\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]

Alternative 6: 98.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.74 \lor \neg \left(x \leq 0.6\right):\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.74) (not (<= x 0.6)))
   (- (* y x) x)
   (- 0.918938533204673 (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.74) || !(x <= 0.6)) {
		tmp = (y * x) - x;
	} 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 <= (-0.74d0)) .or. (.not. (x <= 0.6d0))) then
        tmp = (y * x) - x
    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 <= -0.74) || !(x <= 0.6)) {
		tmp = (y * x) - x;
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.74) or not (x <= 0.6):
		tmp = (y * x) - x
	else:
		tmp = 0.918938533204673 - (y * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.74) || !(x <= 0.6))
		tmp = Float64(Float64(y * x) - x);
	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 <= -0.74) || ~((x <= 0.6)))
		tmp = (y * x) - x;
	else
		tmp = 0.918938533204673 - (y * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.74], N[Not[LessEqual[x, 0.6]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision], N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.73999999999999999 or 0.599999999999999978 < 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. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

      7. associate--l- 100.0%

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

      8. +-commutative 100.0%

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

      9. associate--r+ 100.0%

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

      10. associate--r- 100.0%

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

      11. distribute-lft-out-- 100.0%

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

      12. sub-neg 100.0%

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

      13. +-commutative 100.0%

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

      14. fma-def 100.0%

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

      15. +-commutative 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around inf 99.3%

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

   if -0.73999999999999999 < x < 0.599999999999999978

   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. Taylor expanded in x around 0 97.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.74 \lor \neg \left(x \leq 0.6\right):\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \]

Alternative 7: 73.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -76 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -76.0) (not (<= y 1.0))) (* y x) (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -76.0) || !(y <= 1.0)) {
		tmp = y * x;
	} 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 <= (-76.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * x
    else
        tmp = 0.918938533204673d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -76.0) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -76.0) or not (y <= 1.0):
		tmp = y * x
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -76.0) || !(y <= 1.0))
		tmp = Float64(y * x);
	else
		tmp = Float64(0.918938533204673 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -76.0) || ~((y <= 1.0)))
		tmp = y * x;
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -76.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -76 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. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

      7. associate--l- 100.0%

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

      8. +-commutative 100.0%

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

      9. associate--r+ 100.0%

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

      10. associate--r- 100.0%

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

      11. distribute-lft-out-- 100.0%

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

      12. sub-neg 100.0%

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

      13. +-commutative 100.0%

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

      14. fma-def 100.0%

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

      15. +-commutative 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 56.2%

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

      1. *-commutative 56.2%

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

   8. Simplified 56.2%

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

   9. Taylor expanded in y around inf 56.1%

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

   10. Taylor expanded in y around inf 55.2%

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

   if -76 < 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. Taylor expanded in y around 0 96.3%

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

      1. neg-mul-1 96.3%

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

      2. unsub-neg 96.3%

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

   6. Simplified 96.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -76 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]

Alternative 8: 48.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.92 \lor \neg \left(x \leq 7.2 \cdot 10^{-30}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.92) (not (<= x 7.2e-30))) (- x) 0.918938533204673))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.92) || !(x <= 7.2e-30)) {
		tmp = -x;
	} 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 <= (-0.92d0)) .or. (.not. (x <= 7.2d-30))) then
        tmp = -x
    else
        tmp = 0.918938533204673d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.92) || !(x <= 7.2e-30)) {
		tmp = -x;
	} else {
		tmp = 0.918938533204673;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.92) or not (x <= 7.2e-30):
		tmp = -x
	else:
		tmp = 0.918938533204673
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.92) || !(x <= 7.2e-30))
		tmp = Float64(-x);
	else
		tmp = 0.918938533204673;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.92) || ~((x <= 7.2e-30)))
		tmp = -x;
	else
		tmp = 0.918938533204673;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.92], N[Not[LessEqual[x, 7.2e-30]], $MachinePrecision]], (-x), 0.918938533204673]

Derivation

1. Split input into 2 regimes

2. if x < -0.92000000000000004 or 7.2000000000000006e-30 < 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. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

      7. associate--l- 100.0%

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

      8. +-commutative 100.0%

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

      9. associate--r+ 100.0%

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

      10. associate--r- 100.0%

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

      11. distribute-lft-out-- 100.0%

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

      12. sub-neg 100.0%

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

      13. +-commutative 100.0%

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

      14. fma-def 100.0%

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

      15. +-commutative 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 97.7%

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

      1. *-commutative 97.7%

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

   8. Simplified 97.7%

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

   9. Taylor expanded in y around inf 97.0%

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

   10. Taylor expanded in y around 0 43.4%

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

       1. neg-mul-1 43.4%

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

   12. Simplified 43.4%

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

   if -0.92000000000000004 < x < 7.2000000000000006e-30

   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. Taylor expanded in y around inf 98.5%

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

   5. Taylor expanded in y around 0 51.6%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.92 \lor \neg \left(x \leq 7.2 \cdot 10^{-30}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673\\ \end{array} \]

Alternative 9: 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. 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. Taylor expanded in y around inf 77.1%

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

5. Taylor expanded in y around 0 26.0%

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

6. Final simplification 26.0%

   \[\leadsto 0.918938533204673 \]

Reproduce

herbie shell --seed 2023322 
(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))