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

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 8

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   2. +-commutative 100.0%

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

   3. sub-neg 100.0%

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

   4. distribute-rgt-in 100.0%

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

   5. associate-+r+ 100.0%

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

   6. associate-+l+ 100.0%

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

   7. distribute-rgt-neg-in 100.0%

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

   8. distribute-lft-out 100.0%

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

   9. fma-def 100.0%

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

   10. +-commutative 100.0%

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

   11. metadata-eval 100.0%

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

   12. +-commutative 100.0%

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

   13. cancel-sign-sub-inv 100.0%

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

   14. *-lft-identity 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around 0 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 50.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+42}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-9}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 0.5:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+66}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+150}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8.6e+42)
   (* y x)
   (if (<= x -2.3e-9)
     (- x)
     (if (<= x 0.5)
       (* y -0.5)
       (if (<= x 7.5e+66) (* y x) (if (<= x 2.5e+150) (- x) (* y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8.6e+42) {
		tmp = y * x;
	} else if (x <= -2.3e-9) {
		tmp = -x;
	} else if (x <= 0.5) {
		tmp = y * -0.5;
	} else if (x <= 7.5e+66) {
		tmp = y * x;
	} else if (x <= 2.5e+150) {
		tmp = -x;
	} 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 (x <= (-8.6d+42)) then
        tmp = y * x
    else if (x <= (-2.3d-9)) then
        tmp = -x
    else if (x <= 0.5d0) then
        tmp = y * (-0.5d0)
    else if (x <= 7.5d+66) then
        tmp = y * x
    else if (x <= 2.5d+150) then
        tmp = -x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -8.6e+42) {
		tmp = y * x;
	} else if (x <= -2.3e-9) {
		tmp = -x;
	} else if (x <= 0.5) {
		tmp = y * -0.5;
	} else if (x <= 7.5e+66) {
		tmp = y * x;
	} else if (x <= 2.5e+150) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8.6e+42:
		tmp = y * x
	elif x <= -2.3e-9:
		tmp = -x
	elif x <= 0.5:
		tmp = y * -0.5
	elif x <= 7.5e+66:
		tmp = y * x
	elif x <= 2.5e+150:
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8.6e+42)
		tmp = Float64(y * x);
	elseif (x <= -2.3e-9)
		tmp = Float64(-x);
	elseif (x <= 0.5)
		tmp = Float64(y * -0.5);
	elseif (x <= 7.5e+66)
		tmp = Float64(y * x);
	elseif (x <= 2.5e+150)
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8.6e+42)
		tmp = y * x;
	elseif (x <= -2.3e-9)
		tmp = -x;
	elseif (x <= 0.5)
		tmp = y * -0.5;
	elseif (x <= 7.5e+66)
		tmp = y * x;
	elseif (x <= 2.5e+150)
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8.6e+42], N[(y * x), $MachinePrecision], If[LessEqual[x, -2.3e-9], (-x), If[LessEqual[x, 0.5], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 7.5e+66], N[(y * x), $MachinePrecision], If[LessEqual[x, 2.5e+150], (-x), N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5999999999999996e42 or 0.5 < x < 7.50000000000000024e66 or 2.50000000000000004e150 < 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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 63.8%

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

   5. Taylor expanded in x around inf 63.5%

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

   if -8.5999999999999996e42 < x < -2.2999999999999999e-9 or 7.50000000000000024e66 < x < 2.50000000000000004e150

   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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 inf 88.4%

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

   5. Taylor expanded in y around 0 68.3%

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

      1. neg-mul-1 68.3%

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

   7. Simplified 68.3%

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

   if -2.2999999999999999e-9 < x < 0.5

   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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 47.8%

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

   5. Taylor expanded in x around 0 47.1%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 47.1%

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

   7. Simplified 47.1%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+42}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-9}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 0.5:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+66}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+150}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+142}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+116}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -14000000000:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.3:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.3e+142)
   (* y -0.5)
   (if (<= y -1.45e+116)
     (* y x)
     (if (<= y -14000000000.0)
       (* y -0.5)
       (if (<= y 1.3) (- 0.918938533204673 x) (* y x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.3e+142) {
		tmp = y * -0.5;
	} else if (y <= -1.45e+116) {
		tmp = y * x;
	} else if (y <= -14000000000.0) {
		tmp = y * -0.5;
	} else if (y <= 1.3) {
		tmp = 0.918938533204673 - x;
	} 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 <= (-3.3d+142)) then
        tmp = y * (-0.5d0)
    else if (y <= (-1.45d+116)) then
        tmp = y * x
    else if (y <= (-14000000000.0d0)) then
        tmp = y * (-0.5d0)
    else if (y <= 1.3d0) then
        tmp = 0.918938533204673d0 - x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.3e+142) {
		tmp = y * -0.5;
	} else if (y <= -1.45e+116) {
		tmp = y * x;
	} else if (y <= -14000000000.0) {
		tmp = y * -0.5;
	} else if (y <= 1.3) {
		tmp = 0.918938533204673 - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.3e+142:
		tmp = y * -0.5
	elif y <= -1.45e+116:
		tmp = y * x
	elif y <= -14000000000.0:
		tmp = y * -0.5
	elif y <= 1.3:
		tmp = 0.918938533204673 - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.3e+142)
		tmp = Float64(y * -0.5);
	elseif (y <= -1.45e+116)
		tmp = Float64(y * x);
	elseif (y <= -14000000000.0)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.3)
		tmp = Float64(0.918938533204673 - x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.3e+142)
		tmp = y * -0.5;
	elseif (y <= -1.45e+116)
		tmp = y * x;
	elseif (y <= -14000000000.0)
		tmp = y * -0.5;
	elseif (y <= 1.3)
		tmp = 0.918938533204673 - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.3e+142], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -1.45e+116], N[(y * x), $MachinePrecision], If[LessEqual[y, -14000000000.0], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.3], N[(0.918938533204673 - x), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3000000000000002e142 or -1.4500000000000001e116 < y < -1.4e10

   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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 99.7%

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

   5. Taylor expanded in x around 0 58.2%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 58.2%

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

   7. Simplified 58.2%

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

   if -3.3000000000000002e142 < y < -1.4500000000000001e116 or 1.30000000000000004 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 97.6%

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

   5. Taylor expanded in x around inf 66.6%

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

   if -1.4e10 < y < 1.30000000000000004

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 95.8%

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

      1. neg-mul-1 95.8%

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

      2. sub-neg 95.8%

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

   6. Simplified 95.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+142}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+116}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -14000000000:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.3:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+31} \lor \neg \left(x \leq 350000\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 + y \cdot -0.5\right) - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.3e+31) (not (<= x 350000.0)))
   (* x (+ y -1.0))
   (- (+ 0.918938533204673 (* y -0.5)) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.3e+31) || !(x <= 350000.0)) {
		tmp = x * (y + -1.0);
	} 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 <= (-3.3d+31)) .or. (.not. (x <= 350000.0d0))) then
        tmp = x * (y + (-1.0d0))
    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 <= -3.3e+31) || !(x <= 350000.0)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = (0.918938533204673 + (y * -0.5)) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.3e+31) or not (x <= 350000.0):
		tmp = x * (y + -1.0)
	else:
		tmp = (0.918938533204673 + (y * -0.5)) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.3e+31) || !(x <= 350000.0))
		tmp = Float64(x * Float64(y + -1.0));
	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 <= -3.3e+31) || ~((x <= 350000.0)))
		tmp = x * (y + -1.0);
	else
		tmp = (0.918938533204673 + (y * -0.5)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.3e+31], N[Not[LessEqual[x, 350000.0]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.918938533204673 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.29999999999999992e31 or 3.5e5 < 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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 inf 99.7%

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

   if -3.29999999999999992e31 < x < 3.5e5

   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. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. associate-+r+ 100.0%

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

      6. associate-+l+ 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

      8. distribute-lft-out 100.0%

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

      9. fma-def 100.0%

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

      10. +-commutative 100.0%

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

      11. metadata-eval 100.0%

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

      12. +-commutative 100.0%

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

      13. cancel-sign-sub-inv 100.0%

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

      14. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 99.3%

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

      1. *-commutative 43.9%

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

   7. Simplified 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+31} \lor \neg \left(x \leq 350000\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 + y \cdot -0.5\right) - x\\ \end{array} \]

Alternative 5: 98.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \lor \neg \left(y \leq 1.7\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.25) (not (<= y 1.7)))
   (* y (- x 0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.25) || !(y <= 1.7)) {
		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 <= (-1.25d0)) .or. (.not. (y <= 1.7d0))) 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 <= -1.25) || !(y <= 1.7)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.25) or not (y <= 1.7):
		tmp = y * (x - 0.5)
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.25) || !(y <= 1.7))
		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 <= -1.25) || ~((y <= 1.7)))
		tmp = y * (x - 0.5);
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.25], N[Not[LessEqual[y, 1.7]], $MachinePrecision]], N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25 or 1.69999999999999996 < 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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 97.7%

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

   if -1.25 < y < 1.69999999999999996

   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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 97.8%

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

      1. neg-mul-1 97.8%

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

      2. sub-neg 97.8%

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

   6. Simplified 97.8%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \lor \neg \left(y \leq 1.7\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]

Alternative 6: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.7 \lor \neg \left(x \leq 0.52\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.7) (not (<= x 0.52)))
   (* x (+ y -1.0))
   (- 0.918938533204673 (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.7) || !(x <= 0.52)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-0.7d0)) .or. (.not. (x <= 0.52d0))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = 0.918938533204673d0 - (y * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.7) || !(x <= 0.52)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.7) or not (x <= 0.52):
		tmp = x * (y + -1.0)
	else:
		tmp = 0.918938533204673 - (y * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.7) || !(x <= 0.52))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(0.918938533204673 - Float64(y * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.7) || ~((x <= 0.52)))
		tmp = x * (y + -1.0);
	else
		tmp = 0.918938533204673 - (y * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.7], N[Not[LessEqual[x, 0.52]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.69999999999999996 or 0.52000000000000002 < 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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 inf 97.9%

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

   if -0.69999999999999996 < x < 0.52000000000000002

   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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 98.1%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.7 \lor \neg \left(x \leq 0.52\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \]

Alternative 7: 50.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-13}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.6:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.4e-13) (* y -0.5) (if (<= y 1.6) (- x) (* y -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.4e-13) {
		tmp = y * -0.5;
	} else if (y <= 1.6) {
		tmp = -x;
	} else {
		tmp = y * -0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.4d-13)) then
        tmp = y * (-0.5d0)
    else if (y <= 1.6d0) then
        tmp = -x
    else
        tmp = y * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.4e-13) {
		tmp = y * -0.5;
	} else if (y <= 1.6) {
		tmp = -x;
	} else {
		tmp = y * -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.4e-13:
		tmp = y * -0.5
	elif y <= 1.6:
		tmp = -x
	else:
		tmp = y * -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.4e-13)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.6)
		tmp = Float64(-x);
	else
		tmp = Float64(y * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.4e-13)
		tmp = y * -0.5;
	elseif (y <= 1.6)
		tmp = -x;
	else
		tmp = y * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.4e-13], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.6], (-x), N[(y * -0.5), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3999999999999999e-13 or 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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 93.9%

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

   5. Taylor expanded in x around 0 43.1%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 43.1%

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

   7. Simplified 43.1%

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

   if -2.3999999999999999e-13 < 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. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. fma-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. 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 inf 48.4%

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

   5. Taylor expanded in y around 0 48.3%

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

      1. neg-mul-1 48.3%

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

   7. Simplified 48.3%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-13}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.6:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \]

Alternative 8: 26.4% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -x

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := (-x)

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. fma-neg 100.0%

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

   3. sub-neg 100.0%

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

   4. +-commutative 100.0%

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

   5. remove-double-neg 100.0%

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

   6. sub-neg 100.0%

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

   7. fma-neg 100.0%

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

   8. sub-neg 100.0%

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

   9. remove-double-neg 100.0%

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

   10. +-commutative 100.0%

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

   11. 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 inf 52.0%

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

5. Taylor expanded in y around 0 24.2%

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

   1. neg-mul-1 24.2%

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

7. Simplified 24.2%

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

8. Final simplification 24.2%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023192 
(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))