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

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

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

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

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. 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. 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: 49.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+293}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+240}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -38000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.3:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+184} \lor \neg \left(y \leq 2.8 \cdot 10^{+293}\right):\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.8e+293)
   (* y x)
   (if (<= y -4.5e+240)
     (* y -0.5)
     (if (<= y -38000.0)
       (* y x)
       (if (<= y 1.3)
         (- x)
         (if (or (<= y 6e+184) (not (<= y 2.8e+293))) (* y -0.5) (* y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.8e+293) {
		tmp = y * x;
	} else if (y <= -4.5e+240) {
		tmp = y * -0.5;
	} else if (y <= -38000.0) {
		tmp = y * x;
	} else if (y <= 1.3) {
		tmp = -x;
	} else if ((y <= 6e+184) || !(y <= 2.8e+293)) {
		tmp = y * -0.5;
	} 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 <= (-4.8d+293)) then
        tmp = y * x
    else if (y <= (-4.5d+240)) then
        tmp = y * (-0.5d0)
    else if (y <= (-38000.0d0)) then
        tmp = y * x
    else if (y <= 1.3d0) then
        tmp = -x
    else if ((y <= 6d+184) .or. (.not. (y <= 2.8d+293))) then
        tmp = y * (-0.5d0)
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.8e+293) {
		tmp = y * x;
	} else if (y <= -4.5e+240) {
		tmp = y * -0.5;
	} else if (y <= -38000.0) {
		tmp = y * x;
	} else if (y <= 1.3) {
		tmp = -x;
	} else if ((y <= 6e+184) || !(y <= 2.8e+293)) {
		tmp = y * -0.5;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.8e+293:
		tmp = y * x
	elif y <= -4.5e+240:
		tmp = y * -0.5
	elif y <= -38000.0:
		tmp = y * x
	elif y <= 1.3:
		tmp = -x
	elif (y <= 6e+184) or not (y <= 2.8e+293):
		tmp = y * -0.5
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.8e+293)
		tmp = Float64(y * x);
	elseif (y <= -4.5e+240)
		tmp = Float64(y * -0.5);
	elseif (y <= -38000.0)
		tmp = Float64(y * x);
	elseif (y <= 1.3)
		tmp = Float64(-x);
	elseif ((y <= 6e+184) || !(y <= 2.8e+293))
		tmp = Float64(y * -0.5);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.8e+293)
		tmp = y * x;
	elseif (y <= -4.5e+240)
		tmp = y * -0.5;
	elseif (y <= -38000.0)
		tmp = y * x;
	elseif (y <= 1.3)
		tmp = -x;
	elseif ((y <= 6e+184) || ~((y <= 2.8e+293)))
		tmp = y * -0.5;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.8e+293], N[(y * x), $MachinePrecision], If[LessEqual[y, -4.5e+240], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -38000.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.3], (-x), If[Or[LessEqual[y, 6e+184], N[Not[LessEqual[y, 2.8e+293]], $MachinePrecision]], N[(y * -0.5), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000006e293 or -4.49999999999999979e240 < y < -38000 or 5.99999999999999973e184 < y < 2.79999999999999986e293

   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. 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 inf 67.1%

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

   6. Taylor expanded in y around inf 66.6%

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

   if -4.80000000000000006e293 < y < -4.49999999999999979e240 or 1.30000000000000004 < y < 5.99999999999999973e184 or 2.79999999999999986e293 < 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 95.5%

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

   5. Taylor expanded in x around 0 64.8%

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

      1. *-commutative 64.8%

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

   7. Simplified 64.8%

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

   if -38000 < y < 1.30000000000000004

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. 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. 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 y around inf 53.6%

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

   6. Taylor expanded in y around 0 51.8%

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

      1. neg-mul-1 51.8%

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

   8. Simplified 51.8%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+293}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+240}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -38000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.3:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+184} \lor \neg \left(y \leq 2.8 \cdot 10^{+293}\right):\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+293}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+241}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -38000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.6:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+183} \lor \neg \left(y \leq 1.65 \cdot 10^{+295}\right):\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.15e+293)
   (* y x)
   (if (<= y -3.3e+241)
     (* y -0.5)
     (if (<= y -38000.0)
       (* y x)
       (if (<= y 1.6)
         (- 0.918938533204673 x)
         (if (or (<= y 4e+183) (not (<= y 1.65e+295))) (* y -0.5) (* y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.15e+293) {
		tmp = y * x;
	} else if (y <= -3.3e+241) {
		tmp = y * -0.5;
	} else if (y <= -38000.0) {
		tmp = y * x;
	} else if (y <= 1.6) {
		tmp = 0.918938533204673 - x;
	} else if ((y <= 4e+183) || !(y <= 1.65e+295)) {
		tmp = y * -0.5;
	} 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 <= (-2.15d+293)) then
        tmp = y * x
    else if (y <= (-3.3d+241)) then
        tmp = y * (-0.5d0)
    else if (y <= (-38000.0d0)) then
        tmp = y * x
    else if (y <= 1.6d0) then
        tmp = 0.918938533204673d0 - x
    else if ((y <= 4d+183) .or. (.not. (y <= 1.65d+295))) then
        tmp = y * (-0.5d0)
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.15e+293) {
		tmp = y * x;
	} else if (y <= -3.3e+241) {
		tmp = y * -0.5;
	} else if (y <= -38000.0) {
		tmp = y * x;
	} else if (y <= 1.6) {
		tmp = 0.918938533204673 - x;
	} else if ((y <= 4e+183) || !(y <= 1.65e+295)) {
		tmp = y * -0.5;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.15e+293:
		tmp = y * x
	elif y <= -3.3e+241:
		tmp = y * -0.5
	elif y <= -38000.0:
		tmp = y * x
	elif y <= 1.6:
		tmp = 0.918938533204673 - x
	elif (y <= 4e+183) or not (y <= 1.65e+295):
		tmp = y * -0.5
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.15e+293)
		tmp = Float64(y * x);
	elseif (y <= -3.3e+241)
		tmp = Float64(y * -0.5);
	elseif (y <= -38000.0)
		tmp = Float64(y * x);
	elseif (y <= 1.6)
		tmp = Float64(0.918938533204673 - x);
	elseif ((y <= 4e+183) || !(y <= 1.65e+295))
		tmp = Float64(y * -0.5);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.15e+293)
		tmp = y * x;
	elseif (y <= -3.3e+241)
		tmp = y * -0.5;
	elseif (y <= -38000.0)
		tmp = y * x;
	elseif (y <= 1.6)
		tmp = 0.918938533204673 - x;
	elseif ((y <= 4e+183) || ~((y <= 1.65e+295)))
		tmp = y * -0.5;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.15e+293], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.3e+241], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -38000.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.6], N[(0.918938533204673 - x), $MachinePrecision], If[Or[LessEqual[y, 4e+183], N[Not[LessEqual[y, 1.65e+295]], $MachinePrecision]], N[(y * -0.5), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1500000000000001e293 or -3.3e241 < y < -38000 or 3.99999999999999979e183 < y < 1.65000000000000006e295

   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. 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 inf 67.1%

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

   6. Taylor expanded in y around inf 66.6%

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

   if -2.1500000000000001e293 < y < -3.3e241 or 1.6000000000000001 < y < 3.99999999999999979e183 or 1.65000000000000006e295 < 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 95.5%

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

   5. Taylor expanded in x around 0 64.8%

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

      1. *-commutative 64.8%

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

   7. Simplified 64.8%

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

   if -38000 < y < 1.6000000000000001

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 97.9%

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

      1. neg-mul-1 97.9%

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

      2. sub-neg 97.9%

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

   6. Simplified 97.9%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+293}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+241}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -38000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.6:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+183} \lor \neg \left(y \leq 1.65 \cdot 10^{+295}\right):\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + -1\right)\\ \mathbf{if}\;x \leq -0.0235:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-308}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-79}:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{elif}\;x \leq 0.5:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (+ y -1.0))))
   (if (<= x -0.0235)
     t_0
     (if (<= x -5.8e-308)
       (* y -0.5)
       (if (<= x 1.32e-79)
         (- 0.918938533204673 x)
         (if (<= x 0.5) (* y -0.5) t_0))))))

C

double code(double x, double y) {
	double t_0 = x * (y + -1.0);
	double tmp;
	if (x <= -0.0235) {
		tmp = t_0;
	} else if (x <= -5.8e-308) {
		tmp = y * -0.5;
	} else if (x <= 1.32e-79) {
		tmp = 0.918938533204673 - x;
	} else if (x <= 0.5) {
		tmp = y * -0.5;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + (-1.0d0))
    if (x <= (-0.0235d0)) then
        tmp = t_0
    else if (x <= (-5.8d-308)) then
        tmp = y * (-0.5d0)
    else if (x <= 1.32d-79) then
        tmp = 0.918938533204673d0 - x
    else if (x <= 0.5d0) then
        tmp = y * (-0.5d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (y + -1.0);
	double tmp;
	if (x <= -0.0235) {
		tmp = t_0;
	} else if (x <= -5.8e-308) {
		tmp = y * -0.5;
	} else if (x <= 1.32e-79) {
		tmp = 0.918938533204673 - x;
	} else if (x <= 0.5) {
		tmp = y * -0.5;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y + -1.0)
	tmp = 0
	if x <= -0.0235:
		tmp = t_0
	elif x <= -5.8e-308:
		tmp = y * -0.5
	elif x <= 1.32e-79:
		tmp = 0.918938533204673 - x
	elif x <= 0.5:
		tmp = y * -0.5
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y + -1.0))
	tmp = 0.0
	if (x <= -0.0235)
		tmp = t_0;
	elseif (x <= -5.8e-308)
		tmp = Float64(y * -0.5);
	elseif (x <= 1.32e-79)
		tmp = Float64(0.918938533204673 - x);
	elseif (x <= 0.5)
		tmp = Float64(y * -0.5);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (y + -1.0);
	tmp = 0.0;
	if (x <= -0.0235)
		tmp = t_0;
	elseif (x <= -5.8e-308)
		tmp = y * -0.5;
	elseif (x <= 1.32e-79)
		tmp = 0.918938533204673 - x;
	elseif (x <= 0.5)
		tmp = y * -0.5;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.0235], t$95$0, If[LessEqual[x, -5.8e-308], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1.32e-79], N[(0.918938533204673 - x), $MachinePrecision], If[LessEqual[x, 0.5], N[(y * -0.5), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0235 or 0.5 < 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. 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 inf 97.5%

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

   if -0.0235 < x < -5.8000000000000001e-308 or 1.32e-79 < 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. 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 58.8%

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

   5. Taylor expanded in x around 0 58.5%

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

      1. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   if -5.8000000000000001e-308 < x < 1.32e-79

   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 62.9%

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

      1. neg-mul-1 62.9%

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

      2. sub-neg 62.9%

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

   6. Simplified 62.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0235:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-308}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-79}:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{elif}\;x \leq 0.5:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 5: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-13} \lor \neg \left(x \leq 1.1 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right) - x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.5e-13) (not (<= x 1.1e-7)))
   (- (* y (- x 0.5)) x)
   (- 0.918938533204673 (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.5e-13) || !(x <= 1.1e-7)) {
		tmp = (y * (x - 0.5)) - 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 <= (-3.5d-13)) .or. (.not. (x <= 1.1d-7))) then
        tmp = (y * (x - 0.5d0)) - 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 <= -3.5e-13) || !(x <= 1.1e-7)) {
		tmp = (y * (x - 0.5)) - x;
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.5e-13) or not (x <= 1.1e-7):
		tmp = (y * (x - 0.5)) - x
	else:
		tmp = 0.918938533204673 - (y * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.5e-13) || !(x <= 1.1e-7))
		tmp = Float64(Float64(y * Float64(x - 0.5)) - 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 <= -3.5e-13) || ~((x <= 1.1e-7)))
		tmp = (y * (x - 0.5)) - x;
	else
		tmp = 0.918938533204673 - (y * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.5e-13], N[Not[LessEqual[x, 1.1e-7]], $MachinePrecision]], N[(N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000002e-13 or 1.1000000000000001e-7 < x

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. 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. 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 y around inf 99.1%

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

   if -3.5000000000000002e-13 < x < 1.1000000000000001e-7

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-13} \lor \neg \left(x \leq 1.1 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right) - x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \]

Alternative 6: 98.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \lor \neg \left(y \leq 1.15\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.35) (not (<= y 1.15)))
   (* y (- x 0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.35) || !(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 <= (-1.35d0)) .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 <= -1.35) || !(y <= 1.15)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.35) 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 <= -1.35) || !(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 <= -1.35) || ~((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, -1.35], 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 < -1.3500000000000001 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 96.8%

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

   if -1.3500000000000001 < 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 98.6%

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

      1. neg-mul-1 98.6%

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

      2. sub-neg 98.6%

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

   6. Simplified 98.6%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \lor \neg \left(y \leq 1.15\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]

Alternative 7: 97.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.66 \lor \neg \left(x \leq 0.68\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.66) (not (<= x 0.68)))
   (* x (+ y -1.0))
   (- 0.918938533204673 (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.66) || !(x <= 0.68)) {
		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 <= (-0.66d0)) .or. (.not. (x <= 0.68d0))) 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 <= -0.66) || !(x <= 0.68)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.66) or not (x <= 0.68):
		tmp = x * (y + -1.0)
	else:
		tmp = 0.918938533204673 - (y * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.66) || !(x <= 0.68))
		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 <= -0.66) || ~((x <= 0.68)))
		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, -0.66], N[Not[LessEqual[x, 0.68]], $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 < -0.660000000000000031 or 0.680000000000000049 < 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. 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 inf 97.5%

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

   if -0.660000000000000031 < x < 0.680000000000000049

   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 99.7%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.66 \lor \neg \left(x \leq 0.68\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \]

Alternative 8: 48.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -38000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -38000.0) (not (<= y 1.0))) (* y x) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -38000.0) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = -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 <= (-38000.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * x
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -38000.0) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -38000.0) or not (y <= 1.0):
		tmp = y * x
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -38000.0) || !(y <= 1.0))
		tmp = Float64(y * x);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -38000.0) || ~((y <= 1.0)))
		tmp = y * x;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -38000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -38000 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. 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 inf 54.5%

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

   6. Taylor expanded in y around inf 52.3%

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

   if -38000 < 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. 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. 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 y around inf 53.6%

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

   6. Taylor expanded in y around 0 51.8%

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

      1. neg-mul-1 51.8%

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

   8. Simplified 51.8%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -38000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 9: 25.7% 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. 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. 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 y around inf 76.7%

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

6. Taylor expanded in y around 0 27.4%

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

   1. neg-mul-1 27.4%

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

8. Simplified 27.4%

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

9. Final simplification 27.4%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023319 
(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))