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

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 9

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. cancel-sign-sub-inv 100.0%

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

   2. +-commutative 100.0%

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

   3. sub-neg 100.0%

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

   4. distribute-rgt-in 100.0%

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

   5. metadata-eval 100.0%

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

   6. neg-mul-1 100.0%

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

   7. associate-+r+ 100.0%

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

   8. unsub-neg 100.0%

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

   9. associate-+l- 100.0%

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

   10. distribute-lft-neg-out 100.0%

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

   11. distribute-rgt-neg-in 100.0%

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

   12. distribute-lft-out 100.0%

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

   13. fma-neg 100.0%

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

   14. +-commutative 100.0%

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

   15. metadata-eval 100.0%

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

   16. neg-sub0 100.0%

       \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{0 - \left(x - 0.918938533204673\right)}\right) \]

   17. associate-+l- 100.0%

       \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{\left(0 - x\right) + 0.918938533204673}\right) \]

   18. neg-sub0 100.0%

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

   19. +-commutative 100.0%

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

   20. unsub-neg 100.0%

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

3. Simplified 100.0%

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

   1. fma-undefine 100.0%

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

   2. associate-+r- 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 48.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+160}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+71}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -210 \lor \neg \left(x \leq 0.55\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.5e+160)
   (* y x)
   (if (<= x -7.8e+71)
     (- x)
     (if (or (<= x -210.0) (not (<= x 0.55))) (* y x) 0.918938533204673))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+160) {
		tmp = y * x;
	} else if (x <= -7.8e+71) {
		tmp = -x;
	} else if ((x <= -210.0) || !(x <= 0.55)) {
		tmp = y * x;
	} else {
		tmp = 0.918938533204673;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-9.5d+160)) then
        tmp = y * x
    else if (x <= (-7.8d+71)) then
        tmp = -x
    else if ((x <= (-210.0d0)) .or. (.not. (x <= 0.55d0))) then
        tmp = y * x
    else
        tmp = 0.918938533204673d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+160) {
		tmp = y * x;
	} else if (x <= -7.8e+71) {
		tmp = -x;
	} else if ((x <= -210.0) || !(x <= 0.55)) {
		tmp = y * x;
	} else {
		tmp = 0.918938533204673;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.5e+160:
		tmp = y * x
	elif x <= -7.8e+71:
		tmp = -x
	elif (x <= -210.0) or not (x <= 0.55):
		tmp = y * x
	else:
		tmp = 0.918938533204673
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.5e+160)
		tmp = Float64(y * x);
	elseif (x <= -7.8e+71)
		tmp = Float64(-x);
	elseif ((x <= -210.0) || !(x <= 0.55))
		tmp = Float64(y * x);
	else
		tmp = 0.918938533204673;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.5e+160)
		tmp = y * x;
	elseif (x <= -7.8e+71)
		tmp = -x;
	elseif ((x <= -210.0) || ~((x <= 0.55)))
		tmp = y * x;
	else
		tmp = 0.918938533204673;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.5e+160], N[(y * x), $MachinePrecision], If[LessEqual[x, -7.8e+71], (-x), If[Or[LessEqual[x, -210.0], N[Not[LessEqual[x, 0.55]], $MachinePrecision]], N[(y * x), $MachinePrecision], 0.918938533204673]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5000000000000006e160 or -7.8000000000000002e71 < x < -210 or 0.55000000000000004 < 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. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{0 - \left(x - 0.918938533204673\right)}\right) \]

      17. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{\left(0 - x\right) + 0.918938533204673}\right) \]

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 98.5%

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

      1. *-commutative 98.5%

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

   9. Simplified 98.5%

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

   10. Taylor expanded in y around inf 96.9%

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

   11. Taylor expanded in y around inf 63.6%

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

   if -9.5000000000000006e160 < x < -7.8000000000000002e71

   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. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{0 - \left(x - 0.918938533204673\right)}\right) \]

      17. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{\left(0 - x\right) + 0.918938533204673}\right) \]

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in y around inf 100.0%

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

   11. Taylor expanded in y around 0 74.5%

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

       1. neg-mul-1 74.5%

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

   13. Simplified 74.5%

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

   if -210 < x < 0.55000000000000004

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 98.8%

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

   6. Taylor expanded in y around 0 51.5%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+160}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+71}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -210 \lor \neg \left(x \leq 0.55\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-6} \lor \neg \left(y \leq 1.75 \cdot 10^{-45}\right):\\ \;\;\;\;y \cdot \left(x + -0.5\right) + 0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.3e-6) (not (<= y 1.75e-45)))
   (+ (* y (+ x -0.5)) 0.918938533204673)
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.3e-6) || !(y <= 1.75e-45)) {
		tmp = (y * (x + -0.5)) + 0.918938533204673;
	} 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 <= (-2.3d-6)) .or. (.not. (y <= 1.75d-45))) then
        tmp = (y * (x + (-0.5d0))) + 0.918938533204673d0
    else
        tmp = 0.918938533204673d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.3e-6) || !(y <= 1.75e-45)) {
		tmp = (y * (x + -0.5)) + 0.918938533204673;
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.3e-6) or not (y <= 1.75e-45):
		tmp = (y * (x + -0.5)) + 0.918938533204673
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.3e-6) || !(y <= 1.75e-45))
		tmp = Float64(Float64(y * Float64(x + -0.5)) + 0.918938533204673);
	else
		tmp = Float64(0.918938533204673 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.3e-6) || ~((y <= 1.75e-45)))
		tmp = (y * (x + -0.5)) + 0.918938533204673;
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.3e-6], N[Not[LessEqual[y, 1.75e-45]], $MachinePrecision]], N[(N[(y * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e-6 or 1.75e-45 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.2%

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

      1. associate--r- 99.2%

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

      2. *-commutative 99.2%

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

      3. cancel-sign-sub-inv 99.2%

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

      4. metadata-eval 99.2%

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

      5. distribute-rgt-in 99.2%

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

   7. Applied egg-rr 99.2%

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

   if -2.3e-6 < y < 1.75e-45

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.6%

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

      1. neg-mul-1 99.6%

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

      2. sub-neg 99.6%

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

   7. Simplified 99.6%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-6} \lor \neg \left(y \leq 1.75 \cdot 10^{-45}\right):\\ \;\;\;\;y \cdot \left(x + -0.5\right) + 0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.005 \lor \neg \left(y \leq 1.75 \cdot 10^{-45}\right):\\ \;\;\;\;y \cdot \left(x + -0.5\right) + 0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 + y \cdot x\right) - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.005) (not (<= y 1.75e-45)))
   (+ (* y (+ x -0.5)) 0.918938533204673)
   (- (+ 0.918938533204673 (* y x)) x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.005) || !(y <= 1.75e-45)) {
		tmp = (y * (x + -0.5)) + 0.918938533204673;
	} else {
		tmp = (0.918938533204673 + (y * x)) - 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 <= (-0.005d0)) .or. (.not. (y <= 1.75d-45))) then
        tmp = (y * (x + (-0.5d0))) + 0.918938533204673d0
    else
        tmp = (0.918938533204673d0 + (y * x)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -0.005) || !(y <= 1.75e-45)) {
		tmp = (y * (x + -0.5)) + 0.918938533204673;
	} else {
		tmp = (0.918938533204673 + (y * x)) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.005) or not (y <= 1.75e-45):
		tmp = (y * (x + -0.5)) + 0.918938533204673
	else:
		tmp = (0.918938533204673 + (y * x)) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.005) || !(y <= 1.75e-45))
		tmp = Float64(Float64(y * Float64(x + -0.5)) + 0.918938533204673);
	else
		tmp = Float64(Float64(0.918938533204673 + Float64(y * x)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -0.005) || ~((y <= 1.75e-45)))
		tmp = (y * (x + -0.5)) + 0.918938533204673;
	else
		tmp = (0.918938533204673 + (y * x)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.005], N[Not[LessEqual[y, 1.75e-45]], $MachinePrecision]], N[(N[(y * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision], N[(N[(0.918938533204673 + N[(y * x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0050000000000000001 or 1.75e-45 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. associate--r- 99.8%

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

      2. *-commutative 99.8%

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

      3. cancel-sign-sub-inv 99.8%

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

      4. metadata-eval 99.8%

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

      5. distribute-rgt-in 99.8%

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

   7. Applied egg-rr 99.8%

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

   if -0.0050000000000000001 < y < 1.75e-45

   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. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{0 - \left(x - 0.918938533204673\right)}\right) \]

      17. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{\left(0 - x\right) + 0.918938533204673}\right) \]

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 99.4%

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

      1. *-commutative 99.4%

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

   9. Simplified 99.4%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.005 \lor \neg \left(y \leq 1.75 \cdot 10^{-45}\right):\\ \;\;\;\;y \cdot \left(x + -0.5\right) + 0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 + y \cdot x\right) - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.042:\\ \;\;\;\;y \cdot x + \left(0.918938533204673 - y \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-45}:\\ \;\;\;\;\left(0.918938533204673 + y \cdot x\right) - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -0.5\right) + 0.918938533204673\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.042)
   (+ (* y x) (- 0.918938533204673 (* y 0.5)))
   (if (<= y 1.75e-45)
     (- (+ 0.918938533204673 (* y x)) x)
     (+ (* y (+ x -0.5)) 0.918938533204673))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.042) {
		tmp = (y * x) + (0.918938533204673 - (y * 0.5));
	} else if (y <= 1.75e-45) {
		tmp = (0.918938533204673 + (y * x)) - x;
	} else {
		tmp = (y * (x + -0.5)) + 0.918938533204673;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-0.042d0)) then
        tmp = (y * x) + (0.918938533204673d0 - (y * 0.5d0))
    else if (y <= 1.75d-45) then
        tmp = (0.918938533204673d0 + (y * x)) - x
    else
        tmp = (y * (x + (-0.5d0))) + 0.918938533204673d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.042) {
		tmp = (y * x) + (0.918938533204673 - (y * 0.5));
	} else if (y <= 1.75e-45) {
		tmp = (0.918938533204673 + (y * x)) - x;
	} else {
		tmp = (y * (x + -0.5)) + 0.918938533204673;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.042:
		tmp = (y * x) + (0.918938533204673 - (y * 0.5))
	elif y <= 1.75e-45:
		tmp = (0.918938533204673 + (y * x)) - x
	else:
		tmp = (y * (x + -0.5)) + 0.918938533204673
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.042)
		tmp = Float64(Float64(y * x) + Float64(0.918938533204673 - Float64(y * 0.5)));
	elseif (y <= 1.75e-45)
		tmp = Float64(Float64(0.918938533204673 + Float64(y * x)) - x);
	else
		tmp = Float64(Float64(y * Float64(x + -0.5)) + 0.918938533204673);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.042)
		tmp = (y * x) + (0.918938533204673 - (y * 0.5));
	elseif (y <= 1.75e-45)
		tmp = (0.918938533204673 + (y * x)) - x;
	else
		tmp = (y * (x + -0.5)) + 0.918938533204673;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.042], N[(N[(y * x), $MachinePrecision] + N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-45], N[(N[(0.918938533204673 + N[(y * x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(y * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0420000000000000026

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.8%

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

   if -0.0420000000000000026 < y < 1.75e-45

   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. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{0 - \left(x - 0.918938533204673\right)}\right) \]

      17. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{\left(0 - x\right) + 0.918938533204673}\right) \]

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 99.4%

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

      1. *-commutative 99.4%

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

   9. Simplified 99.4%

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

   if 1.75e-45 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. associate--r- 99.8%

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

      2. *-commutative 99.8%

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

      3. cancel-sign-sub-inv 99.8%

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

      4. metadata-eval 99.8%

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

      5. distribute-rgt-in 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.042:\\ \;\;\;\;y \cdot x + \left(0.918938533204673 - y \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-45}:\\ \;\;\;\;\left(0.918938533204673 + y \cdot x\right) - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -0.5\right) + 0.918938533204673\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \lor \neg \left(y \leq 1.4\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.35) (not (<= y 1.4)))
   (* y (- x 0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.35) || !(y <= 1.4)) {
		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 <= 1.4d0))) 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 <= 1.4)) {
		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 <= 1.4):
		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 <= 1.4))
		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 <= 1.4)))
		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, 1.4]], $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 1.3999999999999999 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 96.7%

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

   if -1.3500000000000001 < y < 1.3999999999999999

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.6%

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

      1. neg-mul-1 98.6%

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

      2. sub-neg 98.6%

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

   7. Simplified 98.6%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \lor \neg \left(y \leq 1.4\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+15} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.6e+15) (not (<= y 1.0))) (* y x) (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.6e+15) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-6.6d+15)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * x
    else
        tmp = 0.918938533204673d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.6e+15) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.6e+15) or not (y <= 1.0):
		tmp = y * x
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.6e+15) || !(y <= 1.0))
		tmp = Float64(y * x);
	else
		tmp = Float64(0.918938533204673 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.6e+15) || ~((y <= 1.0)))
		tmp = y * x;
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.6e+15], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6e15 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. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{0 - \left(x - 0.918938533204673\right)}\right) \]

      17. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{\left(0 - x\right) + 0.918938533204673}\right) \]

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 58.4%

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

      1. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   10. Taylor expanded in y around inf 58.5%

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

   11. Taylor expanded in y around inf 58.4%

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

   if -6.6e15 < y < 1

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 94.4%

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

      1. neg-mul-1 94.4%

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

      2. sub-neg 94.4%

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

   7. Simplified 94.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+15} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.6% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.92000000000000004 or 0.92000000000000004 < x

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{0 - \left(x - 0.918938533204673\right)}\right) \]

      17. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(y, x + -0.5, \color{blue}{\left(0 - x\right) + 0.918938533204673}\right) \]

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 98.7%

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

      1. *-commutative 98.7%

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

   9. Simplified 98.7%

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

   10. Taylor expanded in y around inf 96.8%

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

   11. Taylor expanded in y around 0 40.0%

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

       1. neg-mul-1 40.0%

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

   13. Simplified 40.0%

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

   if -0.92000000000000004 < x < 0.92000000000000004

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.5%

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

   6. Taylor expanded in y around 0 51.8%

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

4. Final simplification 45.7%

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

Alternative 9: 25.6% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 0.918938533204673 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.918938533204673)

C

double code(double x, double y) {
	return 0.918938533204673;
}

Fortran

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

Java

public static double code(double x, double y) {
	return 0.918938533204673;
}

Python

def code(x, y):
	return 0.918938533204673

Julia

function code(x, y)
	return 0.918938533204673
end

MATLAB

function tmp = code(x, y)
	tmp = 0.918938533204673;
end

Wolfram

code[x_, y_] := 0.918938533204673

Derivation

1. Initial program 100.0%

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

   1. associate-+l- 100.0%

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

   2. sub-neg 100.0%

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

   3. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around inf 79.5%

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

6. Taylor expanded in y around 0 26.6%

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

7. Final simplification 26.6%

   \[\leadsto 0.918938533204673 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024071 
(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))