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

Percentage Accurate: 100.0% → 100.0%

Time: 6.7s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ 0.918938533204673 - \mathsf{fma}\left(y, 0.5 - x, x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 0.918938533204673 (fma y (- 0.5 x) x)))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. cancel-sign-sub-inv 100.0%

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

   3. +-commutative 100.0%

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

   4. associate-+r+ 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate-+l- 100.0%

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

   7. sub-neg 100.0%

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

   8. distribute-rgt-in 100.0%

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

   9. metadata-eval 100.0%

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

   10. neg-mul-1 100.0%

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

   11. associate--r+ 100.0%

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

   12. distribute-lft-out-- 100.0%

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

   13. unsub-neg 100.0%

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

   14. fma-neg 100.0%

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

   15. unsub-neg 100.0%

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

   16. remove-double-neg 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto 0.918938533204673 - \mathsf{fma}\left(y, 0.5 - x, x\right) \]
6. Add Preprocessing

Alternative 2: 49.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+218}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -13500000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-146}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-202}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-302}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 0.92:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+79} \lor \neg \left(x \leq 4.2 \cdot 10^{+231}\right) \land x \leq 6.6 \cdot 10^{+285}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.75e+218)
   (* y x)
   (if (<= x -13500000000.0)
     (- x)
     (if (<= x -4.5e-146)
       (* y -0.5)
       (if (<= x -3.5e-202)
         0.918938533204673
         (if (<= x 5e-302)
           (* y -0.5)
           (if (<= x 0.92)
             0.918938533204673
             (if (or (<= x 4.5e+79)
                     (and (not (<= x 4.2e+231)) (<= x 6.6e+285)))
               (- x)
               (* y x)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.75e+218) {
		tmp = y * x;
	} else if (x <= -13500000000.0) {
		tmp = -x;
	} else if (x <= -4.5e-146) {
		tmp = y * -0.5;
	} else if (x <= -3.5e-202) {
		tmp = 0.918938533204673;
	} else if (x <= 5e-302) {
		tmp = y * -0.5;
	} else if (x <= 0.92) {
		tmp = 0.918938533204673;
	} else if ((x <= 4.5e+79) || (!(x <= 4.2e+231) && (x <= 6.6e+285))) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.75d+218)) then
        tmp = y * x
    else if (x <= (-13500000000.0d0)) then
        tmp = -x
    else if (x <= (-4.5d-146)) then
        tmp = y * (-0.5d0)
    else if (x <= (-3.5d-202)) then
        tmp = 0.918938533204673d0
    else if (x <= 5d-302) then
        tmp = y * (-0.5d0)
    else if (x <= 0.92d0) then
        tmp = 0.918938533204673d0
    else if ((x <= 4.5d+79) .or. (.not. (x <= 4.2d+231)) .and. (x <= 6.6d+285)) then
        tmp = -x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.75e+218) {
		tmp = y * x;
	} else if (x <= -13500000000.0) {
		tmp = -x;
	} else if (x <= -4.5e-146) {
		tmp = y * -0.5;
	} else if (x <= -3.5e-202) {
		tmp = 0.918938533204673;
	} else if (x <= 5e-302) {
		tmp = y * -0.5;
	} else if (x <= 0.92) {
		tmp = 0.918938533204673;
	} else if ((x <= 4.5e+79) || (!(x <= 4.2e+231) && (x <= 6.6e+285))) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.75e+218:
		tmp = y * x
	elif x <= -13500000000.0:
		tmp = -x
	elif x <= -4.5e-146:
		tmp = y * -0.5
	elif x <= -3.5e-202:
		tmp = 0.918938533204673
	elif x <= 5e-302:
		tmp = y * -0.5
	elif x <= 0.92:
		tmp = 0.918938533204673
	elif (x <= 4.5e+79) or (not (x <= 4.2e+231) and (x <= 6.6e+285)):
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.75e+218)
		tmp = Float64(y * x);
	elseif (x <= -13500000000.0)
		tmp = Float64(-x);
	elseif (x <= -4.5e-146)
		tmp = Float64(y * -0.5);
	elseif (x <= -3.5e-202)
		tmp = 0.918938533204673;
	elseif (x <= 5e-302)
		tmp = Float64(y * -0.5);
	elseif (x <= 0.92)
		tmp = 0.918938533204673;
	elseif ((x <= 4.5e+79) || (!(x <= 4.2e+231) && (x <= 6.6e+285)))
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.75e+218)
		tmp = y * x;
	elseif (x <= -13500000000.0)
		tmp = -x;
	elseif (x <= -4.5e-146)
		tmp = y * -0.5;
	elseif (x <= -3.5e-202)
		tmp = 0.918938533204673;
	elseif (x <= 5e-302)
		tmp = y * -0.5;
	elseif (x <= 0.92)
		tmp = 0.918938533204673;
	elseif ((x <= 4.5e+79) || (~((x <= 4.2e+231)) && (x <= 6.6e+285)))
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.75e+218], N[(y * x), $MachinePrecision], If[LessEqual[x, -13500000000.0], (-x), If[LessEqual[x, -4.5e-146], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, -3.5e-202], 0.918938533204673, If[LessEqual[x, 5e-302], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 0.92], 0.918938533204673, If[Or[LessEqual[x, 4.5e+79], And[N[Not[LessEqual[x, 4.2e+231]], $MachinePrecision], LessEqual[x, 6.6e+285]]], (-x), N[(y * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.7500000000000002e218 or 4.49999999999999994e79 < x < 4.19999999999999969e231 or 6.5999999999999995e285 < x

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

   6. Taylor expanded in y around inf 70.4%

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

   if -2.7500000000000002e218 < x < -1.35e10 or 0.92000000000000004 < x < 4.49999999999999994e79 or 4.19999999999999969e231 < x < 6.5999999999999995e285

   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 x around inf 96.9%

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

   6. Taylor expanded in y around 0 65.7%

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

      1. neg-mul-1 65.7%

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

   8. Simplified 65.7%

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

   if -1.35e10 < x < -4.5000000000000001e-146 or -3.4999999999999999e-202 < x < 5.00000000000000033e-302

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. cancel-sign-sub-inv 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. cancel-sign-sub-inv 99.9%

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

      6. associate-+l- 99.9%

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

      7. sub-neg 99.9%

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

      8. distribute-rgt-in 99.9%

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

      9. metadata-eval 99.9%

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

      10. neg-mul-1 99.9%

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

      11. associate--r+ 99.9%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fma-neg 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 68.8%

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

   6. Taylor expanded in x around 0 65.0%

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

      1. *-commutative 65.0%

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

   8. Simplified 65.0%

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

   if -4.5000000000000001e-146 < x < -3.4999999999999999e-202 or 5.00000000000000033e-302 < x < 0.92000000000000004

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 63.7%

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

   6. Taylor expanded in x around 0 62.0%

      \[\leadsto \color{blue}{0.918938533204673} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+218}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -13500000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-146}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-202}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-302}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 0.92:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+79} \lor \neg \left(x \leq 4.2 \cdot 10^{+231}\right) \land x \leq 6.6 \cdot 10^{+285}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+219}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -230000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 0.92:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+79} \lor \neg \left(x \leq 3 \cdot 10^{+243}\right) \land x \leq 4 \cdot 10^{+283}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.5e+219)
   (* y x)
   (if (<= x -230000000.0)
     (- x)
     (if (<= x 0.92)
       0.918938533204673
       (if (or (<= x 1.9e+79) (and (not (<= x 3e+243)) (<= x 4e+283)))
         (- x)
         (* y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.5e+219) {
		tmp = y * x;
	} else if (x <= -230000000.0) {
		tmp = -x;
	} else if (x <= 0.92) {
		tmp = 0.918938533204673;
	} else if ((x <= 1.9e+79) || (!(x <= 3e+243) && (x <= 4e+283))) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.5d+219)) then
        tmp = y * x
    else if (x <= (-230000000.0d0)) then
        tmp = -x
    else if (x <= 0.92d0) then
        tmp = 0.918938533204673d0
    else if ((x <= 1.9d+79) .or. (.not. (x <= 3d+243)) .and. (x <= 4d+283)) then
        tmp = -x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.5e+219) {
		tmp = y * x;
	} else if (x <= -230000000.0) {
		tmp = -x;
	} else if (x <= 0.92) {
		tmp = 0.918938533204673;
	} else if ((x <= 1.9e+79) || (!(x <= 3e+243) && (x <= 4e+283))) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.5e+219:
		tmp = y * x
	elif x <= -230000000.0:
		tmp = -x
	elif x <= 0.92:
		tmp = 0.918938533204673
	elif (x <= 1.9e+79) or (not (x <= 3e+243) and (x <= 4e+283)):
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.5e+219)
		tmp = Float64(y * x);
	elseif (x <= -230000000.0)
		tmp = Float64(-x);
	elseif (x <= 0.92)
		tmp = 0.918938533204673;
	elseif ((x <= 1.9e+79) || (!(x <= 3e+243) && (x <= 4e+283)))
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.5e+219)
		tmp = y * x;
	elseif (x <= -230000000.0)
		tmp = -x;
	elseif (x <= 0.92)
		tmp = 0.918938533204673;
	elseif ((x <= 1.9e+79) || (~((x <= 3e+243)) && (x <= 4e+283)))
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.5e+219], N[(y * x), $MachinePrecision], If[LessEqual[x, -230000000.0], (-x), If[LessEqual[x, 0.92], 0.918938533204673, If[Or[LessEqual[x, 1.9e+79], And[N[Not[LessEqual[x, 3e+243]], $MachinePrecision], LessEqual[x, 4e+283]]], (-x), N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4999999999999999e219 or 1.9000000000000001e79 < x < 2.99999999999999984e243 or 3.99999999999999982e283 < x

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

   6. Taylor expanded in y around inf 70.4%

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

   if -1.4999999999999999e219 < x < -2.3e8 or 0.92000000000000004 < x < 1.9000000000000001e79 or 2.99999999999999984e243 < x < 3.99999999999999982e283

   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 x around inf 96.6%

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

   6. Taylor expanded in y around 0 64.9%

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

      1. neg-mul-1 64.9%

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

   8. Simplified 64.9%

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

   if -2.3e8 < x < 0.92000000000000004

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 51.2%

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

   6. Taylor expanded in x around 0 48.7%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+219}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -230000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 0.92:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+79} \lor \neg \left(x \leq 3 \cdot 10^{+243}\right) \land x \leq 4 \cdot 10^{+283}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + -1\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-148}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-202}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-306}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 140000:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (+ y -1.0))))
   (if (<= x -1.15e-10)
     t_0
     (if (<= x -3.05e-148)
       (* y -0.5)
       (if (<= x -3e-202)
         0.918938533204673
         (if (<= x 7.8e-306)
           (* y -0.5)
           (if (<= x 140000.0) (- 0.918938533204673 x) t_0)))))))

C

double code(double x, double y) {
	double t_0 = x * (y + -1.0);
	double tmp;
	if (x <= -1.15e-10) {
		tmp = t_0;
	} else if (x <= -3.05e-148) {
		tmp = y * -0.5;
	} else if (x <= -3e-202) {
		tmp = 0.918938533204673;
	} else if (x <= 7.8e-306) {
		tmp = y * -0.5;
	} else if (x <= 140000.0) {
		tmp = 0.918938533204673 - x;
	} 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 <= (-1.15d-10)) then
        tmp = t_0
    else if (x <= (-3.05d-148)) then
        tmp = y * (-0.5d0)
    else if (x <= (-3d-202)) then
        tmp = 0.918938533204673d0
    else if (x <= 7.8d-306) then
        tmp = y * (-0.5d0)
    else if (x <= 140000.0d0) then
        tmp = 0.918938533204673d0 - x
    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 <= -1.15e-10) {
		tmp = t_0;
	} else if (x <= -3.05e-148) {
		tmp = y * -0.5;
	} else if (x <= -3e-202) {
		tmp = 0.918938533204673;
	} else if (x <= 7.8e-306) {
		tmp = y * -0.5;
	} else if (x <= 140000.0) {
		tmp = 0.918938533204673 - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y + -1.0)
	tmp = 0
	if x <= -1.15e-10:
		tmp = t_0
	elif x <= -3.05e-148:
		tmp = y * -0.5
	elif x <= -3e-202:
		tmp = 0.918938533204673
	elif x <= 7.8e-306:
		tmp = y * -0.5
	elif x <= 140000.0:
		tmp = 0.918938533204673 - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y + -1.0))
	tmp = 0.0
	if (x <= -1.15e-10)
		tmp = t_0;
	elseif (x <= -3.05e-148)
		tmp = Float64(y * -0.5);
	elseif (x <= -3e-202)
		tmp = 0.918938533204673;
	elseif (x <= 7.8e-306)
		tmp = Float64(y * -0.5);
	elseif (x <= 140000.0)
		tmp = Float64(0.918938533204673 - x);
	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 <= -1.15e-10)
		tmp = t_0;
	elseif (x <= -3.05e-148)
		tmp = y * -0.5;
	elseif (x <= -3e-202)
		tmp = 0.918938533204673;
	elseif (x <= 7.8e-306)
		tmp = y * -0.5;
	elseif (x <= 140000.0)
		tmp = 0.918938533204673 - x;
	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, -1.15e-10], t$95$0, If[LessEqual[x, -3.05e-148], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, -3e-202], 0.918938533204673, If[LessEqual[x, 7.8e-306], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 140000.0], N[(0.918938533204673 - x), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.15000000000000004e-10 or 1.4e5 < x

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.5%

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

   if -1.15000000000000004e-10 < x < -3.04999999999999988e-148 or -3.00000000000000011e-202 < x < 7.799999999999999e-306

   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. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fma-neg 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 70.1%

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

   6. Taylor expanded in x around 0 69.5%

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

      1. *-commutative 69.5%

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

   8. Simplified 69.5%

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

   if -3.04999999999999988e-148 < x < -3.00000000000000011e-202

   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 89.7%

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

   6. Taylor expanded in x around 0 89.7%

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

   if 7.799999999999999e-306 < x < 1.4e5

   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. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fma-neg 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 59.8%

      \[\leadsto \color{blue}{0.918938533204673 - x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-148}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-202}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-306}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 140000:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+270}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -380:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.1:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.4e+270)
   (* y -0.5)
   (if (<= y -1.9e+86)
     (* y x)
     (if (<= y -380.0)
       (* y -0.5)
       (if (<= y 1.1) (- 0.918938533204673 x) (* y x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.4e+270) {
		tmp = y * -0.5;
	} else if (y <= -1.9e+86) {
		tmp = y * x;
	} else if (y <= -380.0) {
		tmp = y * -0.5;
	} else if (y <= 1.1) {
		tmp = 0.918938533204673 - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-7.4d+270)) then
        tmp = y * (-0.5d0)
    else if (y <= (-1.9d+86)) then
        tmp = y * x
    else if (y <= (-380.0d0)) then
        tmp = y * (-0.5d0)
    else if (y <= 1.1d0) then
        tmp = 0.918938533204673d0 - x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -7.4e+270) {
		tmp = y * -0.5;
	} else if (y <= -1.9e+86) {
		tmp = y * x;
	} else if (y <= -380.0) {
		tmp = y * -0.5;
	} else if (y <= 1.1) {
		tmp = 0.918938533204673 - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.4e+270:
		tmp = y * -0.5
	elif y <= -1.9e+86:
		tmp = y * x
	elif y <= -380.0:
		tmp = y * -0.5
	elif y <= 1.1:
		tmp = 0.918938533204673 - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.4e+270)
		tmp = Float64(y * -0.5);
	elseif (y <= -1.9e+86)
		tmp = Float64(y * x);
	elseif (y <= -380.0)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.1)
		tmp = Float64(0.918938533204673 - x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.4e+270)
		tmp = y * -0.5;
	elseif (y <= -1.9e+86)
		tmp = y * x;
	elseif (y <= -380.0)
		tmp = y * -0.5;
	elseif (y <= 1.1)
		tmp = 0.918938533204673 - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.4e+270], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -1.9e+86], N[(y * x), $MachinePrecision], If[LessEqual[y, -380.0], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.1], N[(0.918938533204673 - x), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.39999999999999988e270 or -1.89999999999999989e86 < y < -380

   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. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fma-neg 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   6. Taylor expanded in x around 0 73.9%

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

      1. *-commutative 73.9%

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

   8. Simplified 73.9%

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

   if -7.39999999999999988e270 < y < -1.89999999999999989e86 or 1.1000000000000001 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 59.1%

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

   6. Taylor expanded in y around inf 58.6%

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

   if -380 < y < 1.1000000000000001

   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. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fma-neg 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 95.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+270}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -380:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.1:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -56000000 \lor \neg \left(y \leq 1.38 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right) - -0.918938533204673\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -56000000.0) (not (<= y 1.38e+14)))
   (* y (- x 0.5))
   (- (* x (+ y -1.0)) -0.918938533204673)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -56000000.0) || !(y <= 1.38e+14)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = (x * (y + -1.0)) - -0.918938533204673;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-56000000.0d0)) .or. (.not. (y <= 1.38d+14))) then
        tmp = y * (x - 0.5d0)
    else
        tmp = (x * (y + (-1.0d0))) - (-0.918938533204673d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -56000000.0) || !(y <= 1.38e+14)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = (x * (y + -1.0)) - -0.918938533204673;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -56000000.0) or not (y <= 1.38e+14):
		tmp = y * (x - 0.5)
	else:
		tmp = (x * (y + -1.0)) - -0.918938533204673
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -56000000.0) || !(y <= 1.38e+14))
		tmp = Float64(y * Float64(x - 0.5));
	else
		tmp = Float64(Float64(x * Float64(y + -1.0)) - -0.918938533204673);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -56000000.0) || ~((y <= 1.38e+14)))
		tmp = y * (x - 0.5);
	else
		tmp = (x * (y + -1.0)) - -0.918938533204673;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -56000000.0], N[Not[LessEqual[y, 1.38e+14]], $MachinePrecision]], N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] - -0.918938533204673), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6e7 or 1.38e14 < 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. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fma-neg 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -5.6e7 < y < 1.38e14

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -56000000 \lor \neg \left(y \leq 1.38 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right) - -0.918938533204673\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4) (not (<= y 1.0)))
   (* y (- x 0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4) || !(y <= 1.0)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.4d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (x - 0.5d0)
    else
        tmp = 0.918938533204673d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.4) || !(y <= 1.0)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.4) or not (y <= 1.0):
		tmp = y * (x - 0.5)
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.4) || !(y <= 1.0))
		tmp = Float64(y * Float64(x - 0.5));
	else
		tmp = Float64(0.918938533204673 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.4) || ~((y <= 1.0)))
		tmp = y * (x - 0.5);
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.4], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3999999999999999 or 1 < 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. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fma-neg 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 98.9%

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

   if -1.3999999999999999 < 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. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fma-neg 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 96.4%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.74 \lor \neg \left(x \leq 0.62\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.74) (not (<= x 0.62)))
   (* x (+ y -1.0))
   (- 0.918938533204673 (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.74) || !(x <= 0.62)) {
		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 <= (-0.74d0)) .or. (.not. (x <= 0.62d0))) 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 <= -0.74) || !(x <= 0.62)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.74) or not (x <= 0.62):
		tmp = x * (y + -1.0)
	else:
		tmp = 0.918938533204673 - (y * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.74) || !(x <= 0.62))
		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 <= -0.74) || ~((x <= 0.62)))
		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, -0.74], N[Not[LessEqual[x, 0.62]], $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 < -0.73999999999999999 or 0.619999999999999996 < x

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.8%

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

   if -0.73999999999999999 < x < 0.619999999999999996

   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. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fma-neg 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 97.5%

      \[\leadsto 0.918938533204673 - \color{blue}{0.5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 97.5%

         \[\leadsto 0.918938533204673 - \color{blue}{y \cdot 0.5} \]

   7. Simplified 97.5%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.74 \lor \neg \left(x \leq 0.62\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -230000000 \lor \neg \left(x \leq 0.92\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -230000000.0) (not (<= x 0.92))) (- x) 0.918938533204673))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -230000000.0) || !(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 <= (-230000000.0d0)) .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 <= -230000000.0) || !(x <= 0.92)) {
		tmp = -x;
	} else {
		tmp = 0.918938533204673;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -230000000.0) or not (x <= 0.92):
		tmp = -x
	else:
		tmp = 0.918938533204673
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -230000000.0) || !(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 <= -230000000.0) || ~((x <= 0.92)))
		tmp = -x;
	else
		tmp = 0.918938533204673;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -230000000.0], N[Not[LessEqual[x, 0.92]], $MachinePrecision]], (-x), 0.918938533204673]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e8 or 0.92000000000000004 < x

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 98.1%

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

   6. Taylor expanded in y around 0 49.9%

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

      1. neg-mul-1 49.9%

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

   8. Simplified 49.9%

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

   if -2.3e8 < x < 0.92000000000000004

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 51.2%

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

   6. Taylor expanded in x around 0 48.7%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -230000000 \lor \neg \left(x \leq 0.92\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 11: 26.7% accurate, 11.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 0.918938533204673)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 0.918938533204673

Julia

function code(x, y)
	return 0.918938533204673
end

MATLAB

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

Wolfram

code[x_, y_] := 0.918938533204673

Derivation

1. Initial program 100.0%

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

   1. associate-+l- 100.0%

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

   2. sub-neg 100.0%

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

   3. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 76.3%

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

6. Taylor expanded in x around 0 24.4%

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

7. Final simplification 24.4%

   \[\leadsto 0.918938533204673 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(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))