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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 10

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. 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 0 100.0%

   \[\leadsto \color{blue}{\left(0.918938533204673 + x \cdot \left(y - 1\right)\right) - 0.5 \cdot y} \]
6. Step-by-step derivation

   1. cancel-sign-sub-inv 100.0%

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

   2. metadata-eval 100.0%

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

   3. sub-neg 100.0%

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

   4. metadata-eval 100.0%

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

   5. associate-+r+ 100.0%

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

   6. distribute-lft-in 100.0%

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

   7. *-commutative 100.0%

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

   8. neg-mul-1 100.0%

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

   9. +-commutative 100.0%

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

   10. associate-+l+ 100.0%

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

   11. distribute-rgt-in 100.0%

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

   12. metadata-eval 100.0%

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

   13. sub-neg 100.0%

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

   14. +-commutative 100.0%

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

   15. unsub-neg 100.0%

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

   16. sub-neg 100.0%

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

   17. metadata-eval 100.0%

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

7. Simplified 100.0%

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

8. Taylor expanded in y around 0 100.0%

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

9. Final simplification 100.0%

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

Alternative 2: 49.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -110000000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-247}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-180}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;y \leq 0.0096:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -110000000.0)
   (* y x)
   (if (<= y 2.35e-247)
     (- x)
     (if (<= y 2.3e-180) 0.918938533204673 (if (<= y 0.0096) (- x) (* y x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -110000000.0) {
		tmp = y * x;
	} else if (y <= 2.35e-247) {
		tmp = -x;
	} else if (y <= 2.3e-180) {
		tmp = 0.918938533204673;
	} else if (y <= 0.0096) {
		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 (y <= (-110000000.0d0)) then
        tmp = y * x
    else if (y <= 2.35d-247) then
        tmp = -x
    else if (y <= 2.3d-180) then
        tmp = 0.918938533204673d0
    else if (y <= 0.0096d0) 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 (y <= -110000000.0) {
		tmp = y * x;
	} else if (y <= 2.35e-247) {
		tmp = -x;
	} else if (y <= 2.3e-180) {
		tmp = 0.918938533204673;
	} else if (y <= 0.0096) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -110000000.0:
		tmp = y * x
	elif y <= 2.35e-247:
		tmp = -x
	elif y <= 2.3e-180:
		tmp = 0.918938533204673
	elif y <= 0.0096:
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -110000000.0)
		tmp = Float64(y * x);
	elseif (y <= 2.35e-247)
		tmp = Float64(-x);
	elseif (y <= 2.3e-180)
		tmp = 0.918938533204673;
	elseif (y <= 0.0096)
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -110000000.0)
		tmp = y * x;
	elseif (y <= 2.35e-247)
		tmp = -x;
	elseif (y <= 2.3e-180)
		tmp = 0.918938533204673;
	elseif (y <= 0.0096)
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -110000000.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.35e-247], (-x), If[LessEqual[y, 2.3e-180], 0.918938533204673, If[LessEqual[y, 0.0096], (-x), N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e8 or 0.00959999999999999916 < 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 x around 0 100.0%

      \[\leadsto \color{blue}{\left(0.918938533204673 + x \cdot \left(y - 1\right)\right) - 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 100.0%

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

      2. metadata-eval 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. *-commutative 100.0%

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

      8. neg-mul-1 100.0%

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

      9. +-commutative 100.0%

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

      10. associate-+l+ 100.0%

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

      11. distribute-rgt-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. unsub-neg 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 55.2%

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

      1. *-commutative 55.2%

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

   10. Simplified 55.2%

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

   11. Taylor expanded in y around inf 54.4%

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

   if -1.1e8 < y < 2.3499999999999999e-247 or 2.29999999999999996e-180 < y < 0.00959999999999999916

   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 61.1%

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

   6. Taylor expanded in y around 0 58.9%

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

      1. neg-mul-1 58.9%

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

   8. Simplified 58.9%

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

   if 2.3499999999999999e-247 < y < 2.29999999999999996e-180

   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 0 100.0%

      \[\leadsto \color{blue}{\left(0.918938533204673 + x \cdot \left(y - 1\right)\right) - 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 100.0%

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

      2. metadata-eval 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. *-commutative 100.0%

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

      8. neg-mul-1 100.0%

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

      9. +-commutative 100.0%

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

      10. associate-+l+ 100.0%

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

      11. distribute-rgt-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. unsub-neg 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in x around 0 77.3%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -110000000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-247}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-180}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;y \leq 0.0096:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-14} \lor \neg \left(x \leq 0.37\right):\\ \;\;\;\;0.918938533204673 + \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1e-14) (not (<= x 0.37)))
   (+ 0.918938533204673 (- (* y x) x))
   (- 0.918938533204673 (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1e-14) || !(x <= 0.37)) {
		tmp = 0.918938533204673 + ((y * x) - x);
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1d-14)) .or. (.not. (x <= 0.37d0))) then
        tmp = 0.918938533204673d0 + ((y * x) - x)
    else
        tmp = 0.918938533204673d0 - (y * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1e-14) || !(x <= 0.37)) {
		tmp = 0.918938533204673 + ((y * x) - x);
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1e-14) or not (x <= 0.37):
		tmp = 0.918938533204673 + ((y * x) - x)
	else:
		tmp = 0.918938533204673 - (y * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1e-14) || !(x <= 0.37))
		tmp = Float64(0.918938533204673 + Float64(Float64(y * x) - x));
	else
		tmp = Float64(0.918938533204673 - Float64(y * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1e-14) || ~((x <= 0.37)))
		tmp = 0.918938533204673 + ((y * x) - x);
	else
		tmp = 0.918938533204673 - (y * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1e-14], N[Not[LessEqual[x, 0.37]], $MachinePrecision]], N[(0.918938533204673 + N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999999e-15 or 0.37 < 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 0 100.0%

      \[\leadsto \color{blue}{\left(0.918938533204673 + x \cdot \left(y - 1\right)\right) - 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 100.0%

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

      2. metadata-eval 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. *-commutative 100.0%

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

      8. neg-mul-1 100.0%

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

      9. +-commutative 100.0%

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

      10. associate-+l+ 100.0%

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

      11. distribute-rgt-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. unsub-neg 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 99.2%

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

      1. *-commutative 99.2%

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

   10. Simplified 99.2%

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

   if -9.99999999999999999e-15 < x < 0.37

   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 0 98.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-14} \lor \neg \left(x \leq 0.37\right):\\ \;\;\;\;0.918938533204673 + \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7000000 \lor \neg \left(x \leq 7600\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -7000000.0) (not (<= x 7600.0)))
   (* x (+ y -1.0))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -7000000.0) || !(x <= 7600.0)) {
		tmp = x * (y + -1.0);
	} 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 ((x <= (-7000000.0d0)) .or. (.not. (x <= 7600.0d0))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = 0.918938533204673d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -7000000.0) || !(x <= 7600.0)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -7000000.0) or not (x <= 7600.0):
		tmp = x * (y + -1.0)
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -7000000.0) || !(x <= 7600.0))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(0.918938533204673 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -7000000.0) || ~((x <= 7600.0)))
		tmp = x * (y + -1.0);
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -7000000.0], N[Not[LessEqual[x, 7600.0]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7e6 or 7600 < 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 99.7%

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

   if -7e6 < x < 7600

   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 46.6%

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

      1. neg-mul-1 46.6%

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

      2. unsub-neg 46.6%

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

   7. Simplified 46.6%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7000000 \lor \neg \left(x \leq 7600\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \lor \neg \left(y \leq 1.2\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.32) (not (<= y 1.2)))
   (* y (- x 0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.32) || !(y <= 1.2)) {
		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 <= (-1.32d0)) .or. (.not. (y <= 1.2d0))) 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 <= -1.32) || !(y <= 1.2)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.32) or not (y <= 1.2):
		tmp = y * (x - 0.5)
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.32) || !(y <= 1.2))
		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 <= -1.32) || ~((y <= 1.2)))
		tmp = y * (x - 0.5);
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.32], N[Not[LessEqual[y, 1.2]], $MachinePrecision]], N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.32000000000000006 or 1.19999999999999996 < 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 98.5%

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

   if -1.32000000000000006 < y < 1.19999999999999996

   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 96.0%

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

      1. neg-mul-1 96.0%

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

      2. unsub-neg 96.0%

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

   7. Simplified 96.0%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \lor \neg \left(y \leq 1.2\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.66 \lor \neg \left(x \leq 0.92\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.66) (not (<= x 0.92)))
   (* x (+ y -1.0))
   (- 0.918938533204673 (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.66) || !(x <= 0.92)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-0.66d0)) .or. (.not. (x <= 0.92d0))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = 0.918938533204673d0 - (y * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.66) || !(x <= 0.92)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.66) or not (x <= 0.92):
		tmp = x * (y + -1.0)
	else:
		tmp = 0.918938533204673 - (y * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.66) || !(x <= 0.92))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(0.918938533204673 - Float64(y * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.66) || ~((x <= 0.92)))
		tmp = x * (y + -1.0);
	else
		tmp = 0.918938533204673 - (y * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.66], N[Not[LessEqual[x, 0.92]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.660000000000000031 or 0.92000000000000004 < 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 98.7%

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

   if -0.660000000000000031 < 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 x around 0 97.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.66 \lor \neg \left(x \leq 0.92\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(0.918938533204673 + N[(N[(y * N[(x + -0.5), $MachinePrecision]), $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. 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 0 100.0%

   \[\leadsto \color{blue}{\left(0.918938533204673 + x \cdot \left(y - 1\right)\right) - 0.5 \cdot y} \]
6. Step-by-step derivation

   1. cancel-sign-sub-inv 100.0%

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

   2. metadata-eval 100.0%

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

   3. sub-neg 100.0%

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

   4. metadata-eval 100.0%

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

   5. associate-+r+ 100.0%

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

   6. distribute-lft-in 100.0%

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

   7. *-commutative 100.0%

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

   8. neg-mul-1 100.0%

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

   9. +-commutative 100.0%

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

   10. associate-+l+ 100.0%

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

   11. distribute-rgt-in 100.0%

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

   12. metadata-eval 100.0%

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

   13. sub-neg 100.0%

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

   14. +-commutative 100.0%

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

   15. unsub-neg 100.0%

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

   16. sub-neg 100.0%

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

   17. metadata-eval 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 8: 73.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+19} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.6e+19) (not (<= y 1.0))) (* y x) (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.6e+19) || !(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 <= (-3.6d+19)) .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 <= -3.6e+19) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.6e+19) 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 <= -3.6e+19) || !(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 <= -3.6e+19) || ~((y <= 1.0)))
		tmp = y * x;
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.6e+19], 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 < -3.6e19 or 1 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. 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 0 100.0%

      \[\leadsto \color{blue}{\left(0.918938533204673 + x \cdot \left(y - 1\right)\right) - 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 100.0%

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

      2. metadata-eval 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. *-commutative 100.0%

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

      8. neg-mul-1 100.0%

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

      9. +-commutative 100.0%

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

      10. associate-+l+ 100.0%

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

      11. distribute-rgt-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. unsub-neg 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 56.1%

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

      1. *-commutative 56.1%

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

   10. Simplified 56.1%

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

   11. Taylor expanded in y around inf 55.6%

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

   if -3.6e19 < 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 94.0%

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

      1. neg-mul-1 94.0%

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

      2. unsub-neg 94.0%

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

   7. Simplified 94.0%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+19} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.1% accurate, 1.8× 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. 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 98.7%

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

   6. Taylor expanded in y around 0 48.9%

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

      1. neg-mul-1 48.9%

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

   8. Simplified 48.9%

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

   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 x around 0 100.0%

      \[\leadsto \color{blue}{\left(0.918938533204673 + x \cdot \left(y - 1\right)\right) - 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 100.0%

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

      2. metadata-eval 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. *-commutative 100.0%

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

      8. neg-mul-1 100.0%

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

      9. +-commutative 100.0%

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

      10. associate-+l+ 100.0%

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

      11. distribute-rgt-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. unsub-neg 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 45.8%

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

      1. *-commutative 45.8%

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

   10. Simplified 45.8%

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

   11. Taylor expanded in x around 0 45.4%

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

4. Final simplification 47.4%

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

Alternative 10: 26.2% 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 x around 0 100.0%

   \[\leadsto \color{blue}{\left(0.918938533204673 + x \cdot \left(y - 1\right)\right) - 0.5 \cdot y} \]
6. Step-by-step derivation

   1. cancel-sign-sub-inv 100.0%

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

   2. metadata-eval 100.0%

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

   3. sub-neg 100.0%

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

   4. metadata-eval 100.0%

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

   5. associate-+r+ 100.0%

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

   6. distribute-lft-in 100.0%

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

   7. *-commutative 100.0%

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

   8. neg-mul-1 100.0%

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

   9. +-commutative 100.0%

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

   10. associate-+l+ 100.0%

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

   11. distribute-rgt-in 100.0%

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

   12. metadata-eval 100.0%

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

   13. sub-neg 100.0%

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

   14. +-commutative 100.0%

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

   15. unsub-neg 100.0%

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

   16. sub-neg 100.0%

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

   17. metadata-eval 100.0%

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

7. Simplified 100.0%

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

8. Taylor expanded in x around inf 76.0%

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

   1. *-commutative 76.0%

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

10. Simplified 76.0%

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

11. Taylor expanded in x around 0 21.5%

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

12. Final simplification 21.5%

    \[\leadsto 0.918938533204673 \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(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))