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

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 12

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× 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]

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%

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

Alternative 2: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 30000000000000:\\ \;\;\;\;x \cdot y + \left(0.918938533204673 - y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 + x \cdot y\right) - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.6e+18)
   (* x (+ y -1.0))
   (if (<= x 30000000000000.0)
     (+ (* x y) (- 0.918938533204673 (* y 0.5)))
     (- (+ 0.918938533204673 (* x y)) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.6e+18) {
		tmp = x * (y + -1.0);
	} else if (x <= 30000000000000.0) {
		tmp = (x * y) + (0.918938533204673 - (y * 0.5));
	} else {
		tmp = (0.918938533204673 + (x * 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 <= (-2.6d+18)) then
        tmp = x * (y + (-1.0d0))
    else if (x <= 30000000000000.0d0) then
        tmp = (x * y) + (0.918938533204673d0 - (y * 0.5d0))
    else
        tmp = (0.918938533204673d0 + (x * y)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.6e+18) {
		tmp = x * (y + -1.0);
	} else if (x <= 30000000000000.0) {
		tmp = (x * y) + (0.918938533204673 - (y * 0.5));
	} else {
		tmp = (0.918938533204673 + (x * y)) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.6e+18:
		tmp = x * (y + -1.0)
	elif x <= 30000000000000.0:
		tmp = (x * y) + (0.918938533204673 - (y * 0.5))
	else:
		tmp = (0.918938533204673 + (x * y)) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.6e+18)
		tmp = Float64(x * Float64(y + -1.0));
	elseif (x <= 30000000000000.0)
		tmp = Float64(Float64(x * y) + Float64(0.918938533204673 - Float64(y * 0.5)));
	else
		tmp = Float64(Float64(0.918938533204673 + Float64(x * y)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.6e+18)
		tmp = x * (y + -1.0);
	elseif (x <= 30000000000000.0)
		tmp = (x * y) + (0.918938533204673 - (y * 0.5));
	else
		tmp = (0.918938533204673 + (x * y)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.6e+18], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 30000000000000.0], N[(N[(x * y), $MachinePrecision] + N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.918938533204673 + N[(x * y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6e18

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate-+l- 100.0%

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

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 100.0%

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

   if -2.6e18 < x < 3e13

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.6%

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

   if 3e13 < x

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate-+l- 100.0%

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

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 30000000000000:\\ \;\;\;\;x \cdot y + \left(0.918938533204673 - y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 + x \cdot y\right) - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0075:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 0.58:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+121}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.0075)
   (* x y)
   (if (<= x 0.58) 0.918938533204673 (if (<= x 3.7e+121) (* x y) (- x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.0075) {
		tmp = x * y;
	} else if (x <= 0.58) {
		tmp = 0.918938533204673;
	} else if (x <= 3.7e+121) {
		tmp = x * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.0075d0)) then
        tmp = x * y
    else if (x <= 0.58d0) then
        tmp = 0.918938533204673d0
    else if (x <= 3.7d+121) then
        tmp = x * y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.0075) {
		tmp = x * y;
	} else if (x <= 0.58) {
		tmp = 0.918938533204673;
	} else if (x <= 3.7e+121) {
		tmp = x * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.0075:
		tmp = x * y
	elif x <= 0.58:
		tmp = 0.918938533204673
	elif x <= 3.7e+121:
		tmp = x * y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.0075)
		tmp = Float64(x * y);
	elseif (x <= 0.58)
		tmp = 0.918938533204673;
	elseif (x <= 3.7e+121)
		tmp = Float64(x * y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.0075)
		tmp = x * y;
	elseif (x <= 0.58)
		tmp = 0.918938533204673;
	elseif (x <= 3.7e+121)
		tmp = x * y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.0075], N[(x * y), $MachinePrecision], If[LessEqual[x, 0.58], 0.918938533204673, If[LessEqual[x, 3.7e+121], N[(x * y), $MachinePrecision], (-x)]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0074999999999999997 or 0.57999999999999996 < x < 3.70000000000000013e121

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 99.9%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate-+l- 100.0%

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

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 99.9%

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

      2. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 96.2%

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

   8. Taylor expanded in y around inf 50.9%

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

   if -0.0074999999999999997 < x < 0.57999999999999996

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.6%

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

   6. Taylor expanded in y around 0 54.6%

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

   if 3.70000000000000013e121 < x

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate-+l- 100.0%

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

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 100.0%

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

   8. Taylor expanded in y around 0 60.5%

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

      1. neg-mul-1 60.5%

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

   10. Simplified 60.5%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0075:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 0.58:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+121}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -125000000 \lor \neg \left(y \leq 410000\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 + x \cdot y\right) - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -125000000.0) (not (<= y 410000.0)))
   (* y (- x 0.5))
   (- (+ 0.918938533204673 (* x y)) x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -125000000.0) || !(y <= 410000.0)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = (0.918938533204673 + (x * 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 <= (-125000000.0d0)) .or. (.not. (y <= 410000.0d0))) then
        tmp = y * (x - 0.5d0)
    else
        tmp = (0.918938533204673d0 + (x * y)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -125000000.0) || !(y <= 410000.0)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = (0.918938533204673 + (x * y)) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -125000000.0) or not (y <= 410000.0):
		tmp = y * (x - 0.5)
	else:
		tmp = (0.918938533204673 + (x * y)) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -125000000.0) || !(y <= 410000.0))
		tmp = Float64(y * Float64(x - 0.5));
	else
		tmp = Float64(Float64(0.918938533204673 + Float64(x * y)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -125000000.0) || ~((y <= 410000.0)))
		tmp = y * (x - 0.5);
	else
		tmp = (0.918938533204673 + (x * y)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -125000000.0], N[Not[LessEqual[y, 410000.0]], $MachinePrecision]], N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(0.918938533204673 + N[(x * y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e8 or 4.1e5 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.9%

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

   if -1.25e8 < y < 4.1e5

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate-+l- 100.0%

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

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 98.7%

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

      1. *-commutative 98.7%

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

   9. Simplified 98.7%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -125000000 \lor \neg \left(y \leq 410000\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.918938533204673 + x \cdot y\right) - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0125 \lor \neg \left(x \leq 155\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.0125) (not (<= x 155.0)))
   (* x (+ y -1.0))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.0125) || !(x <= 155.0)) {
		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 <= (-0.0125d0)) .or. (.not. (x <= 155.0d0))) 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 <= -0.0125) || !(x <= 155.0)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.0125) or not (x <= 155.0):
		tmp = x * (y + -1.0)
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.0125) || !(x <= 155.0))
		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 <= -0.0125) || ~((x <= 155.0)))
		tmp = x * (y + -1.0);
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.0125], N[Not[LessEqual[x, 155.0]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.012500000000000001 or 155 < x

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate-+l- 100.0%

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

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 97.3%

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

   if -0.012500000000000001 < x < 155

   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 55.0%

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

      1. neg-mul-1 55.0%

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

      2. sub-neg 55.0%

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

   7. Simplified 55.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0125 \lor \neg \left(x \leq 155\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \lor \neg \left(y \leq 1.55\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.55) (not (<= y 1.55)))
   (* y (- x 0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.55) || !(y <= 1.55)) {
		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 <= (-1.55d0)) .or. (.not. (y <= 1.55d0))) 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 <= -1.55) || !(y <= 1.55)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.55) or not (y <= 1.55):
		tmp = y * (x - 0.5)
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.55) || !(y <= 1.55))
		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 <= -1.55) || ~((y <= 1.55)))
		tmp = y * (x - 0.5);
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.55], N[Not[LessEqual[y, 1.55]], $MachinePrecision]], N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000004 or 1.55000000000000004 < y

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 96.3%

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

   if -1.55000000000000004 < y < 1.55000000000000004

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.1%

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

      1. neg-mul-1 98.1%

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

      2. sub-neg 98.1%

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

   7. Simplified 98.1%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \lor \neg \left(y \leq 1.55\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75 \lor \neg \left(x \leq 0.9\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.75) (not (<= x 0.9)))
   (* x (+ y -1.0))
   (- 0.918938533204673 (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.75) || !(x <= 0.9)) {
		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 <= (-0.75d0)) .or. (.not. (x <= 0.9d0))) 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 <= -0.75) || !(x <= 0.9)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = 0.918938533204673 - (y * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.75) or not (x <= 0.9):
		tmp = x * (y + -1.0)
	else:
		tmp = 0.918938533204673 - (y * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.75) || !(x <= 0.9))
		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 <= -0.75) || ~((x <= 0.9)))
		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, -0.75], N[Not[LessEqual[x, 0.9]], $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 < -0.75 or 0.900000000000000022 < x

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate-+l- 100.0%

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

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 98.7%

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

   if -0.75 < x < 0.900000000000000022

   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 96.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75 \lor \neg \left(x \leq 0.9\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* x (+ y -1.0))
   (if (<= x 0.6) (- 0.918938533204673 (* y 0.5)) (- (* x y) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = x * (y + -1.0);
	} else if (x <= 0.6) {
		tmp = 0.918938533204673 - (y * 0.5);
	} else {
		tmp = (x * 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 <= (-0.75d0)) then
        tmp = x * (y + (-1.0d0))
    else if (x <= 0.6d0) then
        tmp = 0.918938533204673d0 - (y * 0.5d0)
    else
        tmp = (x * y) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = x * (y + -1.0);
	} else if (x <= 0.6) {
		tmp = 0.918938533204673 - (y * 0.5);
	} else {
		tmp = (x * y) - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = x * (y + -1.0)
	elif x <= 0.6:
		tmp = 0.918938533204673 - (y * 0.5)
	else:
		tmp = (x * y) - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(x * Float64(y + -1.0));
	elseif (x <= 0.6)
		tmp = Float64(0.918938533204673 - Float64(y * 0.5));
	else
		tmp = Float64(Float64(x * y) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = x * (y + -1.0);
	elseif (x <= 0.6)
		tmp = 0.918938533204673 - (y * 0.5);
	else
		tmp = (x * y) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.6], N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate-+l- 100.0%

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

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 99.5%

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

   if -0.75 < x < 0.599999999999999978

   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 96.9%

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

   if 0.599999999999999978 < x

   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. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate-+l- 100.0%

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

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 97.9%

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

      1. sub-neg 97.9%

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

      2. distribute-rgt-in 97.9%

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

      3. *-commutative 97.9%

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

      4. metadata-eval 97.9%

         \[\leadsto x \cdot y + \color{blue}{-1} \cdot x \]

      5. neg-mul-1 97.9%

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

   9. Applied egg-rr 97.9%

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

       1. unsub-neg 97.9%

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

       2. *-commutative 97.9%

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

   11. Applied egg-rr 97.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;0.918938533204673 - y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \lor \neg \left(y \leq 1.6\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.5) (not (<= y 1.6))) (* x y) (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.5) || !(y <= 1.6)) {
		tmp = x * y;
	} 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 <= (-4.5d0)) .or. (.not. (y <= 1.6d0))) then
        tmp = x * y
    else
        tmp = 0.918938533204673d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.5) || !(y <= 1.6)) {
		tmp = x * y;
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.5) or not (y <= 1.6):
		tmp = x * y
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.5) || !(y <= 1.6))
		tmp = Float64(x * y);
	else
		tmp = Float64(0.918938533204673 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.5) || ~((y <= 1.6)))
		tmp = x * y;
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.5], N[Not[LessEqual[y, 1.6]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5 or 1.6000000000000001 < y

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 99.9%

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

      13. fma-neg 99.9%

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

      14. +-commutative 99.9%

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

      15. metadata-eval 99.9%

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

      16. neg-sub0 99.9%

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

      17. associate-+l- 99.9%

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

      18. neg-sub0 99.9%

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

      19. +-commutative 99.9%

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

      20. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 49.4%

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

   8. Taylor expanded in y around inf 46.3%

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

   if -4.5 < y < 1.6000000000000001

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.1%

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

      1. neg-mul-1 98.1%

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

      2. sub-neg 98.1%

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

   7. Simplified 98.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \lor \neg \left(y \leq 1.6\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -960000000 \lor \neg \left(x \leq 30000000000000\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -960000000.0) (not (<= x 30000000000000.0)))
   (- x)
   0.918938533204673))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -960000000.0) || !(x <= 30000000000000.0)) {
		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 <= (-960000000.0d0)) .or. (.not. (x <= 30000000000000.0d0))) 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 <= -960000000.0) || !(x <= 30000000000000.0)) {
		tmp = -x;
	} else {
		tmp = 0.918938533204673;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -960000000.0) or not (x <= 30000000000000.0):
		tmp = -x
	else:
		tmp = 0.918938533204673
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -960000000.0) || !(x <= 30000000000000.0))
		tmp = Float64(-x);
	else
		tmp = 0.918938533204673;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -960000000.0) || ~((x <= 30000000000000.0)))
		tmp = -x;
	else
		tmp = 0.918938533204673;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -960000000.0], N[Not[LessEqual[x, 30000000000000.0]], $MachinePrecision]], (-x), 0.918938533204673]

Derivation

1. Split input into 2 regimes

2. if x < -9.6e8 or 3e13 < x

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-+r+ 100.0%

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

      8. unsub-neg 100.0%

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

      9. associate-+l- 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. distribute-lft-out 100.0%

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

      13. fma-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. metadata-eval 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate-+l- 100.0%

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

      18. neg-sub0 100.0%

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

      19. +-commutative 100.0%

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

      20. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 99.9%

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

   8. Taylor expanded in y around 0 50.9%

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

      1. neg-mul-1 50.9%

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

   10. Simplified 50.9%

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

   if -9.6e8 < x < 3e13

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.6%

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

   6. Taylor expanded in y around 0 52.4%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -960000000 \lor \neg \left(x \leq 30000000000000\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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. cancel-sign-sub-inv 100.0%

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

   2. +-commutative 100.0%

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

   3. sub-neg 100.0%

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

   4. distribute-rgt-in 100.0%

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

   5. metadata-eval 100.0%

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

   6. neg-mul-1 100.0%

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

   7. associate-+r+ 100.0%

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

   8. unsub-neg 100.0%

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

   9. associate-+l- 100.0%

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

   10. distribute-lft-neg-out 100.0%

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

   11. distribute-rgt-neg-in 100.0%

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

   12. distribute-lft-out 100.0%

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

   13. fma-neg 100.0%

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

   14. +-commutative 100.0%

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

   15. metadata-eval 100.0%

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

   16. neg-sub0 100.0%

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

   17. associate-+l- 100.0%

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

   18. neg-sub0 100.0%

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

   19. +-commutative 100.0%

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

   20. unsub-neg 100.0%

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

3. Simplified 100.0%

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

   1. fma-undefine 100.0%

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

   2. associate-+r- 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 12: 26.0% accurate, 11.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 0.918938533204673)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 0.918938533204673

Julia

function code(x, y)
	return 0.918938533204673
end

MATLAB

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

Wolfram

code[x_, y_] := 0.918938533204673

Derivation

1. Initial program 100.0%

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

   1. associate-+l- 100.0%

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

   2. sub-neg 100.0%

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

   3. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around inf 76.3%

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

6. Taylor expanded in y around 0 30.0%

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

7. Final simplification 30.0%

   \[\leadsto 0.918938533204673 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024078 
(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))