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

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 9

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. +-commutative 100.0%

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

   2. cancel-sign-sub-inv 100.0%

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

   3. +-commutative 100.0%

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

   4. associate-+r+ 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate-+l- 100.0%

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

   7. sub-neg 100.0%

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

   8. distribute-rgt-in 100.0%

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

   9. metadata-eval 100.0%

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

   10. neg-mul-1 100.0%

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

   11. associate--r+ 100.0%

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

   12. distribute-lft-out-- 100.0%

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

   13. unsub-neg 100.0%

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

   14. fmm-def 100.0%

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

   15. unsub-neg 100.0%

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

   16. remove-double-neg 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 100.0%

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

Alternative 2: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + -1\right)\\ \mathbf{if}\;x \leq -0.00085:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-297}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+14}:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (+ y -1.0))))
   (if (<= x -0.00085)
     t_0
     (if (<= x 1.1e-297)
       (* y -0.5)
       (if (<= x 3.1e+14) (- 0.918938533204673 x) t_0)))))

C

double code(double x, double y) {
	double t_0 = x * (y + -1.0);
	double tmp;
	if (x <= -0.00085) {
		tmp = t_0;
	} else if (x <= 1.1e-297) {
		tmp = y * -0.5;
	} else if (x <= 3.1e+14) {
		tmp = 0.918938533204673 - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + (-1.0d0))
    if (x <= (-0.00085d0)) then
        tmp = t_0
    else if (x <= 1.1d-297) then
        tmp = y * (-0.5d0)
    else if (x <= 3.1d+14) then
        tmp = 0.918938533204673d0 - x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (y + -1.0);
	double tmp;
	if (x <= -0.00085) {
		tmp = t_0;
	} else if (x <= 1.1e-297) {
		tmp = y * -0.5;
	} else if (x <= 3.1e+14) {
		tmp = 0.918938533204673 - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y + -1.0)
	tmp = 0
	if x <= -0.00085:
		tmp = t_0
	elif x <= 1.1e-297:
		tmp = y * -0.5
	elif x <= 3.1e+14:
		tmp = 0.918938533204673 - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y + -1.0))
	tmp = 0.0
	if (x <= -0.00085)
		tmp = t_0;
	elseif (x <= 1.1e-297)
		tmp = Float64(y * -0.5);
	elseif (x <= 3.1e+14)
		tmp = Float64(0.918938533204673 - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (y + -1.0);
	tmp = 0.0;
	if (x <= -0.00085)
		tmp = t_0;
	elseif (x <= 1.1e-297)
		tmp = y * -0.5;
	elseif (x <= 3.1e+14)
		tmp = 0.918938533204673 - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.00085], t$95$0, If[LessEqual[x, 1.1e-297], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 3.1e+14], N[(0.918938533204673 - x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.49999999999999953e-4 or 3.1e14 < 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. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.7%

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

      1. mul-1-neg 97.7%

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

      2. neg-sub0 97.7%

         \[\leadsto \color{blue}{0 - x \cdot \left(1 + -1 \cdot y\right)} \]

      3. mul-1-neg 97.7%

         \[\leadsto 0 - x \cdot \left(1 + \color{blue}{\left(-y\right)}\right) \]

      4. distribute-rgt-in 97.8%

         \[\leadsto 0 - \color{blue}{\left(1 \cdot x + \left(-y\right) \cdot x\right)} \]

      5. fma-define 97.8%

         \[\leadsto 0 - \color{blue}{\mathsf{fma}\left(1, x, \left(-y\right) \cdot x\right)} \]

      6. distribute-lft-neg-in 97.8%

         \[\leadsto 0 - \mathsf{fma}\left(1, x, \color{blue}{-y \cdot x}\right) \]

      7. fmm-def 97.8%

         \[\leadsto 0 - \color{blue}{\left(1 \cdot x - y \cdot x\right)} \]

      8. *-lft-identity 97.8%

         \[\leadsto 0 - \left(\color{blue}{x} - y \cdot x\right) \]

      9. associate-+l- 97.8%

         \[\leadsto \color{blue}{\left(0 - x\right) + y \cdot x} \]

      10. neg-sub0 97.8%

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

      11. neg-mul-1 97.8%

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

      12. distribute-rgt-in 97.7%

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

      13. +-commutative 97.7%

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

   7. Simplified 97.7%

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

   if -8.49999999999999953e-4 < x < 1.0999999999999999e-297

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 61.3%

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

   6. Taylor expanded in x around 0 59.7%

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

   if 1.0999999999999999e-297 < x < 3.1e14

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 59.0%

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

Alternative 3: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.053 \lor \neg \left(y \leq 7 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot x + \left(0.918938533204673 - y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.053) (not (<= y 7e-7)))
   (+ (* y x) (- 0.918938533204673 (* y 0.5)))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.053) || !(y <= 7e-7)) {
		tmp = (y * x) + (0.918938533204673 - (y * 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 <= (-0.053d0)) .or. (.not. (y <= 7d-7))) then
        tmp = (y * x) + (0.918938533204673d0 - (y * 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 <= -0.053) || !(y <= 7e-7)) {
		tmp = (y * x) + (0.918938533204673 - (y * 0.5));
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.053) or not (y <= 7e-7):
		tmp = (y * x) + (0.918938533204673 - (y * 0.5))
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.053) || !(y <= 7e-7))
		tmp = Float64(Float64(y * x) + Float64(0.918938533204673 - Float64(y * 0.5)));
	else
		tmp = Float64(0.918938533204673 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -0.053) || ~((y <= 7e-7)))
		tmp = (y * x) + (0.918938533204673 - (y * 0.5));
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.053], N[Not[LessEqual[y, 7e-7]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] + N[(0.918938533204673 - N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0529999999999999985 or 6.99999999999999968e-7 < 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 99.1%

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

   if -0.0529999999999999985 < y < 6.99999999999999968e-7

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.4%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.053 \lor \neg \left(y \leq 7 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot x + \left(0.918938533204673 - y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -540000000000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.85:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+215}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -540000000000.0)
   (* y x)
   (if (<= y 1.85)
     (- 0.918938533204673 x)
     (if (<= y 2.3e+215) (* y -0.5) (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -540000000000.0) {
		tmp = y * x;
	} else if (y <= 1.85) {
		tmp = 0.918938533204673 - x;
	} else if (y <= 2.3e+215) {
		tmp = y * -0.5;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-540000000000.0d0)) then
        tmp = y * x
    else if (y <= 1.85d0) then
        tmp = 0.918938533204673d0 - x
    else if (y <= 2.3d+215) then
        tmp = y * (-0.5d0)
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -540000000000.0) {
		tmp = y * x;
	} else if (y <= 1.85) {
		tmp = 0.918938533204673 - x;
	} else if (y <= 2.3e+215) {
		tmp = y * -0.5;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -540000000000.0:
		tmp = y * x
	elif y <= 1.85:
		tmp = 0.918938533204673 - x
	elif y <= 2.3e+215:
		tmp = y * -0.5
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -540000000000.0)
		tmp = Float64(y * x);
	elseif (y <= 1.85)
		tmp = Float64(0.918938533204673 - x);
	elseif (y <= 2.3e+215)
		tmp = Float64(y * -0.5);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -540000000000.0)
		tmp = y * x;
	elseif (y <= 1.85)
		tmp = 0.918938533204673 - x;
	elseif (y <= 2.3e+215)
		tmp = y * -0.5;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -540000000000.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.85], N[(0.918938533204673 - x), $MachinePrecision], If[LessEqual[y, 2.3e+215], N[(y * -0.5), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4e11 or 2.3000000000000001e215 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   6. Taylor expanded in x around inf 56.9%

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

      1. *-commutative 56.9%

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

   8. Simplified 56.9%

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

   if -5.4e11 < y < 1.8500000000000001

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.5%

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

   if 1.8500000000000001 < y < 2.3000000000000001e215

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 94.2%

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

   6. Taylor expanded in x around 0 61.9%

      \[\leadsto y \cdot \color{blue}{-0.5} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 48.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.5:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 0.85:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+139}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.5)
   (* y x)
   (if (<= x 0.85) (* y -0.5) (if (<= x 6.8e+139) (- x) (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.5) {
		tmp = y * x;
	} else if (x <= 0.85) {
		tmp = y * -0.5;
	} else if (x <= 6.8e+139) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.5d0)) then
        tmp = y * x
    else if (x <= 0.85d0) then
        tmp = y * (-0.5d0)
    else if (x <= 6.8d+139) then
        tmp = -x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.5) {
		tmp = y * x;
	} else if (x <= 0.85) {
		tmp = y * -0.5;
	} else if (x <= 6.8e+139) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.5:
		tmp = y * x
	elif x <= 0.85:
		tmp = y * -0.5
	elif x <= 6.8e+139:
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.5)
		tmp = Float64(y * x);
	elseif (x <= 0.85)
		tmp = Float64(y * -0.5);
	elseif (x <= 6.8e+139)
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.5)
		tmp = y * x;
	elseif (x <= 0.85)
		tmp = y * -0.5;
	elseif (x <= 6.8e+139)
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.5], N[(y * x), $MachinePrecision], If[LessEqual[x, 0.85], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 6.8e+139], (-x), N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.5 or 6.8000000000000005e139 < 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. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 57.7%

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

   6. Taylor expanded in x around inf 57.0%

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

      1. *-commutative 57.0%

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

   8. Simplified 57.0%

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

   if -0.5 < x < 0.849999999999999978

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 53.2%

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

   6. Taylor expanded in x around 0 52.2%

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

   if 0.849999999999999978 < x < 6.8000000000000005e139

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 62.2%

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

   6. Taylor expanded in x around inf 53.9%

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

      1. neg-mul-1 53.9%

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

   8. Simplified 53.9%

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

Alternative 6: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \lor \neg \left(y \leq 1.25\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.3) (not (<= y 1.25)))
   (* y (- x 0.5))
   (- 0.918938533204673 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.3) || !(y <= 1.25)) {
		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 <= (-1.3d0)) .or. (.not. (y <= 1.25d0))) 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 <= -1.3) || !(y <= 1.25)) {
		tmp = y * (x - 0.5);
	} else {
		tmp = 0.918938533204673 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.3) or not (y <= 1.25):
		tmp = y * (x - 0.5)
	else:
		tmp = 0.918938533204673 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.3) || !(y <= 1.25))
		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 <= -1.3) || ~((y <= 1.25)))
		tmp = y * (x - 0.5);
	else
		tmp = 0.918938533204673 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.3], N[Not[LessEqual[y, 1.25]], $MachinePrecision]], N[(y * N[(x - 0.5), $MachinePrecision]), $MachinePrecision], N[(0.918938533204673 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.30000000000000004 or 1.25 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 97.9%

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

   if -1.30000000000000004 < y < 1.25

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.2%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \lor \neg \left(y \leq 1.25\right):\\ \;\;\;\;y \cdot \left(x - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -24.5 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -24.5) (not (<= y 1.0))) (* y -0.5) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -24.5) || !(y <= 1.0)) {
		tmp = y * -0.5;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-24.5d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (-0.5d0)
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -24.5) || !(y <= 1.0)) {
		tmp = y * -0.5;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -24.5) or not (y <= 1.0):
		tmp = y * -0.5
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -24.5) || !(y <= 1.0))
		tmp = Float64(y * -0.5);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -24.5) || ~((y <= 1.0)))
		tmp = y * -0.5;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -24.5], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * -0.5), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -24.5 or 1 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 97.9%

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

   6. Taylor expanded in x around 0 50.7%

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

   if -24.5 < y < 1

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-+l- 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate--r+ 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. unsub-neg 100.0%

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

      14. fmm-def 100.0%

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

      15. unsub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.2%

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

   6. Taylor expanded in x around inf 47.8%

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

      1. neg-mul-1 47.8%

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

   8. Simplified 47.8%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -24.5 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 27.1% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -x

Julia

function code(x, y)
	return Float64(-x)
end

MATLAB

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

Wolfram

code[x_, y_] := (-x)

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. cancel-sign-sub-inv 100.0%

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

   3. +-commutative 100.0%

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

   4. associate-+r+ 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate-+l- 100.0%

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

   7. sub-neg 100.0%

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

   8. distribute-rgt-in 100.0%

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

   9. metadata-eval 100.0%

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

   10. neg-mul-1 100.0%

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

   11. associate--r+ 100.0%

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

   12. distribute-lft-out-- 100.0%

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

   13. unsub-neg 100.0%

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

   14. fmm-def 100.0%

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

   15. unsub-neg 100.0%

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

   16. remove-double-neg 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 48.1%

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

6. Taylor expanded in x around inf 24.1%

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

   1. neg-mul-1 24.1%

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

8. Simplified 24.1%

   \[\leadsto \color{blue}{-x} \]
9. Add Preprocessing

Alternative 9: 2.6% accurate, 11.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. cancel-sign-sub-inv 100.0%

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

   3. +-commutative 100.0%

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

   4. associate-+r+ 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate-+l- 100.0%

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

   7. sub-neg 100.0%

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

   8. distribute-rgt-in 100.0%

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

   9. metadata-eval 100.0%

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

   10. neg-mul-1 100.0%

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

   11. associate--r+ 100.0%

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

   12. distribute-lft-out-- 100.0%

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

   13. unsub-neg 100.0%

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

   14. fmm-def 100.0%

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

   15. unsub-neg 100.0%

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

   16. remove-double-neg 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 48.1%

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

6. Taylor expanded in x around inf 24.1%

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

   1. neg-mul-1 24.1%

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

8. Simplified 24.1%

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

   1. neg-sub0 24.1%

      \[\leadsto \color{blue}{0 - x} \]

   2. sub-neg 24.1%

      \[\leadsto \color{blue}{0 + \left(-x\right)} \]

   3. add-sqr-sqrt 11.5%

      \[\leadsto 0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

   4. sqrt-unprod 12.7%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

   5. sqr-neg 12.7%

      \[\leadsto 0 + \sqrt{\color{blue}{x \cdot x}} \]

   6. sqrt-unprod 1.5%

      \[\leadsto 0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

   7. add-sqr-sqrt 2.7%

      \[\leadsto 0 + \color{blue}{x} \]

10. Applied egg-rr 2.7%

    \[\leadsto \color{blue}{0 + x} \]
11. Step-by-step derivation

    1. +-lft-identity 2.7%

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

12. Simplified 2.7%

    \[\leadsto \color{blue}{x} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024172 
(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))