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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 9

Speedup: 1.5×

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, 1.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(\frac{918938533204673}{1000000000000000} + x \cdot \left(y - 1\right)\right) - \frac{1}{2} \cdot y} \]

5. Applied rewrites 100.0%

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

Alternative 2: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, y, 0.918938533204673\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-9}:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+265}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, y, 0.918938533204673\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.4e-8)
   (fma -0.5 y 0.918938533204673)
   (if (<= y 2.25e-9)
     (- 0.918938533204673 x)
     (if (<= y 2.65e+265) (fma -0.5 y 0.918938533204673) (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.4e-8) {
		tmp = fma(-0.5, y, 0.918938533204673);
	} else if (y <= 2.25e-9) {
		tmp = 0.918938533204673 - x;
	} else if (y <= 2.65e+265) {
		tmp = fma(-0.5, y, 0.918938533204673);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.4e-8)
		tmp = fma(-0.5, y, 0.918938533204673);
	elseif (y <= 2.25e-9)
		tmp = Float64(0.918938533204673 - x);
	elseif (y <= 2.65e+265)
		tmp = fma(-0.5, y, 0.918938533204673);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.4e-8], N[(-0.5 * y + 0.918938533204673), $MachinePrecision], If[LessEqual[y, 2.25e-9], N[(0.918938533204673 - x), $MachinePrecision], If[LessEqual[y, 2.65e+265], N[(-0.5 * y + 0.918938533204673), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.40000000000000005e-8 or 2.24999999999999988e-9 < y < 2.65000000000000017e265

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} - \frac{1}{2} \cdot y} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2} \cdot y\right)\right) + \frac{918938533204673}{1000000000000000}} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot y} + \frac{918938533204673}{1000000000000000} \]

      4. metadata-eval N/A

         \[\leadsto \color{blue}{\frac{-1}{2}} \cdot y + \frac{918938533204673}{1000000000000000} \]

      5. lower-fma.f64 57.2

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

   5. Applied rewrites 57.2%

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

   if -5.40000000000000005e-8 < y < 2.24999999999999988e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} + -1 \cdot x} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{918938533204673}{1000000000000000} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} - x} \]

      3. lower--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   if 2.65000000000000017e265 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{918938533204673}{1000000000000000} + x \cdot \left(y - 1\right)\right) - \frac{1}{2} \cdot y} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(\frac{1}{2} + -1 \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(\frac{1}{2} + -1 \cdot x\right) \cdot y\right)} \]

      2. mul-1-neg N/A

         \[\leadsto -1 \cdot \left(\left(\frac{1}{2} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \cdot y\right) \]

      3. sub-neg N/A

         \[\leadsto -1 \cdot \left(\color{blue}{\left(\frac{1}{2} - x\right)} \cdot y\right) \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{1}{2} - x\right)\right) \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{1}{2} - x\right)\right) \cdot y} \]

      6. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{2} - x\right)\right)\right)} \cdot y \]

      7. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \left(\frac{1}{2} - x\right)\right)} \cdot y \]

      8. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(0 - \frac{1}{2}\right) + x\right)} \cdot y \]

      9. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} + x\right) \cdot y \]

      10. +-commutative N/A

          \[\leadsto \color{blue}{\left(x + \frac{-1}{2}\right)} \cdot y \]

      11. metadata-eval N/A

          \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right) \cdot y \]

      12. sub-neg N/A

          \[\leadsto \color{blue}{\left(x - \frac{1}{2}\right)} \cdot y \]

      13. lower--.f64 100.0

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

   8. Applied rewrites 100.0%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 86.8%

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

Alternative 3: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -270:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;y \leq 1.82:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+265}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -270.0)
   (* -0.5 y)
   (if (<= y 1.82)
     (- 0.918938533204673 x)
     (if (<= y 2.65e+265) (* -0.5 y) (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -270.0) {
		tmp = -0.5 * y;
	} else if (y <= 1.82) {
		tmp = 0.918938533204673 - x;
	} else if (y <= 2.65e+265) {
		tmp = -0.5 * y;
	} 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 <= (-270.0d0)) then
        tmp = (-0.5d0) * y
    else if (y <= 1.82d0) then
        tmp = 0.918938533204673d0 - x
    else if (y <= 2.65d+265) then
        tmp = (-0.5d0) * y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -270.0) {
		tmp = -0.5 * y;
	} else if (y <= 1.82) {
		tmp = 0.918938533204673 - x;
	} else if (y <= 2.65e+265) {
		tmp = -0.5 * y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -270.0:
		tmp = -0.5 * y
	elif y <= 1.82:
		tmp = 0.918938533204673 - x
	elif y <= 2.65e+265:
		tmp = -0.5 * y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -270.0)
		tmp = Float64(-0.5 * y);
	elseif (y <= 1.82)
		tmp = Float64(0.918938533204673 - x);
	elseif (y <= 2.65e+265)
		tmp = Float64(-0.5 * y);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -270.0)
		tmp = -0.5 * y;
	elseif (y <= 1.82)
		tmp = 0.918938533204673 - x;
	elseif (y <= 2.65e+265)
		tmp = -0.5 * y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -270.0], N[(-0.5 * y), $MachinePrecision], If[LessEqual[y, 1.82], N[(0.918938533204673 - x), $MachinePrecision], If[LessEqual[y, 2.65e+265], N[(-0.5 * y), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -270 or 1.82000000000000006 < y < 2.65000000000000017e265

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{918938533204673}{1000000000000000} + x \cdot \left(y - 1\right)\right) - \frac{1}{2} \cdot y} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(\frac{1}{2} + -1 \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(\frac{1}{2} + -1 \cdot x\right) \cdot y\right)} \]

      2. mul-1-neg N/A

         \[\leadsto -1 \cdot \left(\left(\frac{1}{2} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \cdot y\right) \]

      3. sub-neg N/A

         \[\leadsto -1 \cdot \left(\color{blue}{\left(\frac{1}{2} - x\right)} \cdot y\right) \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{1}{2} - x\right)\right) \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{1}{2} - x\right)\right) \cdot y} \]

      6. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{2} - x\right)\right)\right)} \cdot y \]

      7. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \left(\frac{1}{2} - x\right)\right)} \cdot y \]

      8. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(0 - \frac{1}{2}\right) + x\right)} \cdot y \]

      9. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} + x\right) \cdot y \]

      10. +-commutative N/A

          \[\leadsto \color{blue}{\left(x + \frac{-1}{2}\right)} \cdot y \]

      11. metadata-eval N/A

          \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right) \cdot y \]

      12. sub-neg N/A

          \[\leadsto \color{blue}{\left(x - \frac{1}{2}\right)} \cdot y \]

      13. lower--.f64 99.1

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

   8. Applied rewrites 99.1%

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

   9. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 55.2%

       \[\leadsto -0.5 \cdot y \]

   if -270 < y < 1.82000000000000006

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} + -1 \cdot x} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{918938533204673}{1000000000000000} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} - x} \]

      3. lower--.f64 97.3

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

   5. Applied rewrites 97.3%

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

   if 2.65000000000000017e265 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{918938533204673}{1000000000000000} + x \cdot \left(y - 1\right)\right) - \frac{1}{2} \cdot y} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(\frac{1}{2} + -1 \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(\frac{1}{2} + -1 \cdot x\right) \cdot y\right)} \]

      2. mul-1-neg N/A

         \[\leadsto -1 \cdot \left(\left(\frac{1}{2} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \cdot y\right) \]

      3. sub-neg N/A

         \[\leadsto -1 \cdot \left(\color{blue}{\left(\frac{1}{2} - x\right)} \cdot y\right) \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{1}{2} - x\right)\right) \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{1}{2} - x\right)\right) \cdot y} \]

      6. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{2} - x\right)\right)\right)} \cdot y \]

      7. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \left(\frac{1}{2} - x\right)\right)} \cdot y \]

      8. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(0 - \frac{1}{2}\right) + x\right)} \cdot y \]

      9. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} + x\right) \cdot y \]

      10. +-commutative N/A

          \[\leadsto \color{blue}{\left(x + \frac{-1}{2}\right)} \cdot y \]

      11. metadata-eval N/A

          \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right) \cdot y \]

      12. sub-neg N/A

          \[\leadsto \color{blue}{\left(x - \frac{1}{2}\right)} \cdot y \]

      13. lower--.f64 100.0

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

   8. Applied rewrites 100.0%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 86.8%

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

Alternative 4: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 0.5\right) \cdot y + 0.918938533204673\\ \mathbf{if}\;y \leq -0.092:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.04:\\ \;\;\;\;0.918938533204673 - \mathsf{fma}\left(-x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (* (- x 0.5) y) 0.918938533204673)))
   (if (<= y -0.092)
     t_0
     (if (<= y 0.04) (- 0.918938533204673 (fma (- x) y x)) t_0))))

C

double code(double x, double y) {
	double t_0 = ((x - 0.5) * y) + 0.918938533204673;
	double tmp;
	if (y <= -0.092) {
		tmp = t_0;
	} else if (y <= 0.04) {
		tmp = 0.918938533204673 - fma(-x, y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(x - 0.5) * y) + 0.918938533204673)
	tmp = 0.0
	if (y <= -0.092)
		tmp = t_0;
	elseif (y <= 0.04)
		tmp = Float64(0.918938533204673 - fma(Float64(-x), y, x));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(x - 0.5), $MachinePrecision] * y), $MachinePrecision] + 0.918938533204673), $MachinePrecision]}, If[LessEqual[y, -0.092], t$95$0, If[LessEqual[y, 0.04], N[(0.918938533204673 - N[((-x) * y + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.091999999999999998 or 0.0400000000000000008 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(x - \frac{1}{2}\right)} + \frac{918938533204673}{1000000000000000} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto y \cdot \color{blue}{\left(x + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)} + \frac{918938533204673}{1000000000000000} \]

      2. remove-double-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right) + \frac{918938533204673}{1000000000000000} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{-1 \cdot x}\right)\right) + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right) + \frac{918938533204673}{1000000000000000} \]

      4. distribute-neg-in N/A

         \[\leadsto y \cdot \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot x + \frac{1}{2}\right)\right)\right)} + \frac{918938533204673}{1000000000000000} \]

      5. +-commutative N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{1}{2} + -1 \cdot x\right)}\right)\right) + \frac{918938533204673}{1000000000000000} \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{2} + -1 \cdot x\right)\right)\right) \cdot y} + \frac{918938533204673}{1000000000000000} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{2} + -1 \cdot x\right)\right)\right) \cdot y} + \frac{918938533204673}{1000000000000000} \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(-1 \cdot x + \frac{1}{2}\right)}\right)\right) \cdot y + \frac{918938533204673}{1000000000000000} \]

      9. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(-1 \cdot x\right)\right) + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)} \cdot y + \frac{918938533204673}{1000000000000000} \]

      10. mul-1-neg N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right) + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right) \cdot y + \frac{918938533204673}{1000000000000000} \]

      11. remove-double-neg N/A

          \[\leadsto \left(\color{blue}{x} + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right) \cdot y + \frac{918938533204673}{1000000000000000} \]

      12. sub-neg N/A

          \[\leadsto \color{blue}{\left(x - \frac{1}{2}\right)} \cdot y + \frac{918938533204673}{1000000000000000} \]

      13. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -0.091999999999999998 < y < 0.0400000000000000008

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{918938533204673}{1000000000000000} + x \cdot \left(y - 1\right)\right) - \frac{1}{2} \cdot y} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \frac{918938533204673}{1000000000000000} - \mathsf{fma}\left(-1 \cdot x, y, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 99.7%

      \[\leadsto 0.918938533204673 - \mathsf{fma}\left(-x, y, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.918938533204673 - \mathsf{fma}\left(-x, y, x\right)\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{-11}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, y, 0.918938533204673\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 0.918938533204673 (fma (- x) y x))))
   (if (<= x -5.1e-11)
     t_0
     (if (<= x 1.25e-7) (fma -0.5 y 0.918938533204673) t_0))))

C

double code(double x, double y) {
	double t_0 = 0.918938533204673 - fma(-x, y, x);
	double tmp;
	if (x <= -5.1e-11) {
		tmp = t_0;
	} else if (x <= 1.25e-7) {
		tmp = fma(-0.5, y, 0.918938533204673);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(0.918938533204673 - fma(Float64(-x), y, x))
	tmp = 0.0
	if (x <= -5.1e-11)
		tmp = t_0;
	elseif (x <= 1.25e-7)
		tmp = fma(-0.5, y, 0.918938533204673);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.918938533204673 - N[((-x) * y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.1e-11], t$95$0, If[LessEqual[x, 1.25e-7], N[(-0.5 * y + 0.918938533204673), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.09999999999999984e-11 or 1.24999999999999994e-7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{918938533204673}{1000000000000000} + x \cdot \left(y - 1\right)\right) - \frac{1}{2} \cdot y} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \frac{918938533204673}{1000000000000000} - \mathsf{fma}\left(-1 \cdot x, y, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 97.9%

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

   if -5.09999999999999984e-11 < x < 1.24999999999999994e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} - \frac{1}{2} \cdot y} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2} \cdot y\right)\right) + \frac{918938533204673}{1000000000000000}} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot y} + \frac{918938533204673}{1000000000000000} \]

      4. metadata-eval N/A

         \[\leadsto \color{blue}{\frac{-1}{2}} \cdot y + \frac{918938533204673}{1000000000000000} \]

      5. lower-fma.f64 100.0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5, y, 0.918938533204673\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 0.5\right) \cdot y\\ \mathbf{if}\;y \leq -1.25:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.2:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (- x 0.5) y)))
   (if (<= y -1.25) t_0 (if (<= y 1.2) (- 0.918938533204673 x) t_0))))

C

double code(double x, double y) {
	double t_0 = (x - 0.5) * y;
	double tmp;
	if (y <= -1.25) {
		tmp = t_0;
	} else if (y <= 1.2) {
		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 - 0.5d0) * y
    if (y <= (-1.25d0)) then
        tmp = t_0
    else if (y <= 1.2d0) 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 - 0.5) * y;
	double tmp;
	if (y <= -1.25) {
		tmp = t_0;
	} else if (y <= 1.2) {
		tmp = 0.918938533204673 - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - 0.5) * y
	tmp = 0
	if y <= -1.25:
		tmp = t_0
	elif y <= 1.2:
		tmp = 0.918938533204673 - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - 0.5) * y)
	tmp = 0.0
	if (y <= -1.25)
		tmp = t_0;
	elseif (y <= 1.2)
		tmp = Float64(0.918938533204673 - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - 0.5) * y;
	tmp = 0.0;
	if (y <= -1.25)
		tmp = t_0;
	elseif (y <= 1.2)
		tmp = 0.918938533204673 - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - 0.5), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.25], t$95$0, If[LessEqual[y, 1.2], N[(0.918938533204673 - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25 or 1.19999999999999996 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{918938533204673}{1000000000000000} + x \cdot \left(y - 1\right)\right) - \frac{1}{2} \cdot y} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(\frac{1}{2} + -1 \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(\frac{1}{2} + -1 \cdot x\right) \cdot y\right)} \]

      2. mul-1-neg N/A

         \[\leadsto -1 \cdot \left(\left(\frac{1}{2} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \cdot y\right) \]

      3. sub-neg N/A

         \[\leadsto -1 \cdot \left(\color{blue}{\left(\frac{1}{2} - x\right)} \cdot y\right) \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{1}{2} - x\right)\right) \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{1}{2} - x\right)\right) \cdot y} \]

      6. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{2} - x\right)\right)\right)} \cdot y \]

      7. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \left(\frac{1}{2} - x\right)\right)} \cdot y \]

      8. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(0 - \frac{1}{2}\right) + x\right)} \cdot y \]

      9. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} + x\right) \cdot y \]

      10. +-commutative N/A

          \[\leadsto \color{blue}{\left(x + \frac{-1}{2}\right)} \cdot y \]

      11. metadata-eval N/A

          \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right) \cdot y \]

      12. sub-neg N/A

          \[\leadsto \color{blue}{\left(x - \frac{1}{2}\right)} \cdot y \]

      13. lower--.f64 99.2

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

   8. Applied rewrites 99.2%

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

   if -1.25 < y < 1.19999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} + -1 \cdot x} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{918938533204673}{1000000000000000} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} - x} \]

      3. lower--.f64 97.3

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

   5. Applied rewrites 97.3%

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

Alternative 7: 72.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+28}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.2:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.6e+28) (* y x) (if (<= y 1.2) (- 0.918938533204673 x) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.6e+28) {
		tmp = y * x;
	} else if (y <= 1.2) {
		tmp = 0.918938533204673 - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.6d+28)) then
        tmp = y * x
    else if (y <= 1.2d0) then
        tmp = 0.918938533204673d0 - x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.6e+28) {
		tmp = y * x;
	} else if (y <= 1.2) {
		tmp = 0.918938533204673 - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.6e+28:
		tmp = y * x
	elif y <= 1.2:
		tmp = 0.918938533204673 - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.6e+28)
		tmp = Float64(y * x);
	elseif (y <= 1.2)
		tmp = Float64(0.918938533204673 - x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.6e+28)
		tmp = y * x;
	elseif (y <= 1.2)
		tmp = 0.918938533204673 - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.6e+28], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.2], N[(0.918938533204673 - x), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6000000000000002e28 or 1.19999999999999996 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{918938533204673}{1000000000000000} + x \cdot \left(y - 1\right)\right) - \frac{1}{2} \cdot y} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(\frac{1}{2} + -1 \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(\frac{1}{2} + -1 \cdot x\right) \cdot y\right)} \]

      2. mul-1-neg N/A

         \[\leadsto -1 \cdot \left(\left(\frac{1}{2} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \cdot y\right) \]

      3. sub-neg N/A

         \[\leadsto -1 \cdot \left(\color{blue}{\left(\frac{1}{2} - x\right)} \cdot y\right) \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{1}{2} - x\right)\right) \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{1}{2} - x\right)\right) \cdot y} \]

      6. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{2} - x\right)\right)\right)} \cdot y \]

      7. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \left(\frac{1}{2} - x\right)\right)} \cdot y \]

      8. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(0 - \frac{1}{2}\right) + x\right)} \cdot y \]

      9. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} + x\right) \cdot y \]

      10. +-commutative N/A

          \[\leadsto \color{blue}{\left(x + \frac{-1}{2}\right)} \cdot y \]

      11. metadata-eval N/A

          \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right) \cdot y \]

      12. sub-neg N/A

          \[\leadsto \color{blue}{\left(x - \frac{1}{2}\right)} \cdot y \]

      13. lower--.f64 99.8

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

   8. Applied rewrites 99.8%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 51.1%

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

   if -2.6000000000000002e28 < y < 1.19999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} + -1 \cdot x} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{918938533204673}{1000000000000000} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} - x} \]

      3. lower--.f64 95.4

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

   5. Applied rewrites 95.4%

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

Alternative 8: 49.8% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 0.918938533204673 - x

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(0.918938533204673 - x), $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. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} + -1 \cdot x} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \frac{918938533204673}{1000000000000000} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \]

   2. unsub-neg N/A

      \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} - x} \]

   3. lower--.f64 51.6

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

5. Applied rewrites 51.6%

   \[\leadsto \color{blue}{0.918938533204673 - x} \]
6. Add Preprocessing

Alternative 9: 26.0% accurate, 20.0× 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. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} + -1 \cdot x} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \frac{918938533204673}{1000000000000000} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \]

   2. unsub-neg N/A

      \[\leadsto \color{blue}{\frac{918938533204673}{1000000000000000} - x} \]

   3. lower--.f64 51.6

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

5. Applied rewrites 51.6%

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

6. Taylor expanded in x around 0

   \[\leadsto \frac{918938533204673}{1000000000000000} \]
7. Step-by-step derivation

8. Applied rewrites 24.4%

   \[\leadsto 0.918938533204673 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024294 
(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))