Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{y + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y y)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / (y + y)

Julia

function code(x, y)
	return Float64(Float64(x + y) / Float64(y + y))
end

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{y + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y y)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / (y + y)

Julia

function code(x, y)
	return Float64(Float64(x + y) / Float64(y + y))
end

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 0.5}{y} - -0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ (* x 0.5) y) -0.5))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[\frac{x + y}{y + y} \]
2. Step-by-step derivation

   1. count-2 99.6%

      \[\leadsto \frac{x + y}{\color{blue}{2 \cdot y}} \]

   2. associate-/l/ 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x + y}{y}}{2}} \]

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. div-sub 100.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{-y}{y}}}{2} \]

   6. /-rgt-identity 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{-\color{blue}{\frac{y}{1}}}{y}}{2} \]

   7. metadata-eval 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{-\frac{y}{\color{blue}{\frac{-1}{-1}}}}{y}}{2} \]

   8. distribute-neg-frac2 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{\frac{y}{-\frac{-1}{-1}}}}{y}}{2} \]

   9. metadata-eval 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{\frac{y}{-\color{blue}{1}}}{y}}{2} \]

   10. metadata-eval 100.0%

       \[\leadsto \frac{\frac{x}{y} - \frac{\frac{y}{\color{blue}{-1}}}{y}}{2} \]

   11. associate-/r* 100.0%

       \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{y}{-1 \cdot y}}}{2} \]

   12. *-commutative 100.0%

       \[\leadsto \frac{\frac{x}{y} - \frac{y}{\color{blue}{y \cdot -1}}}{2} \]

   13. associate-/r* 100.0%

       \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{\frac{y}{y}}{-1}}}{2} \]

   14. *-inverses 100.0%

       \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{1}}{-1}}{2} \]

   15. metadata-eval 100.0%

       \[\leadsto \frac{\frac{x}{y} - \color{blue}{-1}}{2} \]

   16. div-sub 100.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{2} - \frac{-1}{2}} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \frac{0.5}{y} - -0.5} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-*r/ 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

   \[\leadsto \frac{x \cdot 0.5}{y} - -0.5 \]
8. Add Preprocessing

Alternative 2: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-43} \lor \neg \left(x \leq 6.2 \cdot 10^{-12}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.5e-43) (not (<= x 6.2e-12))) (* 0.5 (/ x y)) 0.5))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e-43) || !(x <= 6.2e-12)) {
		tmp = 0.5 * (x / y);
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.5d-43)) .or. (.not. (x <= 6.2d-12))) then
        tmp = 0.5d0 * (x / y)
    else
        tmp = 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e-43) || !(x <= 6.2e-12)) {
		tmp = 0.5 * (x / y);
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.5e-43) or not (x <= 6.2e-12):
		tmp = 0.5 * (x / y)
	else:
		tmp = 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.5e-43) || !(x <= 6.2e-12))
		tmp = Float64(0.5 * Float64(x / y));
	else
		tmp = 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.5e-43) || ~((x <= 6.2e-12)))
		tmp = 0.5 * (x / y);
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.5e-43], N[Not[LessEqual[x, 6.2e-12]], $MachinePrecision]], N[(0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision], 0.5]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000002e-43 or 6.2000000000000002e-12 < x

   1. Initial program 100.0%

      \[\frac{x + y}{y + y} \]
   2. Step-by-step derivation

      1. count-2 100.0%

         \[\leadsto \frac{x + y}{\color{blue}{2 \cdot y}} \]

      2. associate-/l/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x + y}{y}}{2}} \]

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. div-sub 100.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{-y}{y}}}{2} \]

      6. /-rgt-identity 100.0%

         \[\leadsto \frac{\frac{x}{y} - \frac{-\color{blue}{\frac{y}{1}}}{y}}{2} \]

      7. metadata-eval 100.0%

         \[\leadsto \frac{\frac{x}{y} - \frac{-\frac{y}{\color{blue}{\frac{-1}{-1}}}}{y}}{2} \]

      8. distribute-neg-frac2 100.0%

         \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{\frac{y}{-\frac{-1}{-1}}}}{y}}{2} \]

      9. metadata-eval 100.0%

         \[\leadsto \frac{\frac{x}{y} - \frac{\frac{y}{-\color{blue}{1}}}{y}}{2} \]

      10. metadata-eval 100.0%

          \[\leadsto \frac{\frac{x}{y} - \frac{\frac{y}{\color{blue}{-1}}}{y}}{2} \]

      11. associate-/r* 100.0%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{y}{-1 \cdot y}}}{2} \]

      12. *-commutative 100.0%

          \[\leadsto \frac{\frac{x}{y} - \frac{y}{\color{blue}{y \cdot -1}}}{2} \]

      13. associate-/r* 100.0%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{\frac{y}{y}}{-1}}}{2} \]

      14. *-inverses 100.0%

          \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{1}}{-1}}{2} \]

      15. metadata-eval 100.0%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{-1}}{2} \]

      16. div-sub 100.0%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{2} - \frac{-1}{2}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{0.5}{y} - -0.5} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 79.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y}} \]

   if -1.50000000000000002e-43 < x < 6.2000000000000002e-12

   1. Initial program 99.2%

      \[\frac{x + y}{y + y} \]
   2. Step-by-step derivation

      1. count-2 99.2%

         \[\leadsto \frac{x + y}{\color{blue}{2 \cdot y}} \]

      2. associate-/l/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x + y}{y}}{2}} \]

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. div-sub 100.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{-y}{y}}}{2} \]

      6. /-rgt-identity 100.0%

         \[\leadsto \frac{\frac{x}{y} - \frac{-\color{blue}{\frac{y}{1}}}{y}}{2} \]

      7. metadata-eval 100.0%

         \[\leadsto \frac{\frac{x}{y} - \frac{-\frac{y}{\color{blue}{\frac{-1}{-1}}}}{y}}{2} \]

      8. distribute-neg-frac2 100.0%

         \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{\frac{y}{-\frac{-1}{-1}}}}{y}}{2} \]

      9. metadata-eval 100.0%

         \[\leadsto \frac{\frac{x}{y} - \frac{\frac{y}{-\color{blue}{1}}}{y}}{2} \]

      10. metadata-eval 100.0%

          \[\leadsto \frac{\frac{x}{y} - \frac{\frac{y}{\color{blue}{-1}}}{y}}{2} \]

      11. associate-/r* 100.0%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{y}{-1 \cdot y}}}{2} \]

      12. *-commutative 100.0%

          \[\leadsto \frac{\frac{x}{y} - \frac{y}{\color{blue}{y \cdot -1}}}{2} \]

      13. associate-/r* 100.0%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{\frac{y}{y}}{-1}}}{2} \]

      14. *-inverses 100.0%

          \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{1}}{-1}}{2} \]

      15. metadata-eval 100.0%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{-1}}{2} \]

      16. div-sub 100.0%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{2} - \frac{-1}{2}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{0.5}{y} - -0.5} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.7%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-43} \lor \neg \left(x \leq 6.2 \cdot 10^{-12}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{0.5}{y} - -0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* x (/ 0.5 y)) -0.5))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[\frac{x + y}{y + y} \]
2. Step-by-step derivation

   1. count-2 99.6%

      \[\leadsto \frac{x + y}{\color{blue}{2 \cdot y}} \]

   2. associate-/l/ 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x + y}{y}}{2}} \]

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. div-sub 100.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{-y}{y}}}{2} \]

   6. /-rgt-identity 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{-\color{blue}{\frac{y}{1}}}{y}}{2} \]

   7. metadata-eval 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{-\frac{y}{\color{blue}{\frac{-1}{-1}}}}{y}}{2} \]

   8. distribute-neg-frac2 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{\frac{y}{-\frac{-1}{-1}}}}{y}}{2} \]

   9. metadata-eval 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{\frac{y}{-\color{blue}{1}}}{y}}{2} \]

   10. metadata-eval 100.0%

       \[\leadsto \frac{\frac{x}{y} - \frac{\frac{y}{\color{blue}{-1}}}{y}}{2} \]

   11. associate-/r* 100.0%

       \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{y}{-1 \cdot y}}}{2} \]

   12. *-commutative 100.0%

       \[\leadsto \frac{\frac{x}{y} - \frac{y}{\color{blue}{y \cdot -1}}}{2} \]

   13. associate-/r* 100.0%

       \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{\frac{y}{y}}{-1}}}{2} \]

   14. *-inverses 100.0%

       \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{1}}{-1}}{2} \]

   15. metadata-eval 100.0%

       \[\leadsto \frac{\frac{x}{y} - \color{blue}{-1}}{2} \]

   16. div-sub 100.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{2} - \frac{-1}{2}} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \frac{0.5}{y} - -0.5} \]
4. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto x \cdot \frac{0.5}{y} - -0.5 \]
6. Add Preprocessing

Alternative 4: 2.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

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

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 99.6%

   \[\frac{x + y}{y + y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. expm1-log1p-u 73.8%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x + y}{y + y}\right)\right)} \]

   2. expm1-undefine 73.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x + y}{y + y}\right)} - 1} \]

   3. div-inv 73.7%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(x + y\right) \cdot \frac{1}{y + y}}\right)} - 1 \]

   4. flip-+ 0.0%

      \[\leadsto e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \frac{1}{\color{blue}{\frac{y \cdot y - y \cdot y}{y - y}}}\right)} - 1 \]

   5. +-inverses 0.0%

      \[\leadsto e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \frac{1}{\frac{\color{blue}{0}}{y - y}}\right)} - 1 \]

   6. +-inverses 0.0%

      \[\leadsto e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \frac{1}{\frac{\color{blue}{y - y}}{y - y}}\right)} - 1 \]

   7. +-inverses 0.0%

      \[\leadsto e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \frac{1}{\frac{y - y}{\color{blue}{0}}}\right)} - 1 \]

   8. +-inverses 0.0%

      \[\leadsto e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \frac{1}{\frac{y - y}{\color{blue}{y \cdot y - y \cdot y}}}\right)} - 1 \]

   9. clear-num 0.0%

      \[\leadsto e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \color{blue}{\frac{y \cdot y - y \cdot y}{y - y}}\right)} - 1 \]

   10. flip-+ 3.3%

       \[\leadsto e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \color{blue}{\left(y + y\right)}\right)} - 1 \]

   11. flip-+ 0.0%

       \[\leadsto e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \color{blue}{\frac{y \cdot y - y \cdot y}{y - y}}\right)} - 1 \]

   12. +-inverses 0.0%

       \[\leadsto e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \frac{\color{blue}{0}}{y - y}\right)} - 1 \]

   13. +-inverses 0.0%

       \[\leadsto e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \frac{0}{\color{blue}{0}}\right)} - 1 \]

4. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(x + y\right) \cdot \frac{0}{0}\right)} - 1} \]

6. Simplified 2.3%

   \[\leadsto \color{blue}{-1} \]

7. Final simplification 2.3%

   \[\leadsto -1 \]
8. Add Preprocessing

Alternative 5: 51.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.5)

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return 0.5;
}

Python

def code(x, y):
	return 0.5

Julia

function code(x, y)
	return 0.5
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5;
end

Wolfram

code[x_, y_] := 0.5

Derivation

1. Initial program 99.6%

   \[\frac{x + y}{y + y} \]
2. Step-by-step derivation

   1. count-2 99.6%

      \[\leadsto \frac{x + y}{\color{blue}{2 \cdot y}} \]

   2. associate-/l/ 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x + y}{y}}{2}} \]

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. div-sub 100.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{-y}{y}}}{2} \]

   6. /-rgt-identity 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{-\color{blue}{\frac{y}{1}}}{y}}{2} \]

   7. metadata-eval 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{-\frac{y}{\color{blue}{\frac{-1}{-1}}}}{y}}{2} \]

   8. distribute-neg-frac2 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{\frac{y}{-\frac{-1}{-1}}}}{y}}{2} \]

   9. metadata-eval 100.0%

      \[\leadsto \frac{\frac{x}{y} - \frac{\frac{y}{-\color{blue}{1}}}{y}}{2} \]

   10. metadata-eval 100.0%

       \[\leadsto \frac{\frac{x}{y} - \frac{\frac{y}{\color{blue}{-1}}}{y}}{2} \]

   11. associate-/r* 100.0%

       \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{y}{-1 \cdot y}}}{2} \]

   12. *-commutative 100.0%

       \[\leadsto \frac{\frac{x}{y} - \frac{y}{\color{blue}{y \cdot -1}}}{2} \]

   13. associate-/r* 100.0%

       \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{\frac{y}{y}}{-1}}}{2} \]

   14. *-inverses 100.0%

       \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{1}}{-1}}{2} \]

   15. metadata-eval 100.0%

       \[\leadsto \frac{\frac{x}{y} - \color{blue}{-1}}{2} \]

   16. div-sub 100.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{2} - \frac{-1}{2}} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x \cdot \frac{0.5}{y} - -0.5} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 48.8%

   \[\leadsto \color{blue}{0.5} \]

6. Final simplification 48.8%

   \[\leadsto 0.5 \]
7. Add Preprocessing

Developer target: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \frac{x}{y} + 0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (* 0.5 (/ x y)) 0.5))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024084 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"
  :precision binary64

  :alt
  (+ (* 0.5 (/ x y)) 0.5)

  (/ (+ x y) (+ y y)))