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

Percentage Accurate: 99.9% → 99.9%

Time: 2.9s

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: 99.9% 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: 99.9% 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]

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{y + y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-99} \lor \neg \left(x \leq 12500\right):\\ \;\;\;\;\frac{x}{y + y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2e-99) (not (<= x 12500.0))) (/ x (+ y y)) 0.5))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2e-99) || !(x <= 12500.0)) {
		tmp = x / (y + 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 <= (-2d-99)) .or. (.not. (x <= 12500.0d0))) then
        tmp = x / (y + y)
    else
        tmp = 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2e-99) || !(x <= 12500.0)) {
		tmp = x / (y + y);
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2e-99) or not (x <= 12500.0):
		tmp = x / (y + y)
	else:
		tmp = 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2e-99) || !(x <= 12500.0))
		tmp = Float64(x / Float64(y + y));
	else
		tmp = 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2e-99) || ~((x <= 12500.0)))
		tmp = x / (y + y);
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2e-99], N[Not[LessEqual[x, 12500.0]], $MachinePrecision]], N[(x / N[(y + y), $MachinePrecision]), $MachinePrecision], 0.5]

Derivation

1. Split input into 2 regimes

2. if x < -2e-99 or 12500 < x

   1. Initial program 100.0%

      \[\frac{x + y}{y + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.5%

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

   if -2e-99 < x < 12500

   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 100.0%

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

   5. Taylor expanded in x around 0 84.1%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-99} \lor \neg \left(x \leq 12500\right):\\ \;\;\;\;\frac{x}{y + y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]
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 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 99.9%

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

Alternative 4: 51.4% 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 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 99.9%

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

5. Taylor expanded in x around 0 52.1%

   \[\leadsto \color{blue}{0.5} \]
6. Add Preprocessing

Alternative 5: 2.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ -8 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -8.0)

C

double code(double x, double y) {
	return -8.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -8.0d0
end function

Java

public static double code(double x, double y) {
	return -8.0;
}

Python

def code(x, y):
	return -8.0

Julia

function code(x, y)
	return -8.0
end

MATLAB

function tmp = code(x, y)
	tmp = -8.0;
end

Wolfram

code[x_, y_] := -8.0

Derivation

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 99.9%

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

5. Taylor expanded in y around 0 100.0%

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

7. Simplified 3.4%

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

9. Applied egg-rr 2.1%

   \[\leadsto \color{blue}{-8} \]
10. Add Preprocessing

Developer Target 1: 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 2024135 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (* 1/2 (/ x y)) 1/2))

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