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

Percentage Accurate: 99.9% → 99.9%

Time: 2.9s

Alternatives: 4

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. Final simplification 100.0%

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

Alternative 2: 74.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-30}:\\ \;\;\;\;0.5\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+82}:\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.8e-30) 0.5 (if (<= y 2.4e+82) (* 0.5 (/ x y)) 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.8e-30) {
		tmp = 0.5;
	} else if (y <= 2.4e+82) {
		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 (y <= (-1.8d-30)) then
        tmp = 0.5d0
    else if (y <= 2.4d+82) 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 (y <= -1.8e-30) {
		tmp = 0.5;
	} else if (y <= 2.4e+82) {
		tmp = 0.5 * (x / y);
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.8e-30:
		tmp = 0.5
	elif y <= 2.4e+82:
		tmp = 0.5 * (x / y)
	else:
		tmp = 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.8e-30)
		tmp = 0.5;
	elseif (y <= 2.4e+82)
		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 (y <= -1.8e-30)
		tmp = 0.5;
	elseif (y <= 2.4e+82)
		tmp = 0.5 * (x / y);
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.8e-30], 0.5, If[LessEqual[y, 2.4e+82], N[(0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision], 0.5]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8000000000000002e-30 or 2.39999999999999998e82 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + y} \]

   2. Taylor expanded in x around 0 80.1%

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

   if -1.8000000000000002e-30 < y < 2.39999999999999998e82

   1. Initial program 100.0%

      \[\frac{x + y}{y + y} \]

   2. Taylor expanded in x around inf 77.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y}} \]
   3. Step-by-step derivation

      1. *-commutative 77.2%

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

   4. Simplified 77.2%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-30}:\\ \;\;\;\;0.5\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+82}:\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. --rgt-identity 100.0%

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

   3. associate-+l- 100.0%

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

   4. neg-sub0 100.0%

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

   5. div-sub 100.0%

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

   6. neg-mul-1 100.0%

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

   7. associate-*r/ 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. metadata-eval 100.0%

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

   10. metadata-eval 100.0%

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

   11. count-2 100.0%

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

   12. associate-/r* 100.0%

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

   13. times-frac 100.0%

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

   14. neg-mul-1 100.0%

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

   15. associate-*l/ 99.8%

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

   16. cancel-sign-sub 99.8%

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

   17. count-2 99.8%

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

   18. *-commutative 99.8%

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

   19. associate-/r* 99.8%

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

   20. *-inverses 99.8%

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

   21. metadata-eval 99.8%

       \[\leadsto \color{blue}{0.5} - \left(-\frac{-1}{-y}\right) \cdot \frac{x}{2} \]

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 4: 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 100.0%

   \[\frac{x + y}{y + y} \]

2. Taylor expanded in x around 0 50.4%

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

3. Final simplification 50.4%

   \[\leadsto 0.5 \]

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 2023297 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"
  :precision binary64

  :herbie-target
  (+ (* 0.5 (/ x y)) 0.5)

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