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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 6

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

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

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. Final simplification 100.0%

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

Alternative 2: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+139} \lor \neg \left(x \leq 5.2 \cdot 10^{+17}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.5e+139) (not (<= x 5.2e+17))) (* 0.5 (/ x y)) 0.5))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.5e+139) || !(x <= 5.2e+17)) {
		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 <= (-3.5d+139)) .or. (.not. (x <= 5.2d+17))) 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 <= -3.5e+139) || !(x <= 5.2e+17)) {
		tmp = 0.5 * (x / y);
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.5e+139) or not (x <= 5.2e+17):
		tmp = 0.5 * (x / y)
	else:
		tmp = 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.5e+139) || !(x <= 5.2e+17))
		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 <= -3.5e+139) || ~((x <= 5.2e+17)))
		tmp = 0.5 * (x / y);
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.5e+139], N[Not[LessEqual[x, 5.2e+17]], $MachinePrecision]], N[(0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision], 0.5]

Derivation

1. Split input into 2 regimes

2. if x < -3.49999999999999978e139 or 5.2e17 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.1%

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

   if -3.49999999999999978e139 < x < 5.2e17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+139} \lor \neg \left(x \leq 5.2 \cdot 10^{+17}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{0.5}{y}\\ \mathbf{elif}\;x \leq 2500000000000:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.5e+139)
   (* x (/ 0.5 y))
   (if (<= x 2500000000000.0) 0.5 (* 0.5 (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.5e+139) {
		tmp = x * (0.5 / y);
	} else if (x <= 2500000000000.0) {
		tmp = 0.5;
	} else {
		tmp = 0.5 * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.5d+139)) then
        tmp = x * (0.5d0 / y)
    else if (x <= 2500000000000.0d0) then
        tmp = 0.5d0
    else
        tmp = 0.5d0 * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.5e+139) {
		tmp = x * (0.5 / y);
	} else if (x <= 2500000000000.0) {
		tmp = 0.5;
	} else {
		tmp = 0.5 * (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.5e+139:
		tmp = x * (0.5 / y)
	elif x <= 2500000000000.0:
		tmp = 0.5
	else:
		tmp = 0.5 * (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.5e+139)
		tmp = Float64(x * Float64(0.5 / y));
	elseif (x <= 2500000000000.0)
		tmp = 0.5;
	else
		tmp = Float64(0.5 * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.5e+139)
		tmp = x * (0.5 / y);
	elseif (x <= 2500000000000.0)
		tmp = 0.5;
	else
		tmp = 0.5 * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.5e+139], N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2500000000000.0], 0.5, N[(0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.49999999999999978e139

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.6%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) \cdot \sqrt[3]{x + y}}}{y + y} \]

      2. count-2 98.6%

         \[\leadsto \frac{\left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) \cdot \sqrt[3]{x + y}}{\color{blue}{2 \cdot y}} \]

      3. times-frac 98.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}}{2} \cdot \frac{\sqrt[3]{x + y}}{y}} \]

      4. pow2 98.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x + y}\right)}^{2}}}{2} \cdot \frac{\sqrt[3]{x + y}}{y} \]

   4. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x + y}\right)}^{2}}{2} \cdot \frac{\sqrt[3]{x + y}}{y}} \]

   5. Taylor expanded in x around inf 85.2%

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

      1. associate-*r/ 87.3%

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

      2. associate-/l* 87.2%

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

   7. Simplified 87.2%

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

      1. associate-/r/ 87.1%

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

   9. Applied egg-rr 87.1%

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

   if -3.49999999999999978e139 < x < 2.5e12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.8%

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

   if 2.5e12 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.5%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{0.5}{y}\\ \mathbf{elif}\;x \leq 2500000000000:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+139}:\\ \;\;\;\;\frac{0.5}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 860000000000:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.5e+139)
   (/ 0.5 (/ y x))
   (if (<= x 860000000000.0) 0.5 (* 0.5 (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.5e+139) {
		tmp = 0.5 / (y / x);
	} else if (x <= 860000000000.0) {
		tmp = 0.5;
	} else {
		tmp = 0.5 * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.5d+139)) then
        tmp = 0.5d0 / (y / x)
    else if (x <= 860000000000.0d0) then
        tmp = 0.5d0
    else
        tmp = 0.5d0 * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.5e+139) {
		tmp = 0.5 / (y / x);
	} else if (x <= 860000000000.0) {
		tmp = 0.5;
	} else {
		tmp = 0.5 * (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.5e+139:
		tmp = 0.5 / (y / x)
	elif x <= 860000000000.0:
		tmp = 0.5
	else:
		tmp = 0.5 * (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.5e+139)
		tmp = Float64(0.5 / Float64(y / x));
	elseif (x <= 860000000000.0)
		tmp = 0.5;
	else
		tmp = Float64(0.5 * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.5e+139)
		tmp = 0.5 / (y / x);
	elseif (x <= 860000000000.0)
		tmp = 0.5;
	else
		tmp = 0.5 * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.5e+139], N[(0.5 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 860000000000.0], 0.5, N[(0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.49999999999999978e139

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.6%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) \cdot \sqrt[3]{x + y}}}{y + y} \]

      2. count-2 98.6%

         \[\leadsto \frac{\left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) \cdot \sqrt[3]{x + y}}{\color{blue}{2 \cdot y}} \]

      3. times-frac 98.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}}{2} \cdot \frac{\sqrt[3]{x + y}}{y}} \]

      4. pow2 98.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x + y}\right)}^{2}}}{2} \cdot \frac{\sqrt[3]{x + y}}{y} \]

   4. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x + y}\right)}^{2}}{2} \cdot \frac{\sqrt[3]{x + y}}{y}} \]

   5. Taylor expanded in x around inf 85.2%

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

      1. associate-*r/ 87.3%

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

      2. associate-/l* 87.2%

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

   7. Simplified 87.2%

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

   if -3.49999999999999978e139 < x < 8.6e11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.8%

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

   if 8.6e11 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.5%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+139}:\\ \;\;\;\;\frac{0.5}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 860000000000:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 100.0%

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

   1. add0 100.0%

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

   2. div-inv 99.7%

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

   3. flip-+ 0.0%

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

   4. +-inverses 0.0%

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

   5. +-inverses 0.0%

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

   6. +-inverses 0.0%

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

   7. +-inverses 0.0%

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

   8. clear-num 0.0%

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

   9. flip-+ 4.4%

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

   10. flip-+ 0.0%

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

   11. +-inverses 0.0%

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

   12. +-inverses 0.0%

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

4. Applied egg-rr 0.0%

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

6. Simplified 2.1%

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

7. Final simplification 2.1%

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

Alternative 6: 50.6% 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. Add Preprocessing

3. Taylor expanded in x around 0 54.2%

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

4. Final simplification 54.2%

   \[\leadsto 0.5 \]
5. 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 2024034 
(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)))