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

Percentage Accurate: 100.0% → 100.0%

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: 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 2: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{0.5 \cdot x}{y}\\ \mathbf{if}\;x \leq -3700000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+18}:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* 0.5 x) y)))
   (if (<= x -3700000.0) t_0 (if (<= x 2.8e+18) 0.5 t_0))))

C

double code(double x, double y) {
	double t_0 = (0.5 * x) / y;
	double tmp;
	if (x <= -3700000.0) {
		tmp = t_0;
	} else if (x <= 2.8e+18) {
		tmp = 0.5;
	} 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 = (0.5d0 * x) / y
    if (x <= (-3700000.0d0)) then
        tmp = t_0
    else if (x <= 2.8d+18) then
        tmp = 0.5d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (0.5 * x) / y;
	double tmp;
	if (x <= -3700000.0) {
		tmp = t_0;
	} else if (x <= 2.8e+18) {
		tmp = 0.5;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (0.5 * x) / y
	tmp = 0
	if x <= -3700000.0:
		tmp = t_0
	elif x <= 2.8e+18:
		tmp = 0.5
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(0.5 * x) / y)
	tmp = 0.0
	if (x <= -3700000.0)
		tmp = t_0;
	elseif (x <= 2.8e+18)
		tmp = 0.5;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (0.5 * x) / y;
	tmp = 0.0;
	if (x <= -3700000.0)
		tmp = t_0;
	elseif (x <= 2.8e+18)
		tmp = 0.5;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(0.5 * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[x, -3700000.0], t$95$0, If[LessEqual[x, 2.8e+18], 0.5, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7e6 or 2.8e18 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.7e6 < x < 2.8e18

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{0.5}{y} \cdot x\\ \mathbf{if}\;x \leq -160000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+18}:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ 0.5 y) x)))
   (if (<= x -160000000.0) t_0 (if (<= x 2.8e+18) 0.5 t_0))))

C

double code(double x, double y) {
	double t_0 = (0.5 / y) * x;
	double tmp;
	if (x <= -160000000.0) {
		tmp = t_0;
	} else if (x <= 2.8e+18) {
		tmp = 0.5;
	} 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 = (0.5d0 / y) * x
    if (x <= (-160000000.0d0)) then
        tmp = t_0
    else if (x <= 2.8d+18) then
        tmp = 0.5d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (0.5 / y) * x;
	double tmp;
	if (x <= -160000000.0) {
		tmp = t_0;
	} else if (x <= 2.8e+18) {
		tmp = 0.5;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (0.5 / y) * x
	tmp = 0
	if x <= -160000000.0:
		tmp = t_0
	elif x <= 2.8e+18:
		tmp = 0.5
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(0.5 / y) * x)
	tmp = 0.0
	if (x <= -160000000.0)
		tmp = t_0;
	elseif (x <= 2.8e+18)
		tmp = 0.5;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (0.5 / y) * x;
	tmp = 0.0;
	if (x <= -160000000.0)
		tmp = t_0;
	elseif (x <= 2.8e+18)
		tmp = 0.5;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(0.5 / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -160000000.0], t$95$0, If[LessEqual[x, 2.8e+18], 0.5, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e8 or 2.8e18 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.6e8 < x < 2.8e18

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.2% 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 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. 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 2024110 
(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)))