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

Percentage Accurate: 99.9% → 99.9%

Time: 4.5s

Alternatives: 7

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. Final simplification 100.0%

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

Alternative 2: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-33} \lor \neg \left(x \leq 5.6 \cdot 10^{+29}\right):\\ \;\;\;\;x \cdot \frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -9.5e-33) (not (<= x 5.6e+29))) (* x (/ 0.5 y)) 0.5))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -9.5e-33) || !(x <= 5.6e+29)) {
		tmp = x * (0.5 / 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 <= (-9.5d-33)) .or. (.not. (x <= 5.6d+29))) then
        tmp = x * (0.5d0 / y)
    else
        tmp = 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -9.5e-33) || !(x <= 5.6e+29)) {
		tmp = x * (0.5 / y);
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -9.5e-33) or not (x <= 5.6e+29):
		tmp = x * (0.5 / y)
	else:
		tmp = 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -9.5e-33) || !(x <= 5.6e+29))
		tmp = Float64(x * Float64(0.5 / y));
	else
		tmp = 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -9.5e-33) || ~((x <= 5.6e+29)))
		tmp = x * (0.5 / y);
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -9.5e-33], N[Not[LessEqual[x, 5.6e+29]], $MachinePrecision]], N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision], 0.5]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000019e-33 or 5.5999999999999999e29 < x

   1. Initial program 100.0%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 76.5%

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

   if -9.50000000000000019e-33 < x < 5.5999999999999999e29

   1. Initial program 100.0%

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

   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 76.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-33} \lor \neg \left(x \leq 5.6 \cdot 10^{+29}\right):\\ \;\;\;\;x \cdot \frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-28} \lor \neg \left(x \leq 4.5 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x \cdot 0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.4e-28) (not (<= x 4.5e+29))) (/ (* x 0.5) y) 0.5))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.4e-28) || !(x <= 4.5e+29)) {
		tmp = (x * 0.5) / 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 <= (-2.4d-28)) .or. (.not. (x <= 4.5d+29))) then
        tmp = (x * 0.5d0) / y
    else
        tmp = 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.4e-28) || !(x <= 4.5e+29)) {
		tmp = (x * 0.5) / y;
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.4e-28) or not (x <= 4.5e+29):
		tmp = (x * 0.5) / y
	else:
		tmp = 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.4e-28) || !(x <= 4.5e+29))
		tmp = Float64(Float64(x * 0.5) / y);
	else
		tmp = 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.4e-28) || ~((x <= 4.5e+29)))
		tmp = (x * 0.5) / y;
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.4e-28], N[Not[LessEqual[x, 4.5e+29]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] / y), $MachinePrecision], 0.5]

Derivation

1. Split input into 2 regimes

2. if x < -2.4000000000000002e-28 or 4.5000000000000002e29 < x

   1. Initial program 100.0%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 76.5%

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

      1. associate-*r/ 76.7%

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

   10. Applied egg-rr 76.7%

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

   if -2.4000000000000002e-28 < x < 4.5000000000000002e29

   1. Initial program 100.0%

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

   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 76.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-28} \lor \neg \left(x \leq 4.5 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x \cdot 0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 99.9%

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

   1. associate-*r/ 100.0%

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

   2. clear-num 99.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{x \cdot 0.5}}} - -0.5 \]

6. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\frac{1}{\frac{y}{x \cdot 0.5}}} - -0.5 \]

7. Taylor expanded in y around 0 100.0%

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

   1. associate-*r/ 100.0%

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

   2. associate-*l/ 99.9%

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

   3. associate-/r/ 99.9%

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

9. Simplified 99.9%

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

10. Final simplification 99.9%

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

Alternative 6: 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. expm1-log1p-u 70.5%

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

   2. expm1-undefine 70.5%

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

   3. div-inv 70.5%

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

   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-+ 2.9%

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

   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 2.5%

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

7. Final simplification 2.5%

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

Alternative 7: 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%

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

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 50.3%

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

6. Final simplification 50.3%

   \[\leadsto 0.5 \]
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 2024095 
(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)))