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

Percentage Accurate: 99.9% → 100.0%

Time: 1.8s

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: 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. Taylor expanded in x around 0 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+100}:\\ \;\;\;\;0.5\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+40} \lor \neg \left(y \leq -3.3 \cdot 10^{-50}\right) \land y \leq 1.25 \cdot 10^{+21}:\\ \;\;\;\;\frac{0.5 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.65e+100)
   0.5
   (if (or (<= y -1.75e+40) (and (not (<= y -3.3e-50)) (<= y 1.25e+21)))
     (/ (* 0.5 x) y)
     0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.65e+100) {
		tmp = 0.5;
	} else if ((y <= -1.75e+40) || (!(y <= -3.3e-50) && (y <= 1.25e+21))) {
		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 <= (-1.65d+100)) then
        tmp = 0.5d0
    else if ((y <= (-1.75d+40)) .or. (.not. (y <= (-3.3d-50))) .and. (y <= 1.25d+21)) 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 <= -1.65e+100) {
		tmp = 0.5;
	} else if ((y <= -1.75e+40) || (!(y <= -3.3e-50) && (y <= 1.25e+21))) {
		tmp = (0.5 * x) / y;
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.65e+100:
		tmp = 0.5
	elif (y <= -1.75e+40) or (not (y <= -3.3e-50) and (y <= 1.25e+21)):
		tmp = (0.5 * x) / y
	else:
		tmp = 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.65e+100)
		tmp = 0.5;
	elseif ((y <= -1.75e+40) || (!(y <= -3.3e-50) && (y <= 1.25e+21)))
		tmp = Float64(Float64(0.5 * x) / y);
	else
		tmp = 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.65e+100)
		tmp = 0.5;
	elseif ((y <= -1.75e+40) || (~((y <= -3.3e-50)) && (y <= 1.25e+21)))
		tmp = (0.5 * x) / y;
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.65e+100], 0.5, If[Or[LessEqual[y, -1.75e+40], And[N[Not[LessEqual[y, -3.3e-50]], $MachinePrecision], LessEqual[y, 1.25e+21]]], N[(N[(0.5 * x), $MachinePrecision] / y), $MachinePrecision], 0.5]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6500000000000001e100 or -1.75e40 < y < -3.2999999999999998e-50 or 1.25e21 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 83.3%

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

   if -1.6500000000000001e100 < y < -1.75e40 or -3.2999999999999998e-50 < y < 1.25e21

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.1%

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

   4. Simplified 78.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+100}:\\ \;\;\;\;0.5\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+40} \lor \neg \left(y \leq -3.3 \cdot 10^{-50}\right) \land y \leq 1.25 \cdot 10^{+21}:\\ \;\;\;\;\frac{0.5 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]

Alternative 3: 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. Step-by-step derivation

   1. frac-2neg 100.0%

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

   2. div-inv 99.7%

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

   3. flip-+ 0.0%

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

   4. +-inverses 0.0%

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

   5. +-inverses 0.0%

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

   6. distribute-neg-frac 0.0%

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

   7. +-inverses 0.0%

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

   8. metadata-eval 0.0%

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

   9. +-inverses 0.0%

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

   10. clear-num 0.0%

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

   11. +-inverses 0.0%

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

   12. +-inverses 0.0%

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

3. Applied egg-rr 0.0%

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

5. Simplified 2.4%

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

6. Final simplification 2.4%

   \[\leadsto -1 \]

Alternative 4: 50.7% 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 49.3%

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

3. Final simplification 49.3%

   \[\leadsto 0.5 \]

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 2023200 
(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)))