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

Percentage Accurate: 99.9% → 99.9%

Time: 2.5s

Alternatives: 5

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: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -24000000 \lor \neg \left(x \leq -4.2 \cdot 10^{-59}\right) \land \left(x \leq -9.2 \cdot 10^{-95} \lor \neg \left(x \leq 9.6 \cdot 10^{-5}\right)\right):\\ \;\;\;\;\frac{x \cdot 0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -24000000.0)
         (and (not (<= x -4.2e-59)) (or (<= x -9.2e-95) (not (<= x 9.6e-5)))))
   (/ (* x 0.5) y)
   0.5))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -24000000.0) || (!(x <= -4.2e-59) && ((x <= -9.2e-95) || !(x <= 9.6e-5)))) {
		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 <= (-24000000.0d0)) .or. (.not. (x <= (-4.2d-59))) .and. (x <= (-9.2d-95)) .or. (.not. (x <= 9.6d-5))) 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 <= -24000000.0) || (!(x <= -4.2e-59) && ((x <= -9.2e-95) || !(x <= 9.6e-5)))) {
		tmp = (x * 0.5) / y;
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -24000000.0) or (not (x <= -4.2e-59) and ((x <= -9.2e-95) or not (x <= 9.6e-5))):
		tmp = (x * 0.5) / y
	else:
		tmp = 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -24000000.0) || (!(x <= -4.2e-59) && ((x <= -9.2e-95) || !(x <= 9.6e-5))))
		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 <= -24000000.0) || (~((x <= -4.2e-59)) && ((x <= -9.2e-95) || ~((x <= 9.6e-5)))))
		tmp = (x * 0.5) / y;
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -24000000.0], And[N[Not[LessEqual[x, -4.2e-59]], $MachinePrecision], Or[LessEqual[x, -9.2e-95], N[Not[LessEqual[x, 9.6e-5]], $MachinePrecision]]]], N[(N[(x * 0.5), $MachinePrecision] / y), $MachinePrecision], 0.5]

Derivation

1. Split input into 2 regimes

2. if x < -2.4e7 or -4.19999999999999993e-59 < x < -9.19999999999999997e-95 or 9.6000000000000002e-5 < x

   1. Initial program 100.0%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 79.0%

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

   6. Simplified 79.0%

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

   if -2.4e7 < x < -4.19999999999999993e-59 or -9.19999999999999997e-95 < x < 9.6000000000000002e-5

   1. Initial program 100.0%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 75.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -24000000 \lor \neg \left(x \leq -4.2 \cdot 10^{-59}\right) \land \left(x \leq -9.2 \cdot 10^{-95} \lor \neg \left(x \leq 9.6 \cdot 10^{-5}\right)\right):\\ \;\;\;\;\frac{x \cdot 0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]

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%

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

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: 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. flip-+ 0.0%

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

   2. associate-/r/ 0.0%

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

   3. +-inverses 0.0%

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

   4. +-inverses 0.0%

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

   5. associate-/r/ 0.0%

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

   6. div-inv 0.0%

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

   7. *-commutative 0.0%

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

   8. +-inverses 0.0%

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

   9. +-inverses 0.0%

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

   10. associate-/r/ 0.0%

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

   11. flip-+ 4.3%

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

   12. frac-2neg 4.3%

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

   13. flip-+ 0.0%

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

   14. distribute-neg-frac 0.0%

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

   15. +-inverses 0.0%

       \[\leadsto \frac{x + y}{\frac{-1}{\frac{-\color{blue}{0}}{y - y}}} \]

   16. metadata-eval 0.0%

       \[\leadsto \frac{x + y}{\frac{-1}{\frac{\color{blue}{0}}{y - y}}} \]

   17. +-inverses 0.0%

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

   18. flip-+ 1.1%

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

   19. *-un-lft-identity 1.1%

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

   20. *-un-lft-identity 1.1%

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

3. Applied egg-rr 0.0%

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

5. Simplified 2.5%

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

6. Final simplification 2.5%

   \[\leadsto -1 \]

Alternative 5: 51.1% 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 99.8%

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

4. Taylor expanded in x around 0 45.1%

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

5. Final simplification 45.1%

   \[\leadsto 0.5 \]

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 2023301 
(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)))