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

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

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: 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

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

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(-0.5 * Float64(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[(-0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-neg-out 100.0%

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

   4. distribute-neg-out 100.0%

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

   5. remove-double-neg 100.0%

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

   6. unsub-neg 100.0%

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

   7. div-sub 100.0%

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

   8. count-2 100.0%

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

   9. *-commutative 100.0%

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

   10. associate-/r* 100.0%

       \[\leadsto \color{blue}{\frac{\frac{y}{y}}{2}} - \frac{-x}{y + y} \]

   11. *-inverses 100.0%

       \[\leadsto \frac{\color{blue}{1}}{2} - \frac{-x}{y + y} \]

   12. metadata-eval 100.0%

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

   13. count-2 100.0%

       \[\leadsto 0.5 - \frac{-x}{\color{blue}{2 \cdot y}} \]

   14. neg-mul-1 100.0%

       \[\leadsto 0.5 - \frac{\color{blue}{-1 \cdot x}}{2 \cdot y} \]

   15. times-frac 100.0%

       \[\leadsto 0.5 - \color{blue}{\frac{-1}{2} \cdot \frac{x}{y}} \]

   16. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-35} \lor \neg \left(x \leq 7.6 \cdot 10^{-19} \lor \neg \left(x \leq 7.5 \cdot 10^{+15}\right) \land x \leq 7.8 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{0.5}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.5e-35)
         (not (or (<= x 7.6e-19) (and (not (<= x 7.5e+15)) (<= x 7.8e+87)))))
   (/ 0.5 (/ y x))
   0.5))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.5e-35) || !((x <= 7.6e-19) || (!(x <= 7.5e+15) && (x <= 7.8e+87)))) {
		tmp = 0.5 / (y / x);
	} 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 <= (-4.5d-35)) .or. (.not. (x <= 7.6d-19) .or. (.not. (x <= 7.5d+15)) .and. (x <= 7.8d+87))) then
        tmp = 0.5d0 / (y / x)
    else
        tmp = 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.5e-35) || !((x <= 7.6e-19) || (!(x <= 7.5e+15) && (x <= 7.8e+87)))) {
		tmp = 0.5 / (y / x);
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.5e-35) or not ((x <= 7.6e-19) or (not (x <= 7.5e+15) and (x <= 7.8e+87))):
		tmp = 0.5 / (y / x)
	else:
		tmp = 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.5e-35) || !((x <= 7.6e-19) || (!(x <= 7.5e+15) && (x <= 7.8e+87))))
		tmp = Float64(0.5 / Float64(y / x));
	else
		tmp = 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.5e-35) || ~(((x <= 7.6e-19) || (~((x <= 7.5e+15)) && (x <= 7.8e+87)))))
		tmp = 0.5 / (y / x);
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.5e-35], N[Not[Or[LessEqual[x, 7.6e-19], And[N[Not[LessEqual[x, 7.5e+15]], $MachinePrecision], LessEqual[x, 7.8e+87]]]], $MachinePrecision]], N[(0.5 / N[(y / x), $MachinePrecision]), $MachinePrecision], 0.5]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000001e-35 or 7.6e-19 < x < 7.5e15 or 7.80000000000000039e87 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-neg-out 99.9%

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

      4. distribute-neg-out 99.9%

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

      5. remove-double-neg 99.9%

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

      6. unsub-neg 99.9%

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

      7. div-sub 100.0%

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

      8. count-2 100.0%

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

      9. *-commutative 100.0%

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

      10. associate-/r* 100.0%

          \[\leadsto \color{blue}{\frac{\frac{y}{y}}{2}} - \frac{-x}{y + y} \]

      11. *-inverses 100.0%

          \[\leadsto \frac{\color{blue}{1}}{2} - \frac{-x}{y + y} \]

      12. metadata-eval 100.0%

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

      13. count-2 100.0%

          \[\leadsto 0.5 - \frac{-x}{\color{blue}{2 \cdot y}} \]

      14. neg-mul-1 100.0%

          \[\leadsto 0.5 - \frac{\color{blue}{-1 \cdot x}}{2 \cdot y} \]

      15. times-frac 100.0%

          \[\leadsto 0.5 - \color{blue}{\frac{-1}{2} \cdot \frac{x}{y}} \]

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 81.5%

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

      1. associate-*r/ 81.5%

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

      2. associate-/l* 81.3%

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

   6. Simplified 81.3%

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

   if -4.5000000000000001e-35 < x < 7.6e-19 or 7.5e15 < x < 7.80000000000000039e87

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-out 100.0%

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

      4. distribute-neg-out 100.0%

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

      5. remove-double-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. div-sub 100.0%

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

      8. count-2 100.0%

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

      9. *-commutative 100.0%

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

      10. associate-/r* 100.0%

          \[\leadsto \color{blue}{\frac{\frac{y}{y}}{2}} - \frac{-x}{y + y} \]

      11. *-inverses 100.0%

          \[\leadsto \frac{\color{blue}{1}}{2} - \frac{-x}{y + y} \]

      12. metadata-eval 100.0%

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

      13. count-2 100.0%

          \[\leadsto 0.5 - \frac{-x}{\color{blue}{2 \cdot y}} \]

      14. neg-mul-1 100.0%

          \[\leadsto 0.5 - \frac{\color{blue}{-1 \cdot x}}{2 \cdot y} \]

      15. times-frac 100.0%

          \[\leadsto 0.5 - \color{blue}{\frac{-1}{2} \cdot \frac{x}{y}} \]

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 80.1%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-35} \lor \neg \left(x \leq 7.6 \cdot 10^{-19} \lor \neg \left(x \leq 7.5 \cdot 10^{+15}\right) \land x \leq 7.8 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{0.5}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-35} \lor \neg \left(x \leq 10^{-17} \lor \neg \left(x \leq 8.2 \cdot 10^{+17}\right) \land x \leq 3 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{\frac{y}{0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.4e-35)
         (not (or (<= x 1e-17) (and (not (<= x 8.2e+17)) (<= x 3e+88)))))
   (/ x (/ y 0.5))
   0.5))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.4e-35) || !((x <= 1e-17) || (!(x <= 8.2e+17) && (x <= 3e+88)))) {
		tmp = x / (y / 0.5);
	} 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 <= (-3.4d-35)) .or. (.not. (x <= 1d-17) .or. (.not. (x <= 8.2d+17)) .and. (x <= 3d+88))) then
        tmp = x / (y / 0.5d0)
    else
        tmp = 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -3.4e-35) || !((x <= 1e-17) || (!(x <= 8.2e+17) && (x <= 3e+88)))) {
		tmp = x / (y / 0.5);
	} else {
		tmp = 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.4e-35) or not ((x <= 1e-17) or (not (x <= 8.2e+17) and (x <= 3e+88))):
		tmp = x / (y / 0.5)
	else:
		tmp = 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.4e-35) || !((x <= 1e-17) || (!(x <= 8.2e+17) && (x <= 3e+88))))
		tmp = Float64(x / Float64(y / 0.5));
	else
		tmp = 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.4e-35) || ~(((x <= 1e-17) || (~((x <= 8.2e+17)) && (x <= 3e+88)))))
		tmp = x / (y / 0.5);
	else
		tmp = 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.4e-35], N[Not[Or[LessEqual[x, 1e-17], And[N[Not[LessEqual[x, 8.2e+17]], $MachinePrecision], LessEqual[x, 3e+88]]]], $MachinePrecision]], N[(x / N[(y / 0.5), $MachinePrecision]), $MachinePrecision], 0.5]

Derivation

1. Split input into 2 regimes

2. if x < -3.4000000000000003e-35 or 1.00000000000000007e-17 < x < 8.2e17 or 3.00000000000000005e88 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-neg-out 99.9%

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

      4. distribute-neg-out 99.9%

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

      5. remove-double-neg 99.9%

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

      6. unsub-neg 99.9%

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

      7. div-sub 100.0%

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

      8. count-2 100.0%

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

      9. *-commutative 100.0%

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

      10. associate-/r* 100.0%

          \[\leadsto \color{blue}{\frac{\frac{y}{y}}{2}} - \frac{-x}{y + y} \]

      11. *-inverses 100.0%

          \[\leadsto \frac{\color{blue}{1}}{2} - \frac{-x}{y + y} \]

      12. metadata-eval 100.0%

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

      13. count-2 100.0%

          \[\leadsto 0.5 - \frac{-x}{\color{blue}{2 \cdot y}} \]

      14. neg-mul-1 100.0%

          \[\leadsto 0.5 - \frac{\color{blue}{-1 \cdot x}}{2 \cdot y} \]

      15. times-frac 100.0%

          \[\leadsto 0.5 - \color{blue}{\frac{-1}{2} \cdot \frac{x}{y}} \]

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 81.5%

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

      1. associate-*r/ 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-/l* 81.5%

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

   6. Simplified 81.5%

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

   if -3.4000000000000003e-35 < x < 1.00000000000000007e-17 or 8.2e17 < x < 3.00000000000000005e88

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-out 100.0%

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

      4. distribute-neg-out 100.0%

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

      5. remove-double-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. div-sub 100.0%

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

      8. count-2 100.0%

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

      9. *-commutative 100.0%

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

      10. associate-/r* 100.0%

          \[\leadsto \color{blue}{\frac{\frac{y}{y}}{2}} - \frac{-x}{y + y} \]

      11. *-inverses 100.0%

          \[\leadsto \frac{\color{blue}{1}}{2} - \frac{-x}{y + y} \]

      12. metadata-eval 100.0%

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

      13. count-2 100.0%

          \[\leadsto 0.5 - \frac{-x}{\color{blue}{2 \cdot y}} \]

      14. neg-mul-1 100.0%

          \[\leadsto 0.5 - \frac{\color{blue}{-1 \cdot x}}{2 \cdot y} \]

      15. times-frac 100.0%

          \[\leadsto 0.5 - \color{blue}{\frac{-1}{2} \cdot \frac{x}{y}} \]

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 80.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-35} \lor \neg \left(x \leq 10^{-17} \lor \neg \left(x \leq 8.2 \cdot 10^{+17}\right) \land x \leq 3 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{\frac{y}{0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]

Alternative 4: 2.6% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.0)

C

double code(double x, double y) {
	return 0.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0
end function

Java

public static double code(double x, double y) {
	return 0.0;
}

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0;
end

Wolfram

code[x_, y_] := 0.0

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. +-inverses 0.0%

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

   3. +-inverses 0.0%

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

   4. associate-/r/ 0.0%

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

   5. +-inverses 0.0%

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

   6. +-inverses 0.0%

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

3. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{\frac{x + y}{0} \cdot 0} \]
4. Step-by-step derivation

   1. mul0-rgt 2.7%

      \[\leadsto \color{blue}{0} \]

5. Simplified 2.7%

   \[\leadsto \color{blue}{0} \]

6. Final simplification 2.7%

   \[\leadsto 0 \]

Alternative 5: 50.0% 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. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-neg-out 100.0%

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

   4. distribute-neg-out 100.0%

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

   5. remove-double-neg 100.0%

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

   6. unsub-neg 100.0%

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

   7. div-sub 100.0%

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

   8. count-2 100.0%

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

   9. *-commutative 100.0%

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

   10. associate-/r* 100.0%

       \[\leadsto \color{blue}{\frac{\frac{y}{y}}{2}} - \frac{-x}{y + y} \]

   11. *-inverses 100.0%

       \[\leadsto \frac{\color{blue}{1}}{2} - \frac{-x}{y + y} \]

   12. metadata-eval 100.0%

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

   13. count-2 100.0%

       \[\leadsto 0.5 - \frac{-x}{\color{blue}{2 \cdot y}} \]

   14. neg-mul-1 100.0%

       \[\leadsto 0.5 - \frac{\color{blue}{-1 \cdot x}}{2 \cdot y} \]

   15. times-frac 100.0%

       \[\leadsto 0.5 - \color{blue}{\frac{-1}{2} \cdot \frac{x}{y}} \]

   16. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around 0 52.0%

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

5. Final simplification 52.0%

   \[\leadsto 0.5 \]

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 2023274 
(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)))