Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.2% → 99.7%

Time: 6.2s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{0.5}{y} - \frac{0.5}{x}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 (- (/ 0.5 y) (/ 0.5 x))))

C

double code(double x, double y) {
	return 1.0 / ((0.5 / y) - (0.5 / x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 / ((0.5d0 / y) - (0.5d0 / x))
end function

Java

public static double code(double x, double y) {
	return 1.0 / ((0.5 / y) - (0.5 / x));
}

Python

def code(x, y):
	return 1.0 / ((0.5 / y) - (0.5 / x))

Julia

function code(x, y)
	return Float64(1.0 / Float64(Float64(0.5 / y) - Float64(0.5 / x)))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 / ((0.5 / y) - (0.5 / x));
end

Wolfram

code[x_, y_] := N[(1.0 / N[(N[(0.5 / y), $MachinePrecision] - N[(0.5 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.4%

   \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
2. Step-by-step derivation

   1. associate-/l* 88.2%

      \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

   2. associate-*l* 88.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

3. Simplified 88.2%

   \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-*r* 88.2%

      \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

   2. associate-/l* 82.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot 2\right) \cdot y}{x - y}} \]

   3. clear-num 82.1%

      \[\leadsto \color{blue}{\frac{1}{\frac{x - y}{\left(x \cdot 2\right) \cdot y}}} \]

   4. associate-*l* 82.1%

      \[\leadsto \frac{1}{\frac{x - y}{\color{blue}{x \cdot \left(2 \cdot y\right)}}} \]

6. Applied egg-rr 82.1%

   \[\leadsto \color{blue}{\frac{1}{\frac{x - y}{x \cdot \left(2 \cdot y\right)}}} \]

7. Taylor expanded in x around inf 99.6%

   \[\leadsto \frac{1}{\color{blue}{0.5 \cdot \frac{1}{y} - 0.5 \cdot \frac{1}{x}}} \]
8. Step-by-step derivation

   1. associate-*r/ 99.6%

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

   2. metadata-eval 99.6%

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

   3. associate-*r/ 99.6%

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

   4. metadata-eval 99.6%

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

9. Simplified 99.6%

   \[\leadsto \frac{1}{\color{blue}{\frac{0.5}{y} - \frac{0.5}{x}}} \]
10. Add Preprocessing

Alternative 2: 92.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-61} \lor \neg \left(y \leq 2.2 \cdot 10^{-168}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.38e-61) (not (<= y 2.2e-168)))
   (* x (* 2.0 (/ y (- x y))))
   (* y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.38e-61) || !(y <= 2.2e-168)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.38d-61)) .or. (.not. (y <= 2.2d-168))) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.38e-61) || !(y <= 2.2e-168)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.38e-61) or not (y <= 2.2e-168):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.38e-61) || !(y <= 2.2e-168))
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.38e-61) || ~((y <= 2.2e-168)))
		tmp = x * (2.0 * (y / (x - y)));
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.38e-61], N[Not[LessEqual[y, 2.2e-168]], $MachinePrecision]], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.37999999999999992e-61 or 2.1999999999999998e-168 < y

   1. Initial program 84.5%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.2%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 99.2%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   if -1.37999999999999992e-61 < y < 2.1999999999999998e-168

   1. Initial program 78.1%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 65.5%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 65.5%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 65.5%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 88.6%

      \[\leadsto \color{blue}{2 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 88.6%

         \[\leadsto \color{blue}{y \cdot 2} \]

   7. Simplified 88.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-61} \lor \neg \left(y \leq 2.2 \cdot 10^{-168}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-61} \lor \neg \left(y \leq 5.5 \cdot 10^{-158}\right):\\ \;\;\;\;2 \cdot \frac{x}{\frac{x}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.38e-61) (not (<= y 5.5e-158)))
   (* 2.0 (/ x (+ (/ x y) -1.0)))
   (* y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.38e-61) || !(y <= 5.5e-158)) {
		tmp = 2.0 * (x / ((x / y) + -1.0));
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.38d-61)) .or. (.not. (y <= 5.5d-158))) then
        tmp = 2.0d0 * (x / ((x / y) + (-1.0d0)))
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.38e-61) || !(y <= 5.5e-158)) {
		tmp = 2.0 * (x / ((x / y) + -1.0));
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.38e-61) or not (y <= 5.5e-158):
		tmp = 2.0 * (x / ((x / y) + -1.0))
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.38e-61) || !(y <= 5.5e-158))
		tmp = Float64(2.0 * Float64(x / Float64(Float64(x / y) + -1.0)));
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.38e-61) || ~((y <= 5.5e-158)))
		tmp = 2.0 * (x / ((x / y) + -1.0));
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.38e-61], N[Not[LessEqual[y, 5.5e-158]], $MachinePrecision]], N[(2.0 * N[(x / N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.37999999999999992e-61 or 5.50000000000000025e-158 < y

   1. Initial program 84.2%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.2%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 99.2%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 99.2%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. clear-num 98.7%

         \[\leadsto \left(x \cdot 2\right) \cdot \color{blue}{\frac{1}{\frac{x - y}{y}}} \]

      3. un-div-inv 98.8%

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

   6. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]
   7. Step-by-step derivation

      1. *-commutative 98.8%

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

      2. associate-/l* 98.8%

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

      3. div-sub 98.8%

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

      4. sub-neg 98.8%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{\frac{x}{y} + \left(-\frac{y}{y}\right)}} \]

      5. *-inverses 98.8%

         \[\leadsto 2 \cdot \frac{x}{\frac{x}{y} + \left(-\color{blue}{1}\right)} \]

      6. metadata-eval 98.8%

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

   8. Simplified 98.8%

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

   if -1.37999999999999992e-61 < y < 5.50000000000000025e-158

   1. Initial program 78.8%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 66.7%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 66.7%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 89.0%

      \[\leadsto \color{blue}{2 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 89.0%

         \[\leadsto \color{blue}{y \cdot 2} \]

   7. Simplified 89.0%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-61} \lor \neg \left(y \leq 5.5 \cdot 10^{-158}\right):\\ \;\;\;\;2 \cdot \frac{x}{\frac{x}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-141}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{2}{x - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.8e-61)
   (* x (* 2.0 (/ y (- x y))))
   (if (<= y 9.8e-141) (* y 2.0) (* x (* y (/ 2.0 (- x y)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.8e-61) {
		tmp = x * (2.0 * (y / (x - y)));
	} else if (y <= 9.8e-141) {
		tmp = y * 2.0;
	} else {
		tmp = x * (y * (2.0 / (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5.8d-61)) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else if (y <= 9.8d-141) then
        tmp = y * 2.0d0
    else
        tmp = x * (y * (2.0d0 / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.8e-61) {
		tmp = x * (2.0 * (y / (x - y)));
	} else if (y <= 9.8e-141) {
		tmp = y * 2.0;
	} else {
		tmp = x * (y * (2.0 / (x - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.8e-61:
		tmp = x * (2.0 * (y / (x - y)))
	elif y <= 9.8e-141:
		tmp = y * 2.0
	else:
		tmp = x * (y * (2.0 / (x - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.8e-61)
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	elseif (y <= 9.8e-141)
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(x * Float64(y * Float64(2.0 / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.8e-61)
		tmp = x * (2.0 * (y / (x - y)));
	elseif (y <= 9.8e-141)
		tmp = y * 2.0;
	else
		tmp = x * (y * (2.0 / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.8e-61], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-141], N[(y * 2.0), $MachinePrecision], N[(x * N[(y * N[(2.0 / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999999e-61

   1. Initial program 81.2%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 99.9%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   if -5.7999999999999999e-61 < y < 9.80000000000000012e-141

   1. Initial program 79.7%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 68.2%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 68.2%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 68.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 89.5%

      \[\leadsto \color{blue}{2 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 89.5%

         \[\leadsto \color{blue}{y \cdot 2} \]

   7. Simplified 89.5%

      \[\leadsto \color{blue}{y \cdot 2} \]

   if 9.80000000000000012e-141 < y

   1. Initial program 86.7%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-*l/ 77.4%

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

      2. associate-/l* 77.3%

         \[\leadsto \color{blue}{\left(x \cdot \frac{2}{x - y}\right)} \cdot y \]

      3. associate-*l* 98.4%

         \[\leadsto \color{blue}{x \cdot \left(\frac{2}{x - y} \cdot y\right)} \]

      4. *-commutative 98.4%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{2}{x - y}\right)} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{2}{x - y}\right)} \]
   4. Add Preprocessing
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+65} \lor \neg \left(y \leq 3.8 \cdot 10^{+21}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.6e+65) (not (<= y 3.8e+21))) (* x -2.0) (* y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.6e+65) || !(y <= 3.8e+21)) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.6d+65)) .or. (.not. (y <= 3.8d+21))) then
        tmp = x * (-2.0d0)
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.6e+65) || !(y <= 3.8e+21)) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.6e+65) or not (y <= 3.8e+21):
		tmp = x * -2.0
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.6e+65) || !(y <= 3.8e+21))
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.6e+65) || ~((y <= 3.8e+21)))
		tmp = x * -2.0;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.6e+65], N[Not[LessEqual[y, 3.8e+21]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000003e65 or 3.8e21 < y

   1. Initial program 78.4%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 99.9%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 85.3%

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

   if -2.60000000000000003e65 < y < 3.8e21

   1. Initial program 85.6%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 78.4%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 78.4%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 78.4%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.7%

      \[\leadsto \color{blue}{2 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 80.7%

         \[\leadsto \color{blue}{y \cdot 2} \]

   7. Simplified 80.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+65} \lor \neg \left(y \leq 3.8 \cdot 10^{+21}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x \cdot -2 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x -2.0))

C

double code(double x, double y) {
	return x * -2.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (-2.0d0)
end function

Java

public static double code(double x, double y) {
	return x * -2.0;
}

Python

def code(x, y):
	return x * -2.0

Julia

function code(x, y)
	return Float64(x * -2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = x * -2.0;
end

Wolfram

code[x_, y_] := N[(x * -2.0), $MachinePrecision]

Derivation

1. Initial program 82.4%

   \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
2. Step-by-step derivation

   1. associate-/l* 88.2%

      \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

   2. associate-*l* 88.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

3. Simplified 88.2%

   \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 50.3%

   \[\leadsto x \cdot \color{blue}{-2} \]
6. Add Preprocessing

Developer target: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ (* 2.0 x) (- x y)) y)))
   (if (< x -1.7210442634149447e+81)
     t_0
     (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} 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 = ((2.0d0 * x) / (x - y)) * y
    if (x < (-1.7210442634149447d+81)) then
        tmp = t_0
    else if (x < 83645045635564430.0d0) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((2.0 * x) / (x - y)) * y
	tmp = 0
	if x < -1.7210442634149447e+81:
		tmp = t_0
	elif x < 83645045635564430.0:
		tmp = (x * 2.0) / ((x - y) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(2.0 * x) / Float64(x - y)) * y)
	tmp = 0.0
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((2.0 * x) / (x - y)) * y;
	tmp = 0.0;
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = (x * 2.0) / ((x - y) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[Less[x, -1.7210442634149447e+81], t$95$0, If[Less[x, 83645045635564430.0], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024087 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :alt
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))