Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.3% → 99.0%

Time: 4.5s

Alternatives: 6

Speedup: 0.7×

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: 77.3% 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: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+67}:\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(x + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.5e+101)
   (/ (* x 2.0) (/ (- x y) y))
   (if (<= y 4e+67) (* 2.0 (/ y (- 1.0 (/ y x)))) (* (/ y (- x y)) (+ x x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.5e+101) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else if (y <= 4e+67) {
		tmp = 2.0 * (y / (1.0 - (y / x)));
	} else {
		tmp = (y / (x - y)) * (x + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.5d+101)) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    else if (y <= 4d+67) then
        tmp = 2.0d0 * (y / (1.0d0 - (y / x)))
    else
        tmp = (y / (x - y)) * (x + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.5e+101) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else if (y <= 4e+67) {
		tmp = 2.0 * (y / (1.0 - (y / x)));
	} else {
		tmp = (y / (x - y)) * (x + x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.5e+101:
		tmp = (x * 2.0) / ((x - y) / y)
	elif y <= 4e+67:
		tmp = 2.0 * (y / (1.0 - (y / x)))
	else:
		tmp = (y / (x - y)) * (x + x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.5e+101)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	elseif (y <= 4e+67)
		tmp = Float64(2.0 * Float64(y / Float64(1.0 - Float64(y / x))));
	else
		tmp = Float64(Float64(y / Float64(x - y)) * Float64(x + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.5e+101)
		tmp = (x * 2.0) / ((x - y) / y);
	elseif (y <= 4e+67)
		tmp = 2.0 * (y / (1.0 - (y / x)));
	else
		tmp = (y / (x - y)) * (x + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.5e+101], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+67], N[(2.0 * N[(y / N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision] * N[(x + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999994e101

   1. Initial program 60.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   if -2.49999999999999994e101 < y < 3.99999999999999993e67

   1. Initial program 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-/l* 99.9%

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

      3. associate-/r* 99.9%

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

      4. associate-/r/ 99.9%

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

      5. div-sub 100.0%

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

      6. *-inverses 100.0%

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

   3. Simplified 100.0%

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

   if 3.99999999999999993e67 < y

   1. Initial program 71.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 100.0%

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

      3. clear-num 100.0%

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

      4. add-log-exp 5.0%

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

      5. exp-lft-sqr 5.0%

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

      6. log-prod 5.0%

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

      7. add-log-exp 12.3%

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

      8. add-log-exp 100.0%

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

   5. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+67}:\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(x + x\right)\\ \end{array} \]

Alternative 2: 93.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+172} \lor \neg \left(y \leq 10^{+184}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4e+172) (not (<= y 1e+184)))
   (* x -2.0)
   (* 2.0 (/ y (- 1.0 (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4e+172) || !(y <= 1e+184)) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * (y / (1.0 - (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.4d+172)) .or. (.not. (y <= 1d+184))) then
        tmp = x * (-2.0d0)
    else
        tmp = 2.0d0 * (y / (1.0d0 - (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.4e+172) || !(y <= 1e+184)) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * (y / (1.0 - (y / x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.4e+172) or not (y <= 1e+184):
		tmp = x * -2.0
	else:
		tmp = 2.0 * (y / (1.0 - (y / x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.4e+172) || !(y <= 1e+184))
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(2.0 * Float64(y / Float64(1.0 - Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.4e+172) || ~((y <= 1e+184)))
		tmp = x * -2.0;
	else
		tmp = 2.0 * (y / (1.0 - (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.4e+172], N[Not[LessEqual[y, 1e+184]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(2.0 * N[(y / N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e172 or 1.00000000000000002e184 < y

   1. Initial program 62.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 93.3%

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

      1. *-commutative 93.3%

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

   6. Simplified 93.3%

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

   if -1.4e172 < y < 1.00000000000000002e184

   1. Initial program 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-/l* 98.0%

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

      3. associate-/r* 98.0%

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

      4. associate-/r/ 98.0%

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

      5. div-sub 98.0%

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

      6. *-inverses 98.0%

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

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{x}} \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+172} \lor \neg \left(y \leq 10^{+184}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \end{array} \]

Alternative 3: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+73} \lor \neg \left(y \leq 2.8 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{y}{x - y} \cdot \left(x + x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.1e+73) (not (<= y 2.8e+67)))
   (* (/ y (- x y)) (+ x x))
   (* 2.0 (/ y (- 1.0 (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.1e+73) || !(y <= 2.8e+67)) {
		tmp = (y / (x - y)) * (x + x);
	} else {
		tmp = 2.0 * (y / (1.0 - (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.1d+73)) .or. (.not. (y <= 2.8d+67))) then
        tmp = (y / (x - y)) * (x + x)
    else
        tmp = 2.0d0 * (y / (1.0d0 - (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.1e+73) || !(y <= 2.8e+67)) {
		tmp = (y / (x - y)) * (x + x);
	} else {
		tmp = 2.0 * (y / (1.0 - (y / x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.1e+73) or not (y <= 2.8e+67):
		tmp = (y / (x - y)) * (x + x)
	else:
		tmp = 2.0 * (y / (1.0 - (y / x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.1e+73) || !(y <= 2.8e+67))
		tmp = Float64(Float64(y / Float64(x - y)) * Float64(x + x));
	else
		tmp = Float64(2.0 * Float64(y / Float64(1.0 - Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.1e+73) || ~((y <= 2.8e+67)))
		tmp = (y / (x - y)) * (x + x);
	else
		tmp = 2.0 * (y / (1.0 - (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.1e+73], N[Not[LessEqual[y, 2.8e+67]], $MachinePrecision]], N[(N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision] * N[(x + x), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y / N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e73 or 2.7999999999999998e67 < y

   1. Initial program 65.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

      3. clear-num 100.0%

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

      4. add-log-exp 5.1%

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

      5. exp-lft-sqr 5.1%

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

      6. log-prod 5.1%

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

      7. add-log-exp 11.7%

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

      8. add-log-exp 100.0%

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

   5. Applied egg-rr 100.0%

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

   if -1.1e73 < y < 2.7999999999999998e67

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-/l* 100.0%

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

      3. associate-/r* 100.0%

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

      4. associate-/r/ 100.0%

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

      5. div-sub 100.0%

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

      6. *-inverses 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{x}} \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+73} \lor \neg \left(y \leq 2.8 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{y}{x - y} \cdot \left(x + x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \end{array} \]

Alternative 4: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;x \cdot -2\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{-71}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.5e+69) (* x -2.0) (if (<= y 1.66e-71) (* y 2.0) (* x -2.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.5e+69) {
		tmp = x * -2.0;
	} else if (y <= 1.66e-71) {
		tmp = y * 2.0;
	} else {
		tmp = x * -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 <= (-2.5d+69)) then
        tmp = x * (-2.0d0)
    else if (y <= 1.66d-71) then
        tmp = y * 2.0d0
    else
        tmp = x * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.5e+69) {
		tmp = x * -2.0;
	} else if (y <= 1.66e-71) {
		tmp = y * 2.0;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.5e+69:
		tmp = x * -2.0
	elif y <= 1.66e-71:
		tmp = y * 2.0
	else:
		tmp = x * -2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.5e+69)
		tmp = Float64(x * -2.0);
	elseif (y <= 1.66e-71)
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(x * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.5e+69)
		tmp = x * -2.0;
	elseif (y <= 1.66e-71)
		tmp = y * 2.0;
	else
		tmp = x * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.5e+69], N[(x * -2.0), $MachinePrecision], If[LessEqual[y, 1.66e-71], N[(y * 2.0), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.50000000000000018e69 or 1.6599999999999999e-71 < y

   1. Initial program 72.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 77.1%

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

      1. *-commutative 77.1%

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

   6. Simplified 77.1%

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

   if -2.50000000000000018e69 < y < 1.6599999999999999e-71

   1. Initial program 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/l* 100.0%

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

      3. associate-/r* 100.0%

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

      4. associate-/r/ 100.0%

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

      5. div-sub 100.0%

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

      6. *-inverses 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 73.7%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;x \cdot -2\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{-71}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]

Alternative 5: 50.4% 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 74.6%

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

   1. associate-/l* 89.7%

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

3. Simplified 89.7%

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

4. Taylor expanded in x around 0 51.3%

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

   1. *-commutative 51.3%

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

6. Simplified 51.3%

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

7. Final simplification 51.3%

   \[\leadsto x \cdot -2 \]

Alternative 6: 3.7% accurate, 9.0× 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 74.6%

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

   1. associate-/l* 89.7%

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

3. Simplified 89.7%

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

   1. clear-num 89.5%

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

   2. associate-/r/ 89.5%

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

   3. clear-num 90.0%

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

   4. add-log-exp 5.9%

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

   5. exp-lft-sqr 5.7%

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

   6. log-prod 6.1%

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

   7. add-log-exp 12.4%

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

   8. add-log-exp 90.0%

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

5. Applied egg-rr 90.0%

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

6. Taylor expanded in y around 0 49.8%

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

8. Simplified 3.8%

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

9. Final simplification 3.8%

   \[\leadsto -1 \]

Developer target: 99.4% accurate, 0.7× 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 2023275 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (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)))