Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.6% → 99.2%

Time: 6.5s

Alternatives: 5

Speedup: 0.5×

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: 77.6% 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: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-124} \lor \neg \left(x \leq 2 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y - x} \cdot \frac{y}{-0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.8e-124) (not (<= x 2e-9)))
   (* (/ x (- y x)) (/ y -0.5))
   (/ (* x 2.0) (/ (- x y) y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.8e-124) || !(x <= 2e-9)) {
		tmp = (x / (y - x)) * (y / -0.5);
	} else {
		tmp = (x * 2.0) / ((x - y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-2.8d-124)) .or. (.not. (x <= 2d-9))) then
        tmp = (x / (y - x)) * (y / (-0.5d0))
    else
        tmp = (x * 2.0d0) / ((x - y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.8e-124) || !(x <= 2e-9)) {
		tmp = (x / (y - x)) * (y / -0.5);
	} else {
		tmp = (x * 2.0) / ((x - y) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.8e-124) or not (x <= 2e-9):
		tmp = (x / (y - x)) * (y / -0.5)
	else:
		tmp = (x * 2.0) / ((x - y) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.8e-124) || !(x <= 2e-9))
		tmp = Float64(Float64(x / Float64(y - x)) * Float64(y / -0.5));
	else
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.8e-124) || ~((x <= 2e-9)))
		tmp = (x / (y - x)) * (y / -0.5);
	else
		tmp = (x * 2.0) / ((x - y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.8e-124], N[Not[LessEqual[x, 2e-9]], $MachinePrecision]], N[(N[(x / N[(y - x), $MachinePrecision]), $MachinePrecision] * N[(y / -0.5), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999998e-124 or 2.00000000000000012e-9 < x

   1. Initial program 80.4%

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

      1. sub-neg 80.4%

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

      2. +-commutative 80.4%

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

      3. neg-sub0 80.4%

         \[\leadsto \frac{\left(x \cdot 2\right) \cdot y}{\color{blue}{\left(0 - y\right)} + x} \]

      4. associate-+l- 80.4%

         \[\leadsto \frac{\left(x \cdot 2\right) \cdot y}{\color{blue}{0 - \left(y - x\right)}} \]

      5. sub0-neg 80.4%

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

      6. distribute-frac-neg2 80.4%

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

      7. distribute-frac-neg 80.4%

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

      8. *-commutative 80.4%

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

      9. associate-*r* 80.4%

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

      10. distribute-rgt-neg-in 80.4%

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

      11. associate-/l* 80.2%

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

      12. *-commutative 80.2%

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

      13. metadata-eval 80.2%

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

   3. Simplified 80.2%

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

      1. clear-num 80.2%

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

      2. un-div-inv 80.4%

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

      3. div-inv 80.4%

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

      4. metadata-eval 80.4%

         \[\leadsto \frac{x \cdot y}{\left(y - x\right) \cdot \color{blue}{-0.5}} \]

   6. Applied egg-rr 80.4%

      \[\leadsto \color{blue}{\frac{x \cdot y}{\left(y - x\right) \cdot -0.5}} \]
   7. Step-by-step derivation

      1. times-frac 99.9%

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

   8. Simplified 99.9%

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

   if -2.79999999999999998e-124 < x < 2.00000000000000012e-9

   1. Initial program 75.0%

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

      1. associate-/l* 100.0%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*r* 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-124} \lor \neg \left(x \leq 2 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y - x} \cdot \frac{y}{-0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+54} \lor \neg \left(x \leq 10^{+66}\right):\\ \;\;\;\;\frac{x}{y - x} \cdot \frac{y}{-0.5}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.2e+54) (not (<= x 1e+66)))
   (* (/ x (- y x)) (/ y -0.5))
   (* x (* 2.0 (/ y (- x y))))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.2e+54) || !(x <= 1e+66)) {
		tmp = (x / (y - x)) * (y / -0.5);
	} else {
		tmp = x * (2.0 * (y / (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 ((x <= (-2.2d+54)) .or. (.not. (x <= 1d+66))) then
        tmp = (x / (y - x)) * (y / (-0.5d0))
    else
        tmp = x * (2.0d0 * (y / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.2e+54) || !(x <= 1e+66)) {
		tmp = (x / (y - x)) * (y / -0.5);
	} else {
		tmp = x * (2.0 * (y / (x - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.2e+54) or not (x <= 1e+66):
		tmp = (x / (y - x)) * (y / -0.5)
	else:
		tmp = x * (2.0 * (y / (x - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.2e+54) || !(x <= 1e+66))
		tmp = Float64(Float64(x / Float64(y - x)) * Float64(y / -0.5));
	else
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.2e+54) || ~((x <= 1e+66)))
		tmp = (x / (y - x)) * (y / -0.5);
	else
		tmp = x * (2.0 * (y / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.2e+54], N[Not[LessEqual[x, 1e+66]], $MachinePrecision]], N[(N[(x / N[(y - x), $MachinePrecision]), $MachinePrecision] * N[(y / -0.5), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1999999999999999e54 or 9.99999999999999945e65 < x

   1. Initial program 74.3%

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

      1. sub-neg 74.3%

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

      2. +-commutative 74.3%

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

      3. neg-sub0 74.3%

         \[\leadsto \frac{\left(x \cdot 2\right) \cdot y}{\color{blue}{\left(0 - y\right)} + x} \]

      4. associate-+l- 74.3%

         \[\leadsto \frac{\left(x \cdot 2\right) \cdot y}{\color{blue}{0 - \left(y - x\right)}} \]

      5. sub0-neg 74.3%

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

      6. distribute-frac-neg2 74.3%

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

      7. distribute-frac-neg 74.3%

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

      8. *-commutative 74.3%

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

      9. associate-*r* 74.3%

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

      10. distribute-rgt-neg-in 74.3%

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

      11. associate-/l* 74.0%

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

      12. *-commutative 74.0%

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

      13. metadata-eval 74.0%

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

   3. Simplified 74.0%

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

      1. clear-num 74.0%

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

      2. un-div-inv 74.3%

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

      3. div-inv 74.3%

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

      4. metadata-eval 74.3%

         \[\leadsto \frac{x \cdot y}{\left(y - x\right) \cdot \color{blue}{-0.5}} \]

   6. Applied egg-rr 74.3%

      \[\leadsto \color{blue}{\frac{x \cdot y}{\left(y - x\right) \cdot -0.5}} \]
   7. Step-by-step derivation

      1. times-frac 100.0%

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

   8. Simplified 100.0%

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

   if -2.1999999999999999e54 < x < 9.99999999999999945e65

   1. Initial program 81.3%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+54} \lor \neg \left(x \leq 10^{+66}\right):\\ \;\;\;\;\frac{x}{y - x} \cdot \frac{y}{-0.5}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-133} \lor \neg \left(y \leq 1.15 \cdot 10^{-190}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.9e-133) (not (<= y 1.15e-190)))
   (* x (* 2.0 (/ y (- x y))))
   (* y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.9e-133) || !(y <= 1.15e-190)) {
		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 <= (-2.9d-133)) .or. (.not. (y <= 1.15d-190))) 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 <= -2.9e-133) || !(y <= 1.15e-190)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.9e-133) or not (y <= 1.15e-190):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.9e-133) || !(y <= 1.15e-190))
		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 <= -2.9e-133) || ~((y <= 1.15e-190)))
		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, -2.9e-133], N[Not[LessEqual[y, 1.15e-190]], $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 < -2.8999999999999998e-133 or 1.14999999999999996e-190 < y

   1. Initial program 79.1%

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

      1. associate-/l* 96.9%

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

      2. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   if -2.8999999999999998e-133 < y < 1.14999999999999996e-190

   1. Initial program 76.5%

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

      1. associate-/l* 59.6%

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

      2. associate-*l* 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in x around inf 97.7%

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

      1. *-commutative 97.7%

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

   7. Simplified 97.7%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-133} \lor \neg \left(y \leq 1.15 \cdot 10^{-190}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+55} \lor \neg \left(y \leq 1.15 \cdot 10^{-71}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.08e+55) (not (<= y 1.15e-71))) (* x -2.0) (* y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.08e+55) || !(y <= 1.15e-71)) {
		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 <= (-1.08d+55)) .or. (.not. (y <= 1.15d-71))) 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 <= -1.08e+55) || !(y <= 1.15e-71)) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.08e+55) or not (y <= 1.15e-71):
		tmp = x * -2.0
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.08e+55) || !(y <= 1.15e-71))
		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 <= -1.08e+55) || ~((y <= 1.15e-71)))
		tmp = x * -2.0;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.08e+55], N[Not[LessEqual[y, 1.15e-71]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.08000000000000004e55 or 1.1499999999999999e-71 < y

   1. Initial program 76.9%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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 80.3%

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

   if -1.08000000000000004e55 < y < 1.1499999999999999e-71

   1. Initial program 79.8%

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

      1. associate-/l* 76.9%

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

      2. associate-*l* 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in x around inf 81.4%

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

      1. *-commutative 81.4%

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

   7. Simplified 81.4%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+55} \lor \neg \left(y \leq 1.15 \cdot 10^{-71}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.5% 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 78.5%

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

   1. associate-/l* 87.4%

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

   2. associate-*l* 87.4%

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

3. Simplified 87.4%

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

5. Taylor expanded in y around inf 47.7%

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

Developer Target 1: 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 2024180 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1721044263414944700000000000000000000000000000000000000000000000000000000000000000) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564430) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y))))

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