Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.5% → 99.3%

Time: 8.3s

Alternatives: 6

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: 76.5% 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: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+92} \lor \neg \left(y \leq 1.25 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.3e+92) (not (<= y 1.25e-67)))
   (/ (* x 2.0) (+ (/ x y) -1.0))
   (* y (/ (* x 2.0) (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e+92) || !(y <= 1.25e-67)) {
		tmp = (x * 2.0) / ((x / y) + -1.0);
	} else {
		tmp = y * ((x * 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 <= (-1.3d+92)) .or. (.not. (y <= 1.25d-67))) then
        tmp = (x * 2.0d0) / ((x / y) + (-1.0d0))
    else
        tmp = y * ((x * 2.0d0) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e+92) || !(y <= 1.25e-67)) {
		tmp = (x * 2.0) / ((x / y) + -1.0);
	} else {
		tmp = y * ((x * 2.0) / (x - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.3e+92) or not (y <= 1.25e-67):
		tmp = (x * 2.0) / ((x / y) + -1.0)
	else:
		tmp = y * ((x * 2.0) / (x - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.3e+92) || !(y <= 1.25e-67))
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x / y) + -1.0));
	else
		tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.3e+92) || ~((y <= 1.25e-67)))
		tmp = (x * 2.0) / ((x / y) + -1.0);
	else
		tmp = y * ((x * 2.0) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.3e+92], N[Not[LessEqual[y, 1.25e-67]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2999999999999999e92 or 1.25e-67 < y

   1. Initial program 78.5%

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

      1. associate-*r* 99.9%

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

      2. associate-/l* 78.5%

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

      3. add-log-exp 6.7%

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

      4. *-un-lft-identity 6.7%

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

      5. log-prod 6.7%

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

      6. metadata-eval 6.7%

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

      7. add-log-exp 78.5%

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

      8. associate-/l* 99.9%

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

      9. associate-*r* 99.9%

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

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{0 + x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   7. Step-by-step derivation

      1. +-lft-identity 99.9%

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

      2. associate-*r* 99.9%

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

      3. associate-*r/ 78.5%

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

      4. associate-*l/ 75.1%

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

      5. associate-/r/ 99.9%

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

      6. div-sub 99.9%

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

      7. sub-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   if -1.2999999999999999e92 < y < 1.25e-67

   1. Initial program 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-/l* 100.0%

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

   4. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+92} \lor \neg \left(y \leq 1.25 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-65} \lor \neg \left(y \leq 3.9 \cdot 10^{-116}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9.8e-65) (not (<= y 3.9e-116)))
   (* x (* 2.0 (/ y (- x y))))
   (* y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9.8e-65) || !(y <= 3.9e-116)) {
		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 <= (-9.8d-65)) .or. (.not. (y <= 3.9d-116))) 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 <= -9.8e-65) || !(y <= 3.9e-116)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9.8e-65) or not (y <= 3.9e-116):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9.8e-65) || !(y <= 3.9e-116))
		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 <= -9.8e-65) || ~((y <= 3.9e-116)))
		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, -9.8e-65], N[Not[LessEqual[y, 3.9e-116]], $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 < -9.79999999999999929e-65 or 3.9000000000000001e-116 < y

   1. Initial program 79.8%

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

      1. associate-/l* 99.6%

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

      2. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   if -9.79999999999999929e-65 < y < 3.9000000000000001e-116

   1. Initial program 74.7%

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

      1. associate-/l* 65.6%

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

      2. associate-*l* 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in x around inf 93.0%

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

      1. *-commutative 93.0%

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

   7. Simplified 93.0%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-65} \lor \neg \left(y \leq 3.9 \cdot 10^{-116}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \lor \neg \left(y \leq 1.9 \cdot 10^{+120}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.0) (not (<= y 1.9e+120)))
   (* x (* 2.0 (/ y (- x y))))
   (* y (/ (* x 2.0) (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.0) || !(y <= 1.9e+120)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y * ((x * 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 <= (-5.0d0)) .or. (.not. (y <= 1.9d+120))) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else
        tmp = y * ((x * 2.0d0) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5.0) || !(y <= 1.9e+120)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y * ((x * 2.0) / (x - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.0) or not (y <= 1.9e+120):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = y * ((x * 2.0) / (x - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.0) || !(y <= 1.9e+120))
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	else
		tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5.0) || ~((y <= 1.9e+120)))
		tmp = x * (2.0 * (y / (x - y)));
	else
		tmp = y * ((x * 2.0) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.0], N[Not[LessEqual[y, 1.9e+120]], $MachinePrecision]], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5 or 1.8999999999999999e120 < y

   1. Initial program 73.3%

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

   if -5 < y < 1.8999999999999999e120

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \lor \neg \left(y \leq 1.9 \cdot 10^{+120}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-16} \lor \neg \left(y \leq 1.9 \cdot 10^{+120}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.5e-16) (not (<= y 1.9e+120)))
   (* x (* 2.0 (/ y (- x y))))
   (/ y (/ (- x y) (* x 2.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.5e-16) || !(y <= 1.9e+120)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y / ((x - y) / (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 <= (-5.5d-16)) .or. (.not. (y <= 1.9d+120))) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else
        tmp = y / ((x - y) / (x * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5.5e-16) || !(y <= 1.9e+120)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y / ((x - y) / (x * 2.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.5e-16) or not (y <= 1.9e+120):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = y / ((x - y) / (x * 2.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.5e-16) || !(y <= 1.9e+120))
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	else
		tmp = Float64(y / Float64(Float64(x - y) / Float64(x * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5.5e-16) || ~((y <= 1.9e+120)))
		tmp = x * (2.0 * (y / (x - y)));
	else
		tmp = y / ((x - y) / (x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.5e-16], N[Not[LessEqual[y, 1.9e+120]], $MachinePrecision]], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(x - y), $MachinePrecision] / N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999964e-16 or 1.8999999999999999e120 < y

   1. Initial program 73.7%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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 -5.49999999999999964e-16 < y < 1.8999999999999999e120

   1. Initial program 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-16} \lor \neg \left(y \leq 1.9 \cdot 10^{+120}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+48} \lor \neg \left(y \leq 1.5 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.3e+48) (not (<= y 1.5e+31))) (* x -2.0) (* y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e+48) || !(y <= 1.5e+31)) {
		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 <= (-1.3d+48)) .or. (.not. (y <= 1.5d+31))) 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 <= -1.3e+48) || !(y <= 1.5e+31)) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.3e+48) or not (y <= 1.5e+31):
		tmp = x * -2.0
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.3e+48) || !(y <= 1.5e+31))
		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 <= -1.3e+48) || ~((y <= 1.5e+31)))
		tmp = x * -2.0;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.3e+48], N[Not[LessEqual[y, 1.5e+31]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999998e48 or 1.49999999999999995e31 < y

   1. Initial program 75.3%

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

   5. Taylor expanded in y around inf 79.7%

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

   if -1.29999999999999998e48 < y < 1.49999999999999995e31

   1. Initial program 80.4%

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

      1. associate-/l* 77.3%

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

      2. associate-*l* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in x around inf 80.3%

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

      1. *-commutative 80.3%

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

   7. Simplified 80.3%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+48} \lor \neg \left(y \leq 1.5 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.8% 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 78.0%

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

   1. associate-/l* 87.9%

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

   2. associate-*l* 87.9%

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

3. Simplified 87.9%

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

5. Taylor expanded in y around inf 48.8%

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

6. Final simplification 48.8%

   \[\leadsto x \cdot -2 \]
7. 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 2024071 
(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)))