Linear.Projection:inversePerspective from linear-1.19.1.3, B

Percentage Accurate: 76.8% → 100.0%

Time: 2.9s

Alternatives: 3

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

   1. remove-double-neg 76.9%

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

   2. distribute-rgt-neg-out 76.9%

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

   3. distribute-frac-neg2 76.9%

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

   4. neg-mul-1 76.9%

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

   5. div-sub 76.4%

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

   6. distribute-lft-out-- 76.4%

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

   7. neg-mul-1 76.4%

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

   8. distribute-frac-neg2 76.4%

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

   9. distribute-rgt-neg-out 76.4%

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

   10. remove-double-neg 76.4%

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

   11. cancel-sign-sub-inv 76.4%

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

   12. associate-/r* 82.3%

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

   13. associate-/r* 82.3%

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

   14. *-inverses 82.3%

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

   15. metadata-eval 82.3%

       \[\leadsto \frac{\color{blue}{0.5}}{y} + \left(--1\right) \cdot \frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)} \]

   16. metadata-eval 82.3%

       \[\leadsto \frac{0.5}{y} + \color{blue}{1} \cdot \frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)} \]

   17. *-lft-identity 82.3%

       \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)}} \]

   18. distribute-rgt-neg-out 82.3%

       \[\leadsto \frac{0.5}{y} + \frac{y}{\color{blue}{-\left(x \cdot 2\right) \cdot y}} \]

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \frac{0.5}{y} + \frac{-0.5}{x} \]
6. Add Preprocessing

Alternative 2: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-11} \lor \neg \left(y \leq 6 \cdot 10^{-67}\right) \land \left(y \leq 1.7 \cdot 10^{-17} \lor \neg \left(y \leq 3.4 \cdot 10^{+99}\right)\right):\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.2e-11)
         (and (not (<= y 6e-67)) (or (<= y 1.7e-17) (not (<= y 3.4e+99)))))
   (/ -0.5 x)
   (/ 0.5 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.2e-11) || (!(y <= 6e-67) && ((y <= 1.7e-17) || !(y <= 3.4e+99)))) {
		tmp = -0.5 / x;
	} else {
		tmp = 0.5 / 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 <= (-6.2d-11)) .or. (.not. (y <= 6d-67)) .and. (y <= 1.7d-17) .or. (.not. (y <= 3.4d+99))) then
        tmp = (-0.5d0) / x
    else
        tmp = 0.5d0 / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.2e-11) || (!(y <= 6e-67) && ((y <= 1.7e-17) || !(y <= 3.4e+99)))) {
		tmp = -0.5 / x;
	} else {
		tmp = 0.5 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.2e-11) or (not (y <= 6e-67) and ((y <= 1.7e-17) or not (y <= 3.4e+99))):
		tmp = -0.5 / x
	else:
		tmp = 0.5 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.2e-11) || (!(y <= 6e-67) && ((y <= 1.7e-17) || !(y <= 3.4e+99))))
		tmp = Float64(-0.5 / x);
	else
		tmp = Float64(0.5 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.2e-11) || (~((y <= 6e-67)) && ((y <= 1.7e-17) || ~((y <= 3.4e+99)))))
		tmp = -0.5 / x;
	else
		tmp = 0.5 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.2e-11], And[N[Not[LessEqual[y, 6e-67]], $MachinePrecision], Or[LessEqual[y, 1.7e-17], N[Not[LessEqual[y, 3.4e+99]], $MachinePrecision]]]], N[(-0.5 / x), $MachinePrecision], N[(0.5 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000056e-11 or 6.00000000000000065e-67 < y < 1.6999999999999999e-17 or 3.39999999999999984e99 < y

   1. Initial program 75.2%

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

      1. remove-double-neg 75.2%

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

      2. distribute-rgt-neg-out 75.2%

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

      3. distribute-frac-neg2 75.2%

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

      4. neg-mul-1 75.2%

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

      5. div-sub 75.2%

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

      6. distribute-lft-out-- 75.2%

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

      7. neg-mul-1 75.2%

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

      8. distribute-frac-neg2 75.2%

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

      9. distribute-rgt-neg-out 75.2%

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

      10. remove-double-neg 75.2%

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

      11. cancel-sign-sub-inv 75.2%

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

      12. associate-/r* 84.9%

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

      13. associate-/r* 84.9%

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

      14. *-inverses 84.9%

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

      15. metadata-eval 84.9%

          \[\leadsto \frac{\color{blue}{0.5}}{y} + \left(--1\right) \cdot \frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)} \]

      16. metadata-eval 84.9%

          \[\leadsto \frac{0.5}{y} + \color{blue}{1} \cdot \frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)} \]

      17. *-lft-identity 84.9%

          \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)}} \]

      18. distribute-rgt-neg-out 84.9%

          \[\leadsto \frac{0.5}{y} + \frac{y}{\color{blue}{-\left(x \cdot 2\right) \cdot y}} \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 78.3%

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

   if -6.20000000000000056e-11 < y < 6.00000000000000065e-67 or 1.6999999999999999e-17 < y < 3.39999999999999984e99

   1. Initial program 78.4%

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

      1. remove-double-neg 78.4%

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

      2. distribute-rgt-neg-out 78.4%

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

      3. distribute-frac-neg2 78.4%

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

      4. neg-mul-1 78.4%

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

      5. div-sub 77.4%

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

      6. distribute-lft-out-- 77.4%

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

      7. neg-mul-1 77.4%

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

      8. distribute-frac-neg2 77.4%

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

      9. distribute-rgt-neg-out 77.4%

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

      10. remove-double-neg 77.4%

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

      11. cancel-sign-sub-inv 77.4%

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

      12. associate-/r* 80.1%

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

      13. associate-/r* 80.1%

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

      14. *-inverses 80.1%

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

      15. metadata-eval 80.1%

          \[\leadsto \frac{\color{blue}{0.5}}{y} + \left(--1\right) \cdot \frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)} \]

      16. metadata-eval 80.1%

          \[\leadsto \frac{0.5}{y} + \color{blue}{1} \cdot \frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)} \]

      17. *-lft-identity 80.1%

          \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)}} \]

      18. distribute-rgt-neg-out 80.1%

          \[\leadsto \frac{0.5}{y} + \frac{y}{\color{blue}{-\left(x \cdot 2\right) \cdot y}} \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-11} \lor \neg \left(y \leq 6 \cdot 10^{-67}\right) \land \left(y \leq 1.7 \cdot 10^{-17} \lor \neg \left(y \leq 3.4 \cdot 10^{+99}\right)\right):\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.1% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

   1. remove-double-neg 76.9%

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

   2. distribute-rgt-neg-out 76.9%

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

   3. distribute-frac-neg2 76.9%

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

   4. neg-mul-1 76.9%

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

   5. div-sub 76.4%

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

   6. distribute-lft-out-- 76.4%

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

   7. neg-mul-1 76.4%

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

   8. distribute-frac-neg2 76.4%

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

   9. distribute-rgt-neg-out 76.4%

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

   10. remove-double-neg 76.4%

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

   11. cancel-sign-sub-inv 76.4%

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

   12. associate-/r* 82.3%

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

   13. associate-/r* 82.3%

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

   14. *-inverses 82.3%

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

   15. metadata-eval 82.3%

       \[\leadsto \frac{\color{blue}{0.5}}{y} + \left(--1\right) \cdot \frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)} \]

   16. metadata-eval 82.3%

       \[\leadsto \frac{0.5}{y} + \color{blue}{1} \cdot \frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)} \]

   17. *-lft-identity 82.3%

       \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{y}{\left(x \cdot 2\right) \cdot \left(-y\right)}} \]

   18. distribute-rgt-neg-out 82.3%

       \[\leadsto \frac{0.5}{y} + \frac{y}{\color{blue}{-\left(x \cdot 2\right) \cdot y}} \]

3. Simplified 100.0%

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

5. Taylor expanded in y around inf 48.3%

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

6. Final simplification 48.3%

   \[\leadsto \frac{-0.5}{x} \]
7. Add Preprocessing

Developer target: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024082 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

  :alt
  (- (/ 0.5 y) (/ 0.5 x))

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