Linear.Projection:inversePerspective from linear-1.19.1.3, C

Percentage Accurate: 76.7% → 100.0%

Time: 1.6s

Alternatives: 1

Speedup: 1.0×

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: 76.7% 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, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{-1}{x \cdot -2} - \frac{-0.5}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ -1.0 (* x -2.0)) (/ -0.5 y)))

C

double code(double x, double y) {
	return (-1.0 / (x * -2.0)) - (-0.5 / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((-1.0d0) / (x * (-2.0d0))) - ((-0.5d0) / y)
end function

Java

public static double code(double x, double y) {
	return (-1.0 / (x * -2.0)) - (-0.5 / y);
}

Python

def code(x, y):
	return (-1.0 / (x * -2.0)) - (-0.5 / y)

Julia

function code(x, y)
	return Float64(Float64(-1.0 / Float64(x * -2.0)) - Float64(-0.5 / y))
end

MATLAB

function tmp = code(x, y)
	tmp = (-1.0 / (x * -2.0)) - (-0.5 / y);
end

Wolfram

code[x_, y_] := N[(N[(-1.0 / N[(x * -2.0), $MachinePrecision]), $MachinePrecision] - N[(-0.5 / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.1%

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

   1. +-commutative 79.1%

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

   2. remove-double-neg 79.1%

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

   3. unsub-neg 79.1%

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

   4. div-sub 78.7%

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

   5. associate-/l/ 86.1%

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

   6. *-inverses 86.1%

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

   7. metadata-eval 86.1%

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

   8. distribute-neg-frac 86.1%

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

   9. distribute-frac-neg2 86.1%

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

   10. distribute-rgt-neg-in 86.1%

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

   11. metadata-eval 86.1%

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

   12. distribute-neg-frac 86.1%

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

   13. associate-/r* 100.0%

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

   14. distribute-neg-frac 100.0%

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

   15. associate-/r* 100.0%

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

   16. *-inverses 100.0%

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

   17. metadata-eval 100.0%

       \[\leadsto \frac{-1}{x \cdot -2} - \frac{-\color{blue}{0.5}}{y} \]

   18. metadata-eval 100.0%

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

   19. metadata-eval 100.0%

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

   20. metadata-eval 100.0%

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

   21. metadata-eval 100.0%

       \[\leadsto \frac{-1}{x \cdot -2} - \frac{-\color{blue}{0.5}}{y} \]

   22. metadata-eval 100.0%

       \[\leadsto \frac{-1}{x \cdot -2} - \frac{\color{blue}{-0.5}}{y} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{-1}{x \cdot -2} - \frac{-0.5}{y}} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \frac{-1}{x \cdot -2} - \frac{-0.5}{y} \]
6. Add Preprocessing

Developer target: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024075 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

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

  (/ (+ x y) (* (* x 2.0) y)))