Linear.Projection:inversePerspective from linear-1.19.1.3, C

Percentage Accurate: 77.5% → 100.0%

Time: 3.9s

Alternatives: 5

Speedup: 1.3×

• Unsound rule application detected in e-graph. Results may not be sound.

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: 77.5% 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 77.1%

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

2. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{x}} \]
3. Step-by-step derivation

   1. associate-*r/ 100.0%

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

   2. metadata-eval 100.0%

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

   3. associate-*r/ 100.0%

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

   4. metadata-eval 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \frac{0.5}{y} + \frac{0.5}{x} \]

Alternative 2: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-36} \lor \neg \left(x \leq -6.8 \cdot 10^{-87}\right) \land x \leq -3.4 \cdot 10^{-132}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -6e-36) (and (not (<= x -6.8e-87)) (<= x -3.4e-132)))
   (/ 0.5 y)
   (/ 0.5 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -6e-36) || (!(x <= -6.8e-87) && (x <= -3.4e-132))) {
		tmp = 0.5 / y;
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-6d-36)) .or. (.not. (x <= (-6.8d-87))) .and. (x <= (-3.4d-132))) then
        tmp = 0.5d0 / y
    else
        tmp = 0.5d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -6e-36) || (!(x <= -6.8e-87) && (x <= -3.4e-132))) {
		tmp = 0.5 / y;
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -6e-36) or (not (x <= -6.8e-87) and (x <= -3.4e-132)):
		tmp = 0.5 / y
	else:
		tmp = 0.5 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -6e-36) || (!(x <= -6.8e-87) && (x <= -3.4e-132)))
		tmp = Float64(0.5 / y);
	else
		tmp = Float64(0.5 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -6e-36) || (~((x <= -6.8e-87)) && (x <= -3.4e-132)))
		tmp = 0.5 / y;
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -6e-36], And[N[Not[LessEqual[x, -6.8e-87]], $MachinePrecision], LessEqual[x, -3.4e-132]]], N[(0.5 / y), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000003e-36 or -6.7999999999999997e-87 < x < -3.39999999999999983e-132

   1. Initial program 81.6%

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

   2. Taylor expanded in x around inf 66.5%

      \[\leadsto \color{blue}{\frac{0.5}{y}} \]

   if -6.0000000000000003e-36 < x < -6.7999999999999997e-87 or -3.39999999999999983e-132 < x

   1. Initial program 74.6%

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

   2. Taylor expanded in x around 0 65.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-36} \lor \neg \left(x \leq -6.8 \cdot 10^{-87}\right) \land x \leq -3.4 \cdot 10^{-132}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]

Alternative 3: 50.4% 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 77.1%

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

2. Taylor expanded in x around 0 55.0%

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

3. Final simplification 55.0%

   \[\leadsto \frac{0.5}{x} \]

Alternative 4: 2.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.0)

C

double code(double x, double y) {
	return 0.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0
end function

Java

public static double code(double x, double y) {
	return 0.0;
}

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0;
end

Wolfram

code[x_, y_] := 0.0

Derivation

1. Initial program 77.1%

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

   1. add-log-exp 7.5%

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

   2. *-un-lft-identity 7.5%

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

   3. log-prod 7.5%

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

   4. metadata-eval 7.5%

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

   5. add-log-exp 77.1%

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

   6. associate-*l* 77.1%

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

   7. *-commutative 77.1%

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

3. Applied egg-rr 77.1%

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

   1. +-lft-identity 77.1%

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

   2. *-rgt-identity 77.1%

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

   3. associate-*r/ 75.9%

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

   4. *-commutative 75.9%

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

   5. associate-*r* 75.9%

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

   6. *-commutative 75.9%

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

   7. count-2 75.9%

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

   8. associate-/r* 76.4%

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

   9. count-2 76.4%

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

   10. associate-/r* 76.4%

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

   11. metadata-eval 76.4%

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

5. Simplified 76.4%

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

   1. clear-num 76.0%

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

   2. un-div-inv 77.1%

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

   3. div-inv 77.1%

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

   4. associate-/r* 77.1%

      \[\leadsto \frac{x + y}{\color{blue}{\frac{\frac{y}{0.5}}{\frac{1}{x}}}} \]

   5. div-inv 77.1%

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

   6. metadata-eval 77.1%

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

   7. associate-/l* 87.3%

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

   8. div-inv 87.3%

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

   9. associate-/l/ 77.1%

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

   10. associate-/r* 87.4%

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

   11. +-commutative 87.4%

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

   12. add-log-exp 4.5%

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

   13. exp-lft-sqr 4.5%

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

   14. log-prod 4.5%

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

   15. add-log-exp 10.2%

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

   16. add-log-exp 87.4%

       \[\leadsto \frac{\frac{y + x}{y + \color{blue}{y}}}{x} \]

7. Applied egg-rr 87.4%

   \[\leadsto \color{blue}{\frac{\frac{y + x}{y + y}}{x}} \]

9. Applied egg-rr 2.6%

   \[\leadsto \color{blue}{x - x} \]
10. Step-by-step derivation

    1. +-inverses 2.6%

       \[\leadsto \color{blue}{0} \]

11. Simplified 2.6%

    \[\leadsto \color{blue}{0} \]

12. Final simplification 2.6%

    \[\leadsto 0 \]

Alternative 5: 3.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 77.1%

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

   1. add-log-exp 7.5%

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

   2. *-un-lft-identity 7.5%

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

   3. log-prod 7.5%

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

   4. metadata-eval 7.5%

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

   5. add-log-exp 77.1%

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

   6. associate-*l* 77.1%

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

   7. *-commutative 77.1%

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

3. Applied egg-rr 77.1%

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

   1. +-lft-identity 77.1%

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

   2. *-rgt-identity 77.1%

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

   3. associate-*r/ 75.9%

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

   4. *-commutative 75.9%

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

   5. associate-*r* 75.9%

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

   6. *-commutative 75.9%

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

   7. count-2 75.9%

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

   8. associate-/r* 76.4%

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

   9. count-2 76.4%

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

   10. associate-/r* 76.4%

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

   11. metadata-eval 76.4%

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

5. Simplified 76.4%

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

   1. clear-num 76.0%

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

   2. un-div-inv 77.1%

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

   3. div-inv 77.1%

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

   4. associate-/r* 77.1%

      \[\leadsto \frac{x + y}{\color{blue}{\frac{\frac{y}{0.5}}{\frac{1}{x}}}} \]

   5. div-inv 77.1%

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

   6. metadata-eval 77.1%

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

   7. associate-/l* 87.3%

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

   8. div-inv 87.3%

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

   9. associate-/l/ 77.1%

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

   10. associate-/r* 87.4%

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

   11. +-commutative 87.4%

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

   12. add-log-exp 4.5%

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

   13. exp-lft-sqr 4.5%

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

   14. log-prod 4.5%

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

   15. add-log-exp 10.2%

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

   16. add-log-exp 87.4%

       \[\leadsto \frac{\frac{y + x}{y + \color{blue}{y}}}{x} \]

7. Applied egg-rr 87.4%

   \[\leadsto \color{blue}{\frac{\frac{y + x}{y + y}}{x}} \]

9. Applied egg-rr 2.8%

   \[\leadsto \color{blue}{\left|x\right|} \]
10. Step-by-step derivation

    1. unpow1 2.8%

       \[\leadsto \left|\color{blue}{{x}^{1}}\right| \]

    2. sqr-pow 1.5%

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

    3. fabs-sqr 1.5%

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

    4. sqr-pow 3.3%

       \[\leadsto \color{blue}{{x}^{1}} \]

    5. unpow1 3.3%

       \[\leadsto \color{blue}{x} \]

11. Simplified 3.3%

    \[\leadsto \color{blue}{x} \]

12. Final simplification 3.3%

    \[\leadsto x \]

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 2023174 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (+ (/ 0.5 x) (/ 0.5 y))

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