Numeric.Log:$clog1p from log-domain-0.10.2.1, A

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

Alternatives: 7

Speedup: 1.2×

• 43.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return ((x * 2.0) + (x * x)) + (y * y)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return ((x * 2.0) + (x * x)) + (y * y)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return ((x * 2.0) + (x * x)) + (y * y)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

   \[\leadsto \left(x \cdot 2 + x \cdot x\right) + y \cdot y \]

Alternative 2: 69.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-175}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-75}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-22}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+58}:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.65e-5)
   (* x x)
   (if (<= x -9.5e-175)
     (+ x x)
     (if (<= x 7e-75)
       (* y y)
       (if (<= x 7.5e-22) (+ x x) (if (<= x 1.5e+58) (* y y) (* x x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.65e-5) {
		tmp = x * x;
	} else if (x <= -9.5e-175) {
		tmp = x + x;
	} else if (x <= 7e-75) {
		tmp = y * y;
	} else if (x <= 7.5e-22) {
		tmp = x + x;
	} else if (x <= 1.5e+58) {
		tmp = y * y;
	} else {
		tmp = x * 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 <= (-1.65d-5)) then
        tmp = x * x
    else if (x <= (-9.5d-175)) then
        tmp = x + x
    else if (x <= 7d-75) then
        tmp = y * y
    else if (x <= 7.5d-22) then
        tmp = x + x
    else if (x <= 1.5d+58) then
        tmp = y * y
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.65e-5) {
		tmp = x * x;
	} else if (x <= -9.5e-175) {
		tmp = x + x;
	} else if (x <= 7e-75) {
		tmp = y * y;
	} else if (x <= 7.5e-22) {
		tmp = x + x;
	} else if (x <= 1.5e+58) {
		tmp = y * y;
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.65e-5:
		tmp = x * x
	elif x <= -9.5e-175:
		tmp = x + x
	elif x <= 7e-75:
		tmp = y * y
	elif x <= 7.5e-22:
		tmp = x + x
	elif x <= 1.5e+58:
		tmp = y * y
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.65e-5)
		tmp = Float64(x * x);
	elseif (x <= -9.5e-175)
		tmp = Float64(x + x);
	elseif (x <= 7e-75)
		tmp = Float64(y * y);
	elseif (x <= 7.5e-22)
		tmp = Float64(x + x);
	elseif (x <= 1.5e+58)
		tmp = Float64(y * y);
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.65e-5)
		tmp = x * x;
	elseif (x <= -9.5e-175)
		tmp = x + x;
	elseif (x <= 7e-75)
		tmp = y * y;
	elseif (x <= 7.5e-22)
		tmp = x + x;
	elseif (x <= 1.5e+58)
		tmp = y * y;
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.65e-5], N[(x * x), $MachinePrecision], If[LessEqual[x, -9.5e-175], N[(x + x), $MachinePrecision], If[LessEqual[x, 7e-75], N[(y * y), $MachinePrecision], If[LessEqual[x, 7.5e-22], N[(x + x), $MachinePrecision], If[LessEqual[x, 1.5e+58], N[(y * y), $MachinePrecision], N[(x * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6500000000000001e-5 or 1.5000000000000001e58 < x

   1. Initial program 100.0%

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

      1. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.4%

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

      1. unpow2 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x around inf 87.5%

      \[\leadsto \color{blue}{{x}^{2}} \]
   8. Step-by-step derivation

      1. unpow2 87.5%

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

   9. Simplified 87.5%

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

   if -1.6500000000000001e-5 < x < -9.50000000000000052e-175 or 6.9999999999999997e-75 < x < 7.49999999999999978e-22

   1. Initial program 100.0%

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

      1. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 97.8%

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

      1. count-2 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in x around inf 64.1%

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

      1. count-2 64.1%

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

   9. Simplified 64.1%

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

   if -9.50000000000000052e-175 < x < 6.9999999999999997e-75 or 7.49999999999999978e-22 < x < 1.5000000000000001e58

   1. Initial program 100.0%

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

      1. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 73.0%

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

      1. unpow2 73.0%

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

   6. Simplified 73.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-175}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-75}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-22}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+58}:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 3: 99.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.0) (not (<= x 2.0)))
   (+ (* x x) (* y y))
   (+ (* y y) (+ x x))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -2 or 2 < x

   1. Initial program 100.0%

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

      1. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.2%

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

      1. unpow2 99.2%

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

   6. Simplified 99.2%

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

   if -2 < x < 2

   1. Initial program 100.0%

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

      1. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 98.7%

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

      1. count-2 98.7%

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

   6. Simplified 98.7%

      \[\leadsto \color{blue}{\left(x + x\right)} + y \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot x + y \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot y + \left(x + x\right)\\ \end{array} \]

Alternative 4: 81.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 5.2 \cdot 10^{-243}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + y \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* y y) 5.2e-243) (+ x x) (+ (* x x) (* y y))))

C

double code(double x, double y) {
	double tmp;
	if ((y * y) <= 5.2e-243) {
		tmp = x + x;
	} else {
		tmp = (x * 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 ((y * y) <= 5.2d-243) then
        tmp = x + x
    else
        tmp = (x * x) + (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y * y) <= 5.2e-243) {
		tmp = x + x;
	} else {
		tmp = (x * x) + (y * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y * y) <= 5.2e-243:
		tmp = x + x
	else:
		tmp = (x * x) + (y * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y * y) <= 5.2e-243)
		tmp = Float64(x + x);
	else
		tmp = Float64(Float64(x * x) + Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y * y) <= 5.2e-243)
		tmp = x + x;
	else
		tmp = (x * x) + (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y * y), $MachinePrecision], 5.2e-243], N[(x + x), $MachinePrecision], N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y y) < 5.1999999999999995e-243

   1. Initial program 100.0%

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

      1. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 55.4%

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

      1. count-2 55.4%

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

   6. Simplified 55.4%

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

   7. Taylor expanded in x around inf 55.4%

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

      1. count-2 55.4%

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

   9. Simplified 55.4%

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

   if 5.1999999999999995e-243 < (*.f64 y y)

   1. Initial program 100.0%

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

      1. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 92.8%

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

      1. unpow2 92.8%

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

   6. Simplified 92.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot y \leq 5.2 \cdot 10^{-243}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + y \cdot y\\ \end{array} \]

Alternative 5: 100.0% accurate, 1.2× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (* y y) (* x (+ x 2.0))))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (y * y) + (x * (x + 2.0))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto y \cdot y + x \cdot \left(x + 2\right) \]

Alternative 6: 71.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+59}:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.7e+53) (* x x) (if (<= x 1.05e+59) (* y y) (* x x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.7e+53) {
		tmp = x * x;
	} else if (x <= 1.05e+59) {
		tmp = y * y;
	} else {
		tmp = x * 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 <= (-1.7d+53)) then
        tmp = x * x
    else if (x <= 1.05d+59) then
        tmp = y * y
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.7e+53) {
		tmp = x * x;
	} else if (x <= 1.05e+59) {
		tmp = y * y;
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.7e+53:
		tmp = x * x
	elif x <= 1.05e+59:
		tmp = y * y
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.7e+53)
		tmp = Float64(x * x);
	elseif (x <= 1.05e+59)
		tmp = Float64(y * y);
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.7e+53)
		tmp = x * x;
	elseif (x <= 1.05e+59)
		tmp = y * y;
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.7e+53], N[(x * x), $MachinePrecision], If[LessEqual[x, 1.05e+59], N[(y * y), $MachinePrecision], N[(x * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999999e53 or 1.04999999999999992e59 < x

   1. Initial program 100.0%

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

      1. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. unpow2 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 91.0%

      \[\leadsto \color{blue}{{x}^{2}} \]
   8. Step-by-step derivation

      1. unpow2 91.0%

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

   9. Simplified 91.0%

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

   if -1.69999999999999999e53 < x < 1.04999999999999992e59

   1. Initial program 100.0%

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

      1. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 60.7%

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

      1. unpow2 60.7%

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

   6. Simplified 60.7%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+59}:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 7: 42.1% accurate, 3.7× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (* x x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x * x

Julia

function code(x, y)
	return Float64(x * x)
end

MATLAB

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

Wolfram

code[x_, y_] := N[(x * x), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 79.1%

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

   1. unpow2 79.1%

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

6. Simplified 79.1%

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

7. Taylor expanded in x around inf 42.1%

   \[\leadsto \color{blue}{{x}^{2}} \]
8. Step-by-step derivation

   1. unpow2 42.1%

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

9. Simplified 42.1%

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

10. Final simplification 42.1%

    \[\leadsto x \cdot x \]

Developer target: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (* y y) (+ (* 2.0 x) (* x x))))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (y * y) + ((2.0 * x) + (x * x))

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (+ (* y y) (+ (* 2.0 x) (* x x)))

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