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

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 7

Speedup: 1.2×

• 43.9% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 1.12 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{elif}\;y \cdot y \leq 3.55 \cdot 10^{+193}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \cdot y \leq 1.45 \cdot 10^{+208}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* y y) 1.12e-87)
   (* x (+ x 2.0))
   (if (<= (* y y) 3.55e+193)
     (* y y)
     (if (<= (* y y) 1.45e+208) (* x x) (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y * y) <= 1.12e-87) {
		tmp = x * (x + 2.0);
	} else if ((y * y) <= 3.55e+193) {
		tmp = y * y;
	} else if ((y * y) <= 1.45e+208) {
		tmp = x * x;
	} else {
		tmp = 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) <= 1.12d-87) then
        tmp = x * (x + 2.0d0)
    else if ((y * y) <= 3.55d+193) then
        tmp = y * y
    else if ((y * y) <= 1.45d+208) then
        tmp = x * x
    else
        tmp = y * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y * y) <= 1.12e-87) {
		tmp = x * (x + 2.0);
	} else if ((y * y) <= 3.55e+193) {
		tmp = y * y;
	} else if ((y * y) <= 1.45e+208) {
		tmp = x * x;
	} else {
		tmp = y * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y * y) <= 1.12e-87:
		tmp = x * (x + 2.0)
	elif (y * y) <= 3.55e+193:
		tmp = y * y
	elif (y * y) <= 1.45e+208:
		tmp = x * x
	else:
		tmp = y * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y * y) <= 1.12e-87)
		tmp = Float64(x * Float64(x + 2.0));
	elseif (Float64(y * y) <= 3.55e+193)
		tmp = Float64(y * y);
	elseif (Float64(y * y) <= 1.45e+208)
		tmp = Float64(x * x);
	else
		tmp = Float64(y * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y * y) <= 1.12e-87)
		tmp = x * (x + 2.0);
	elseif ((y * y) <= 3.55e+193)
		tmp = y * y;
	elseif ((y * y) <= 1.45e+208)
		tmp = x * x;
	else
		tmp = y * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y * y), $MachinePrecision], 1.12e-87], N[(x * N[(x + 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * y), $MachinePrecision], 3.55e+193], N[(y * y), $MachinePrecision], If[LessEqual[N[(y * y), $MachinePrecision], 1.45e+208], N[(x * x), $MachinePrecision], N[(y * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y y) < 1.1199999999999999e-87

   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 y around 0 93.5%

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

   if 1.1199999999999999e-87 < (*.f64 y y) < 3.5499999999999999e193 or 1.45000000000000004e208 < (*.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 0 83.7%

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

      1. unpow2 83.7%

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

   6. Simplified 83.7%

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

   if 3.5499999999999999e193 < (*.f64 y y) < 1.45000000000000004e208

   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 y around 0 100.0%

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

   5. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{{x}^{2}} \]

   7. Simplified 100.0%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot y \leq 1.12 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{elif}\;y \cdot y \leq 3.55 \cdot 10^{+193}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \cdot y \leq 1.45 \cdot 10^{+208}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 3: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -450000000000:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-105}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-205}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+44}:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -450000000000.0)
   (* x x)
   (if (<= x -1e-105)
     (* y y)
     (if (<= x -4.5e-205) (* x 2.0) (if (<= x 2.95e+44) (* y y) (* x x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -450000000000.0) {
		tmp = x * x;
	} else if (x <= -1e-105) {
		tmp = y * y;
	} else if (x <= -4.5e-205) {
		tmp = x * 2.0;
	} else if (x <= 2.95e+44) {
		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 <= (-450000000000.0d0)) then
        tmp = x * x
    else if (x <= (-1d-105)) then
        tmp = y * y
    else if (x <= (-4.5d-205)) then
        tmp = x * 2.0d0
    else if (x <= 2.95d+44) 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 <= -450000000000.0) {
		tmp = x * x;
	} else if (x <= -1e-105) {
		tmp = y * y;
	} else if (x <= -4.5e-205) {
		tmp = x * 2.0;
	} else if (x <= 2.95e+44) {
		tmp = y * y;
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -450000000000.0:
		tmp = x * x
	elif x <= -1e-105:
		tmp = y * y
	elif x <= -4.5e-205:
		tmp = x * 2.0
	elif x <= 2.95e+44:
		tmp = y * y
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -450000000000.0)
		tmp = Float64(x * x);
	elseif (x <= -1e-105)
		tmp = Float64(y * y);
	elseif (x <= -4.5e-205)
		tmp = Float64(x * 2.0);
	elseif (x <= 2.95e+44)
		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 <= -450000000000.0)
		tmp = x * x;
	elseif (x <= -1e-105)
		tmp = y * y;
	elseif (x <= -4.5e-205)
		tmp = x * 2.0;
	elseif (x <= 2.95e+44)
		tmp = y * y;
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -450000000000.0], N[(x * x), $MachinePrecision], If[LessEqual[x, -1e-105], N[(y * y), $MachinePrecision], If[LessEqual[x, -4.5e-205], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 2.95e+44], N[(y * y), $MachinePrecision], N[(x * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5e11 or 2.94999999999999982e44 < 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 y around 0 85.5%

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

   5. Taylor expanded in x around inf 85.3%

      \[\leadsto \color{blue}{{x}^{2}} \]

   7. Simplified 85.3%

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

   if -4.5e11 < x < -9.99999999999999965e-106 or -4.49999999999999956e-205 < x < 2.94999999999999982e44

   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 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 69.0%

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

      1. unpow2 69.0%

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

   6. Simplified 69.0%

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

   if -9.99999999999999965e-106 < x < -4.49999999999999956e-205

   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 y around 0 59.9%

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

   5. Taylor expanded in x around 0 59.9%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -450000000000:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-105}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-205}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+44}:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 4: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -920000000000 \lor \neg \left(x \leq 1.56 \cdot 10^{+52}\right):\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot y + \left(x + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -920000000000.0) (not (<= x 1.56e+52)))
   (* x (+ x 2.0))
   (+ (* y y) (+ x x))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -920000000000.0) || !(x <= 1.56e+52)) {
		tmp = x * (x + 2.0);
	} 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 <= (-920000000000.0d0)) .or. (.not. (x <= 1.56d+52))) then
        tmp = x * (x + 2.0d0)
    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 <= -920000000000.0) || !(x <= 1.56e+52)) {
		tmp = x * (x + 2.0);
	} else {
		tmp = (y * y) + (x + x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -920000000000.0) or not (x <= 1.56e+52):
		tmp = x * (x + 2.0)
	else:
		tmp = (y * y) + (x + x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -920000000000.0) || !(x <= 1.56e+52))
		tmp = Float64(x * Float64(x + 2.0));
	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 <= -920000000000.0) || ~((x <= 1.56e+52)))
		tmp = x * (x + 2.0);
	else
		tmp = (y * y) + (x + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -920000000000.0], N[Not[LessEqual[x, 1.56e+52]], $MachinePrecision]], N[(x * N[(x + 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * y), $MachinePrecision] + N[(x + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.2e11 or 1.55999999999999994e52 < 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 y around 0 86.1%

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

   if -9.2e11 < x < 1.55999999999999994e52

   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 96.3%

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

      1. count-2 96.3%

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

   6. Simplified 96.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -920000000000 \lor \neg \left(x \leq 1.56 \cdot 10^{+52}\right):\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot y + \left(x + x\right)\\ \end{array} \]

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: 58.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.0) (* x x) (if (<= x 2.0) (* x 2.0) (* x x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.0) {
		tmp = x * x;
	} else if (x <= 2.0) {
		tmp = x * 2.0;
	} 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 <= (-2.0d0)) then
        tmp = x * x
    else if (x <= 2.0d0) then
        tmp = x * 2.0d0
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if x <= -2.0:
		tmp = x * x
	elif x <= 2.0:
		tmp = x * 2.0
	else:
		tmp = x * x
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[LessEqual[x, -2.0], N[(x * x), $MachinePrecision], If[LessEqual[x, 2.0], N[(x * 2.0), $MachinePrecision], N[(x * x), $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 y around 0 81.1%

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

   5. Taylor expanded in x around inf 80.5%

      \[\leadsto \color{blue}{{x}^{2}} \]

   7. Simplified 80.5%

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

   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 y around 0 38.6%

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

   5. Taylor expanded in x around 0 36.7%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 7: 20.4% accurate, 3.7× 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 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 y around 0 59.3%

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

5. Taylor expanded in x around 0 20.2%

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

6. Final simplification 20.2%

   \[\leadsto x \cdot 2 \]

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 2023224 
(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)))