Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -510000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-76}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-158}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-133}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+34}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -510000000000.0)
   (* x y)
   (if (<= y -3.1e-76)
     z
     (if (<= y -1.4e-158)
       (* x 0.5)
       (if (<= y 3e-133)
         z
         (if (<= y 1.6e-5) (* x 0.5) (if (<= y 1.4e+34) z (* x y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -510000000000.0) {
		tmp = x * y;
	} else if (y <= -3.1e-76) {
		tmp = z;
	} else if (y <= -1.4e-158) {
		tmp = x * 0.5;
	} else if (y <= 3e-133) {
		tmp = z;
	} else if (y <= 1.6e-5) {
		tmp = x * 0.5;
	} else if (y <= 1.4e+34) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-510000000000.0d0)) then
        tmp = x * y
    else if (y <= (-3.1d-76)) then
        tmp = z
    else if (y <= (-1.4d-158)) then
        tmp = x * 0.5d0
    else if (y <= 3d-133) then
        tmp = z
    else if (y <= 1.6d-5) then
        tmp = x * 0.5d0
    else if (y <= 1.4d+34) then
        tmp = z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -510000000000.0) {
		tmp = x * y;
	} else if (y <= -3.1e-76) {
		tmp = z;
	} else if (y <= -1.4e-158) {
		tmp = x * 0.5;
	} else if (y <= 3e-133) {
		tmp = z;
	} else if (y <= 1.6e-5) {
		tmp = x * 0.5;
	} else if (y <= 1.4e+34) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -510000000000.0:
		tmp = x * y
	elif y <= -3.1e-76:
		tmp = z
	elif y <= -1.4e-158:
		tmp = x * 0.5
	elif y <= 3e-133:
		tmp = z
	elif y <= 1.6e-5:
		tmp = x * 0.5
	elif y <= 1.4e+34:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -510000000000.0)
		tmp = Float64(x * y);
	elseif (y <= -3.1e-76)
		tmp = z;
	elseif (y <= -1.4e-158)
		tmp = Float64(x * 0.5);
	elseif (y <= 3e-133)
		tmp = z;
	elseif (y <= 1.6e-5)
		tmp = Float64(x * 0.5);
	elseif (y <= 1.4e+34)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -510000000000.0)
		tmp = x * y;
	elseif (y <= -3.1e-76)
		tmp = z;
	elseif (y <= -1.4e-158)
		tmp = x * 0.5;
	elseif (y <= 3e-133)
		tmp = z;
	elseif (y <= 1.6e-5)
		tmp = x * 0.5;
	elseif (y <= 1.4e+34)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -510000000000.0], N[(x * y), $MachinePrecision], If[LessEqual[y, -3.1e-76], z, If[LessEqual[y, -1.4e-158], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 3e-133], z, If[LessEqual[y, 1.6e-5], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 1.4e+34], z, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.1e11 or 1.40000000000000004e34 < y

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 80.9%

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

   if -5.1e11 < y < -3.0999999999999997e-76 or -1.40000000000000001e-158 < y < 3.00000000000000019e-133 or 1.59999999999999993e-5 < y < 1.40000000000000004e34

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 62.2%

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

   if -3.0999999999999997e-76 < y < -1.40000000000000001e-158 or 3.00000000000000019e-133 < y < 1.59999999999999993e-5

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 63.7%

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

   5. Taylor expanded in y around 0 59.6%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -510000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-76}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-158}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-133}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+34}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-125} \lor \neg \left(x \leq -7.7 \cdot 10^{-146} \lor \neg \left(x \leq -8.8 \cdot 10^{-191}\right) \land x \leq 1.25 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.6e-125)
         (not
          (or (<= x -7.7e-146) (and (not (<= x -8.8e-191)) (<= x 1.25e-34)))))
   (* x (+ y 0.5))
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.6e-125) || !((x <= -7.7e-146) || (!(x <= -8.8e-191) && (x <= 1.25e-34)))) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8.6d-125)) .or. (.not. (x <= (-7.7d-146)) .or. (.not. (x <= (-8.8d-191))) .and. (x <= 1.25d-34))) then
        tmp = x * (y + 0.5d0)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.6e-125) || !((x <= -7.7e-146) || (!(x <= -8.8e-191) && (x <= 1.25e-34)))) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.6e-125) or not ((x <= -7.7e-146) or (not (x <= -8.8e-191) and (x <= 1.25e-34))):
		tmp = x * (y + 0.5)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.6e-125) || !((x <= -7.7e-146) || (!(x <= -8.8e-191) && (x <= 1.25e-34))))
		tmp = Float64(x * Float64(y + 0.5));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.6e-125) || ~(((x <= -7.7e-146) || (~((x <= -8.8e-191)) && (x <= 1.25e-34)))))
		tmp = x * (y + 0.5);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.6e-125], N[Not[Or[LessEqual[x, -7.7e-146], And[N[Not[LessEqual[x, -8.8e-191]], $MachinePrecision], LessEqual[x, 1.25e-34]]]], $MachinePrecision]], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -8.6000000000000004e-125 or -7.69999999999999997e-146 < x < -8.79999999999999992e-191 or 1.2500000000000001e-34 < x

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 80.5%

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

   if -8.6000000000000004e-125 < x < -7.69999999999999997e-146 or -8.79999999999999992e-191 < x < 1.2500000000000001e-34

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 77.0%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-125} \lor \neg \left(x \leq -7.7 \cdot 10^{-146} \lor \neg \left(x \leq -8.8 \cdot 10^{-191}\right) \land x \leq 1.25 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -900000000000 \lor \neg \left(z \leq -2.8 \cdot 10^{-41} \lor \neg \left(z \leq -3.1 \cdot 10^{-103}\right) \land z \leq 5.7 \cdot 10^{-117}\right):\\ \;\;\;\;x \cdot y + z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -900000000000.0)
         (not
          (or (<= z -2.8e-41) (and (not (<= z -3.1e-103)) (<= z 5.7e-117)))))
   (+ (* x y) z)
   (* x (+ y 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -900000000000.0) || !((z <= -2.8e-41) || (!(z <= -3.1e-103) && (z <= 5.7e-117)))) {
		tmp = (x * y) + z;
	} else {
		tmp = x * (y + 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-900000000000.0d0)) .or. (.not. (z <= (-2.8d-41)) .or. (.not. (z <= (-3.1d-103))) .and. (z <= 5.7d-117))) then
        tmp = (x * y) + z
    else
        tmp = x * (y + 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -900000000000.0) || !((z <= -2.8e-41) || (!(z <= -3.1e-103) && (z <= 5.7e-117)))) {
		tmp = (x * y) + z;
	} else {
		tmp = x * (y + 0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -900000000000.0) or not ((z <= -2.8e-41) or (not (z <= -3.1e-103) and (z <= 5.7e-117))):
		tmp = (x * y) + z
	else:
		tmp = x * (y + 0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -900000000000.0) || !((z <= -2.8e-41) || (!(z <= -3.1e-103) && (z <= 5.7e-117))))
		tmp = Float64(Float64(x * y) + z);
	else
		tmp = Float64(x * Float64(y + 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -900000000000.0) || ~(((z <= -2.8e-41) || (~((z <= -3.1e-103)) && (z <= 5.7e-117)))))
		tmp = (x * y) + z;
	else
		tmp = x * (y + 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -900000000000.0], N[Not[Or[LessEqual[z, -2.8e-41], And[N[Not[LessEqual[z, -3.1e-103]], $MachinePrecision], LessEqual[z, 5.7e-117]]]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9e11 or -2.8000000000000002e-41 < z < -3.1000000000000001e-103 or 5.6999999999999999e-117 < z

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in y around inf 89.3%

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

   if -9e11 < z < -2.8000000000000002e-41 or -3.1000000000000001e-103 < z < 5.6999999999999999e-117

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 89.4%

      \[\leadsto \color{blue}{\left(0.5 + y\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -900000000000 \lor \neg \left(z \leq -2.8 \cdot 10^{-41} \lor \neg \left(z \leq -3.1 \cdot 10^{-103}\right) \land z \leq 5.7 \cdot 10^{-117}\right):\\ \;\;\;\;x \cdot y + z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \end{array} \]

Alternative 5: 49.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -112000000000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-41}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-105}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-116}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -112000000000.0)
   z
   (if (<= z -4e-41)
     (* x 0.5)
     (if (<= z -5.5e-105) z (if (<= z 3.8e-116) (* x 0.5) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -112000000000.0) {
		tmp = z;
	} else if (z <= -4e-41) {
		tmp = x * 0.5;
	} else if (z <= -5.5e-105) {
		tmp = z;
	} else if (z <= 3.8e-116) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-112000000000.0d0)) then
        tmp = z
    else if (z <= (-4d-41)) then
        tmp = x * 0.5d0
    else if (z <= (-5.5d-105)) then
        tmp = z
    else if (z <= 3.8d-116) then
        tmp = x * 0.5d0
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -112000000000.0) {
		tmp = z;
	} else if (z <= -4e-41) {
		tmp = x * 0.5;
	} else if (z <= -5.5e-105) {
		tmp = z;
	} else if (z <= 3.8e-116) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -112000000000.0:
		tmp = z
	elif z <= -4e-41:
		tmp = x * 0.5
	elif z <= -5.5e-105:
		tmp = z
	elif z <= 3.8e-116:
		tmp = x * 0.5
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -112000000000.0)
		tmp = z;
	elseif (z <= -4e-41)
		tmp = Float64(x * 0.5);
	elseif (z <= -5.5e-105)
		tmp = z;
	elseif (z <= 3.8e-116)
		tmp = Float64(x * 0.5);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -112000000000.0)
		tmp = z;
	elseif (z <= -4e-41)
		tmp = x * 0.5;
	elseif (z <= -5.5e-105)
		tmp = z;
	elseif (z <= 3.8e-116)
		tmp = x * 0.5;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -112000000000.0], z, If[LessEqual[z, -4e-41], N[(x * 0.5), $MachinePrecision], If[LessEqual[z, -5.5e-105], z, If[LessEqual[z, 3.8e-116], N[(x * 0.5), $MachinePrecision], z]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e11 or -4.00000000000000002e-41 < z < -5.50000000000000029e-105 or 3.8000000000000001e-116 < z

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 61.4%

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

   if -1.12e11 < z < -4.00000000000000002e-41 or -5.50000000000000029e-105 < z < 3.8000000000000001e-116

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 89.4%

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

   5. Taylor expanded in y around 0 45.6%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -112000000000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-41}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-105}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-116}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.5 \lor \neg \left(y \leq 0.0034\right):\\ \;\;\;\;x \cdot y + z\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.5) (not (<= y 0.0034))) (+ (* x y) z) (+ z (* x 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.5) || !(y <= 0.0034)) {
		tmp = (x * y) + z;
	} else {
		tmp = z + (x * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-0.5d0)) .or. (.not. (y <= 0.0034d0))) then
        tmp = (x * y) + z
    else
        tmp = z + (x * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.5) || !(y <= 0.0034)) {
		tmp = (x * y) + z;
	} else {
		tmp = z + (x * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.5) or not (y <= 0.0034):
		tmp = (x * y) + z
	else:
		tmp = z + (x * 0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.5) || !(y <= 0.0034))
		tmp = Float64(Float64(x * y) + z);
	else
		tmp = Float64(z + Float64(x * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.5) || ~((y <= 0.0034)))
		tmp = (x * y) + z;
	else
		tmp = z + (x * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.5], N[Not[LessEqual[y, 0.0034]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision], N[(z + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.5 or 0.00339999999999999981 < y

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in y around inf 99.3%

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

   if -0.5 < y < 0.00339999999999999981

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.5 \lor \neg \left(y \leq 0.0034\right):\\ \;\;\;\;x \cdot y + z\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 0.5\\ \end{array} \]

Alternative 7: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ z + x \cdot \left(y + 0.5\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (* x (+ y 0.5))))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return z + (x * (y + 0.5))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate-+l+ 100.0%

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

   2. *-commutative 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around 0 100.0%

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

5. Final simplification 100.0%

   \[\leadsto z + x \cdot \left(y + 0.5\right) \]

Alternative 8: 39.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 100.0%

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

   1. associate-+l+ 100.0%

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

   2. *-commutative 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around 0 40.8%

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

5. Final simplification 40.8%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2.0) (* y x)) z))