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

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 8

Speedup: 1.3×

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: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-50}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-286}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-170}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7000:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+94)
   (* x y)
   (if (<= y -2.2e-50)
     z
     (if (<= y 1.95e-286)
       (* x 0.5)
       (if (<= y 6.5e-170) z (if (<= y 7000.0) (* x 0.5) (* x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+94) {
		tmp = x * y;
	} else if (y <= -2.2e-50) {
		tmp = z;
	} else if (y <= 1.95e-286) {
		tmp = x * 0.5;
	} else if (y <= 6.5e-170) {
		tmp = z;
	} else if (y <= 7000.0) {
		tmp = x * 0.5;
	} 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 <= (-2.3d+94)) then
        tmp = x * y
    else if (y <= (-2.2d-50)) then
        tmp = z
    else if (y <= 1.95d-286) then
        tmp = x * 0.5d0
    else if (y <= 6.5d-170) then
        tmp = z
    else if (y <= 7000.0d0) then
        tmp = x * 0.5d0
    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 <= -2.3e+94) {
		tmp = x * y;
	} else if (y <= -2.2e-50) {
		tmp = z;
	} else if (y <= 1.95e-286) {
		tmp = x * 0.5;
	} else if (y <= 6.5e-170) {
		tmp = z;
	} else if (y <= 7000.0) {
		tmp = x * 0.5;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+94:
		tmp = x * y
	elif y <= -2.2e-50:
		tmp = z
	elif y <= 1.95e-286:
		tmp = x * 0.5
	elif y <= 6.5e-170:
		tmp = z
	elif y <= 7000.0:
		tmp = x * 0.5
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+94)
		tmp = Float64(x * y);
	elseif (y <= -2.2e-50)
		tmp = z;
	elseif (y <= 1.95e-286)
		tmp = Float64(x * 0.5);
	elseif (y <= 6.5e-170)
		tmp = z;
	elseif (y <= 7000.0)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e+94)
		tmp = x * y;
	elseif (y <= -2.2e-50)
		tmp = z;
	elseif (y <= 1.95e-286)
		tmp = x * 0.5;
	elseif (y <= 6.5e-170)
		tmp = z;
	elseif (y <= 7000.0)
		tmp = x * 0.5;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+94], N[(x * y), $MachinePrecision], If[LessEqual[y, -2.2e-50], z, If[LessEqual[y, 1.95e-286], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 6.5e-170], z, If[LessEqual[y, 7000.0], N[(x * 0.5), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3e94 or 7e3 < 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 88.2%

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

   if -2.3e94 < y < -2.1999999999999999e-50 or 1.94999999999999998e-286 < y < 6.50000000000000035e-170

   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 59.6%

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

   if -2.1999999999999999e-50 < y < 1.94999999999999998e-286 or 6.50000000000000035e-170 < y < 7e3

   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 65.5%

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

   5. Taylor expanded in y around 0 64.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-50}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-286}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-170}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7000:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+81} \lor \neg \left(x \leq 5.5 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.5e+81) (not (<= x 5.5e+48))) (* x (+ y 0.5)) (+ (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.5e+81) || !(x <= 5.5e+48)) {
		tmp = x * (y + 0.5);
	} else {
		tmp = (x * y) + 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 <= (-7.5d+81)) .or. (.not. (x <= 5.5d+48))) then
        tmp = x * (y + 0.5d0)
    else
        tmp = (x * y) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.5e+81) || !(x <= 5.5e+48)) {
		tmp = x * (y + 0.5);
	} else {
		tmp = (x * y) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.5e+81) or not (x <= 5.5e+48):
		tmp = x * (y + 0.5)
	else:
		tmp = (x * y) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.5e+81) || !(x <= 5.5e+48))
		tmp = Float64(x * Float64(y + 0.5));
	else
		tmp = Float64(Float64(x * y) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.5e+81) || ~((x <= 5.5e+48)))
		tmp = x * (y + 0.5);
	else
		tmp = (x * y) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.5e+81], N[Not[LessEqual[x, 5.5e+48]], $MachinePrecision]], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.49999999999999973e81 or 5.5000000000000002e48 < 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 91.1%

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

   if -7.49999999999999973e81 < x < 5.5000000000000002e48

   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 83.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+81} \lor \neg \left(x \leq 5.5 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z\\ \end{array} \]

Alternative 4: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.5) || !(y <= 0.5)) {
		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 <= 0.5d0))) 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 <= 0.5)) {
		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 <= 0.5):
		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 <= 0.5))
		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 <= 0.5)))
		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, 0.5]], $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 0.5 < 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 99.5%

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

   if -0.5 < y < 0.5

   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 y around 0 97.9%

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

4. Final simplification 98.7%

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

Alternative 5: 71.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+199}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4e+199) z (if (<= z 1.45e+164) (* x (+ y 0.5)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e+199) {
		tmp = z;
	} else if (z <= 1.45e+164) {
		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 (z <= (-4d+199)) then
        tmp = z
    else if (z <= 1.45d+164) 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 (z <= -4e+199) {
		tmp = z;
	} else if (z <= 1.45e+164) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4e+199:
		tmp = z
	elif z <= 1.45e+164:
		tmp = x * (y + 0.5)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4e+199)
		tmp = z;
	elseif (z <= 1.45e+164)
		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 (z <= -4e+199)
		tmp = z;
	elseif (z <= 1.45e+164)
		tmp = x * (y + 0.5);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4e+199], z, If[LessEqual[z, 1.45e+164], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000039e199 or 1.4499999999999999e164 < 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 78.6%

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

   if -4.00000000000000039e199 < z < 1.4499999999999999e164

   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 77.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+199}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6: 50.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+53}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.5e+106) (* x 0.5) (if (<= x 5e+53) z (* x 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e+106) {
		tmp = x * 0.5;
	} else if (x <= 5e+53) {
		tmp = z;
	} else {
		tmp = 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 (x <= (-2.5d+106)) then
        tmp = x * 0.5d0
    else if (x <= 5d+53) then
        tmp = z
    else
        tmp = x * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e+106) {
		tmp = x * 0.5;
	} else if (x <= 5e+53) {
		tmp = z;
	} else {
		tmp = x * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.5e+106:
		tmp = x * 0.5
	elif x <= 5e+53:
		tmp = z
	else:
		tmp = x * 0.5
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e+106)
		tmp = Float64(x * 0.5);
	elseif (x <= 5e+53)
		tmp = z;
	else
		tmp = Float64(x * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.5e+106)
		tmp = x * 0.5;
	elseif (x <= 5e+53)
		tmp = z;
	else
		tmp = x * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e+106], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 5e+53], z, N[(x * 0.5), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999999e106 or 5.0000000000000004e53 < 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 91.5%

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

   5. Taylor expanded in y around 0 47.4%

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

   if -2.4999999999999999e106 < x < 5.0000000000000004e53

   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 49.4%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+53}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \]

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: 41.3% 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 32.5%

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

5. Final simplification 32.5%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023240 
(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))