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

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

Alternatives: 7

Speedup: N/A×

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, 1.3× speedup

Math

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

FPCore

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

C

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

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 + ((0.5d0 + y) * x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0023:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-46} \lor \neg \left(z \leq -5.9 \cdot 10^{-93}\right) \land z \leq 7.8 \cdot 10^{+88}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0023)
   z
   (if (or (<= z -1.3e-46) (and (not (<= z -5.9e-93)) (<= z 7.8e+88)))
     (* (+ 0.5 y) x)
     z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0023) {
		tmp = z;
	} else if ((z <= -1.3e-46) || (!(z <= -5.9e-93) && (z <= 7.8e+88))) {
		tmp = (0.5 + y) * x;
	} 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 <= (-0.0023d0)) then
        tmp = z
    else if ((z <= (-1.3d-46)) .or. (.not. (z <= (-5.9d-93))) .and. (z <= 7.8d+88)) then
        tmp = (0.5d0 + y) * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0023) {
		tmp = z;
	} else if ((z <= -1.3e-46) || (!(z <= -5.9e-93) && (z <= 7.8e+88))) {
		tmp = (0.5 + y) * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.0023:
		tmp = z
	elif (z <= -1.3e-46) or (not (z <= -5.9e-93) and (z <= 7.8e+88)):
		tmp = (0.5 + y) * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.0023)
		tmp = z;
	elseif ((z <= -1.3e-46) || (!(z <= -5.9e-93) && (z <= 7.8e+88)))
		tmp = Float64(Float64(0.5 + y) * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.0023)
		tmp = z;
	elseif ((z <= -1.3e-46) || (~((z <= -5.9e-93)) && (z <= 7.8e+88)))
		tmp = (0.5 + y) * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.0023], z, If[Or[LessEqual[z, -1.3e-46], And[N[Not[LessEqual[z, -5.9e-93]], $MachinePrecision], LessEqual[z, 7.8e+88]]], N[(N[(0.5 + y), $MachinePrecision] * x), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0023 or -1.3000000000000001e-46 < z < -5.9e-93 or 7.8000000000000002e88 < 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 73.0%

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

   if -0.0023 < z < -1.3000000000000001e-46 or -5.9e-93 < z < 7.8000000000000002e88

   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 88.9%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0023:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-46} \lor \neg \left(z \leq -5.9 \cdot 10^{-93}\right) \land z \leq 7.8 \cdot 10^{+88}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 3: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.5:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-233}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.5)
   (* y x)
   (if (<= y -1.2e-233) (* 0.5 x) (if (<= y 1.4e+21) z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.5) {
		tmp = y * x;
	} else if (y <= -1.2e-233) {
		tmp = 0.5 * x;
	} else if (y <= 1.4e+21) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	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)) then
        tmp = y * x
    else if (y <= (-1.2d-233)) then
        tmp = 0.5d0 * x
    else if (y <= 1.4d+21) then
        tmp = z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.5) {
		tmp = y * x;
	} else if (y <= -1.2e-233) {
		tmp = 0.5 * x;
	} else if (y <= 1.4e+21) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.5:
		tmp = y * x
	elif y <= -1.2e-233:
		tmp = 0.5 * x
	elif y <= 1.4e+21:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.5)
		tmp = Float64(y * x);
	elseif (y <= -1.2e-233)
		tmp = Float64(0.5 * x);
	elseif (y <= 1.4e+21)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.5)
		tmp = y * x;
	elseif (y <= -1.2e-233)
		tmp = 0.5 * x;
	elseif (y <= 1.4e+21)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.5], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.2e-233], N[(0.5 * x), $MachinePrecision], If[LessEqual[y, 1.4e+21], z, N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.5 or 1.4e21 < 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 69.0%

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

   if -0.5 < y < -1.19999999999999995e-233

   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 58.6%

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

   5. Taylor expanded in y around 0 58.4%

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

   if -1.19999999999999995e-233 < y < 1.4e21

   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 57.2%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.5:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-233}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+163} \lor \neg \left(x \leq 9.6 \cdot 10^{+31}\right):\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9e+163) (not (<= x 9.6e+31))) (* (+ 0.5 y) x) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e+163) || !(x <= 9.6e+31)) {
		tmp = (0.5 + y) * x;
	} else {
		tmp = z + (y * x);
	}
	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 <= (-9d+163)) .or. (.not. (x <= 9.6d+31))) then
        tmp = (0.5d0 + y) * x
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e+163) || !(x <= 9.6e+31)) {
		tmp = (0.5 + y) * x;
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9e+163) or not (x <= 9.6e+31):
		tmp = (0.5 + y) * x
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9e+163) || !(x <= 9.6e+31))
		tmp = Float64(Float64(0.5 + y) * x);
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9e+163) || ~((x <= 9.6e+31)))
		tmp = (0.5 + y) * x;
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9e+163], N[Not[LessEqual[x, 9.6e+31]], $MachinePrecision]], N[(N[(0.5 + y), $MachinePrecision] * x), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999976e163 or 9.59999999999999929e31 < 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 88.6%

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

   if -8.99999999999999976e163 < x < 9.59999999999999929e31

   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 87.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+163} \lor \neg \left(x \leq 9.6 \cdot 10^{+31}\right):\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 5: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -25500000000 \lor \neg \left(y \leq 0.5\right):\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + 0.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -25500000000.0) (not (<= y 0.5)))
   (+ z (* y x))
   (+ z (* 0.5 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -25500000000.0) || !(y <= 0.5)) {
		tmp = z + (y * x);
	} else {
		tmp = z + (0.5 * x);
	}
	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 <= (-25500000000.0d0)) .or. (.not. (y <= 0.5d0))) then
        tmp = z + (y * x)
    else
        tmp = z + (0.5d0 * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -25500000000.0) || !(y <= 0.5)) {
		tmp = z + (y * x);
	} else {
		tmp = z + (0.5 * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -25500000000.0) or not (y <= 0.5):
		tmp = z + (y * x)
	else:
		tmp = z + (0.5 * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -25500000000.0) || !(y <= 0.5))
		tmp = Float64(z + Float64(y * x));
	else
		tmp = Float64(z + Float64(0.5 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -25500000000.0) || ~((y <= 0.5)))
		tmp = z + (y * x);
	else
		tmp = z + (0.5 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -25500000000.0], N[Not[LessEqual[y, 0.5]], $MachinePrecision]], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(z + N[(0.5 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55e10 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 98.9%

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

   if -2.55e10 < 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 98.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -25500000000 \lor \neg \left(y \leq 0.5\right):\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + 0.5 \cdot x\\ \end{array} \]

Alternative 6: 51.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+149}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+31}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e+149) (* 0.5 x) (if (<= x 9.6e+31) z (* 0.5 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+149) {
		tmp = 0.5 * x;
	} else if (x <= 9.6e+31) {
		tmp = z;
	} else {
		tmp = 0.5 * x;
	}
	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 <= (-1.3d+149)) then
        tmp = 0.5d0 * x
    else if (x <= 9.6d+31) then
        tmp = z
    else
        tmp = 0.5d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+149) {
		tmp = 0.5 * x;
	} else if (x <= 9.6e+31) {
		tmp = z;
	} else {
		tmp = 0.5 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e+149:
		tmp = 0.5 * x
	elif x <= 9.6e+31:
		tmp = z
	else:
		tmp = 0.5 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e+149)
		tmp = Float64(0.5 * x);
	elseif (x <= 9.6e+31)
		tmp = z;
	else
		tmp = Float64(0.5 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.3e+149)
		tmp = 0.5 * x;
	elseif (x <= 9.6e+31)
		tmp = z;
	else
		tmp = 0.5 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e+149], N[(0.5 * x), $MachinePrecision], If[LessEqual[x, 9.6e+31], z, N[(0.5 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.29999999999999989e149 or 9.59999999999999929e31 < 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 88.8%

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

   5. Taylor expanded in y around 0 48.4%

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

   if -1.29999999999999989e149 < x < 9.59999999999999929e31

   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 63.2%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+149}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+31}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \]

Alternative 7: 40.9% 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 43.5%

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

5. Final simplification 43.5%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023252 
(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))