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

Percentage Accurate: 100.0% → 100.0%

Time: 1.6s

Alternatives: 5

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, 1.3× 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: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-113} \lor \neg \left(x \leq 0.045\right):\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.6e-113) (not (<= x 0.045))) (* (+ 0.5 y) x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.6e-113) || !(x <= 0.045)) {
		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 ((x <= (-4.6d-113)) .or. (.not. (x <= 0.045d0))) 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 ((x <= -4.6e-113) || !(x <= 0.045)) {
		tmp = (0.5 + y) * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.6e-113) or not (x <= 0.045):
		tmp = (0.5 + y) * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.6e-113) || !(x <= 0.045))
		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 ((x <= -4.6e-113) || ~((x <= 0.045)))
		tmp = (0.5 + y) * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.6e-113], N[Not[LessEqual[x, 0.045]], $MachinePrecision]], N[(N[(0.5 + y), $MachinePrecision] * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -4.60000000000000016e-113 or 0.044999999999999998 < 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 81.2%

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

   if -4.60000000000000016e-113 < x < 0.044999999999999998

   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 77.4%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-113} \lor \neg \left(x \leq 0.045\right):\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 3: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+41}:\\ \;\;\;\;z + 0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e+97)
   (* y x)
   (if (<= y 6e+41) (+ z (* 0.5 x)) (* (+ 0.5 y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+97) {
		tmp = y * x;
	} else if (y <= 6e+41) {
		tmp = z + (0.5 * x);
	} else {
		tmp = (0.5 + 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 <= (-4.5d+97)) then
        tmp = y * x
    else if (y <= 6d+41) then
        tmp = z + (0.5d0 * x)
    else
        tmp = (0.5d0 + y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+97) {
		tmp = y * x;
	} else if (y <= 6e+41) {
		tmp = z + (0.5 * x);
	} else {
		tmp = (0.5 + y) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e+97:
		tmp = y * x
	elif y <= 6e+41:
		tmp = z + (0.5 * x)
	else:
		tmp = (0.5 + y) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e+97)
		tmp = Float64(y * x);
	elseif (y <= 6e+41)
		tmp = Float64(z + Float64(0.5 * x));
	else
		tmp = Float64(Float64(0.5 + y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.5e+97)
		tmp = y * x;
	elseif (y <= 6e+41)
		tmp = z + (0.5 * x);
	else
		tmp = (0.5 + y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e+97], N[(y * x), $MachinePrecision], If[LessEqual[y, 6e+41], N[(z + N[(0.5 * x), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 + y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.49999999999999976e97

   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 75.9%

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

   if -4.49999999999999976e97 < y < 5.9999999999999997e41

   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 94.3%

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

   if 5.9999999999999997e41 < 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 inf 86.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+41}:\\ \;\;\;\;z + 0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \end{array} \]

Alternative 4: 59.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+41}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e+97) (* y x) (if (<= y 4.3e+41) z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e+97) {
		tmp = y * x;
	} else if (y <= 4.3e+41) {
		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 <= (-5d+97)) then
        tmp = y * x
    else if (y <= 4.3d+41) 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 <= -5e+97) {
		tmp = y * x;
	} else if (y <= 4.3e+41) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e+97:
		tmp = y * x
	elif y <= 4.3e+41:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e+97)
		tmp = Float64(y * x);
	elseif (y <= 4.3e+41)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e+97)
		tmp = y * x;
	elseif (y <= 4.3e+41)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e+97], N[(y * x), $MachinePrecision], If[LessEqual[y, 4.3e+41], z, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999999e97 or 4.30000000000000024e41 < 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 81.4%

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

   if -4.99999999999999999e97 < y < 4.30000000000000024e41

   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 58.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+41}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 5: 40.7% 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 45.2%

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

5. Final simplification 45.2%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023181 
(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))