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

Percentage Accurate: 100.0% → 100.0%

Time: 1.6s

Alternatives: 3

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: 85.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2} + x \cdot y\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+64} \lor \neg \left(t_0 \leq 10^{+158}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2} + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (/ x 2.0) (* x y))))
   (if (or (<= t_0 -1e+64) (not (<= t_0 1e+158))) t_0 (+ (/ x 2.0) z))))

C

double code(double x, double y, double z) {
	double t_0 = (x / 2.0) + (x * y);
	double tmp;
	if ((t_0 <= -1e+64) || !(t_0 <= 1e+158)) {
		tmp = t_0;
	} else {
		tmp = (x / 2.0) + 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) :: t_0
    real(8) :: tmp
    t_0 = (x / 2.0d0) + (x * y)
    if ((t_0 <= (-1d+64)) .or. (.not. (t_0 <= 1d+158))) then
        tmp = t_0
    else
        tmp = (x / 2.0d0) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / 2.0) + (x * y);
	double tmp;
	if ((t_0 <= -1e+64) || !(t_0 <= 1e+158)) {
		tmp = t_0;
	} else {
		tmp = (x / 2.0) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / 2.0) + (x * y)
	tmp = 0
	if (t_0 <= -1e+64) or not (t_0 <= 1e+158):
		tmp = t_0
	else:
		tmp = (x / 2.0) + z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / 2.0) + Float64(x * y))
	tmp = 0.0
	if ((t_0 <= -1e+64) || !(t_0 <= 1e+158))
		tmp = t_0;
	else
		tmp = Float64(Float64(x / 2.0) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / 2.0) + (x * y);
	tmp = 0.0;
	if ((t_0 <= -1e+64) || ~((t_0 <= 1e+158)))
		tmp = t_0;
	else
		tmp = (x / 2.0) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / 2.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e+64], N[Not[LessEqual[t$95$0, 1e+158]], $MachinePrecision]], t$95$0, N[(N[(x / 2.0), $MachinePrecision] + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x 2) (*.f64 y x)) < -1.00000000000000002e64 or 9.99999999999999953e157 < (+.f64 (/.f64 x 2) (*.f64 y 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 94.3%

      \[\leadsto \frac{x}{2} + \color{blue}{y \cdot x} \]

   if -1.00000000000000002e64 < (+.f64 (/.f64 x 2) (*.f64 y x)) < 9.99999999999999953e157

   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 88.1%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2} + x \cdot y \leq -1 \cdot 10^{+64} \lor \neg \left(\frac{x}{2} + x \cdot y \leq 10^{+158}\right):\\ \;\;\;\;\frac{x}{2} + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2} + z\\ \end{array} \]

Alternative 3: 64.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{2} + z \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x / 2.0) + 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) + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x / 2.0), $MachinePrecision] + z), $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 68.4%

   \[\leadsto \frac{x}{2} + \color{blue}{z} \]

5. Final simplification 68.4%

   \[\leadsto \frac{x}{2} + z \]

Reproduce

herbie shell --seed 2023257 
(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))