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

Percentage Accurate: 100.0% → 100.0%

Time: 1.1s

Alternatives: 5

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

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

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

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]

Derivation

1. Initial program 100.0%

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

Alternative 2: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot x + z\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{2}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-299}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y x) z)))
   (if (<= y -3.6e-17)
     t_0
     (if (<= y -1.95e-125)
       (/ x 2.0)
       (if (<= y 5.1e-299) t_0 (if (<= y 1.9e-11) (/ x 2.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * x) + z;
	double tmp;
	if (y <= -3.6e-17) {
		tmp = t_0;
	} else if (y <= -1.95e-125) {
		tmp = x / 2.0;
	} else if (y <= 5.1e-299) {
		tmp = t_0;
	} else if (y <= 1.9e-11) {
		tmp = x / 2.0;
	} else {
		tmp = t_0;
	}
	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 = (y * x) + z
    if (y <= (-3.6d-17)) then
        tmp = t_0
    else if (y <= (-1.95d-125)) then
        tmp = x / 2.0d0
    else if (y <= 5.1d-299) then
        tmp = t_0
    else if (y <= 1.9d-11) then
        tmp = x / 2.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * x) + z;
	double tmp;
	if (y <= -3.6e-17) {
		tmp = t_0;
	} else if (y <= -1.95e-125) {
		tmp = x / 2.0;
	} else if (y <= 5.1e-299) {
		tmp = t_0;
	} else if (y <= 1.9e-11) {
		tmp = x / 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * x) + z
	tmp = 0
	if y <= -3.6e-17:
		tmp = t_0
	elif y <= -1.95e-125:
		tmp = x / 2.0
	elif y <= 5.1e-299:
		tmp = t_0
	elif y <= 1.9e-11:
		tmp = x / 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * x) + z)
	tmp = 0.0
	if (y <= -3.6e-17)
		tmp = t_0;
	elseif (y <= -1.95e-125)
		tmp = Float64(x / 2.0);
	elseif (y <= 5.1e-299)
		tmp = t_0;
	elseif (y <= 1.9e-11)
		tmp = Float64(x / 2.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * x) + z;
	tmp = 0.0;
	if (y <= -3.6e-17)
		tmp = t_0;
	elseif (y <= -1.95e-125)
		tmp = x / 2.0;
	elseif (y <= 5.1e-299)
		tmp = t_0;
	elseif (y <= 1.9e-11)
		tmp = x / 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[y, -3.6e-17], t$95$0, If[LessEqual[y, -1.95e-125], N[(x / 2.0), $MachinePrecision], If[LessEqual[y, 5.1e-299], t$95$0, If[LessEqual[y, 1.9e-11], N[(x / 2.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999995e-17 or -1.94999999999999991e-125 < y < 5.10000000000000021e-299 or 1.8999999999999999e-11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{2} + y\right)} + z \]

   5. Applied rewrites 48.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \color{blue}{x} + z \]

   8. Applied rewrites 89.4%

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

   if -3.59999999999999995e-17 < y < -1.94999999999999991e-125 or 5.10000000000000021e-299 < y < 1.8999999999999999e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z + x \cdot \left(\frac{1}{2} + y\right)} \]

   5. Applied rewrites 63.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto x \cdot \color{blue}{\left(\frac{1}{2} + y\right)} \]

   8. Applied rewrites 63.1%

      \[\leadsto \frac{x}{\color{blue}{2}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot x + z\\ \mathbf{if}\;y \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.5:\\ \;\;\;\;\frac{x}{2} + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y x) z)))
   (if (<= y -0.5) t_0 (if (<= y 0.5) (+ (/ x 2.0) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * x) + z;
	double tmp;
	if (y <= -0.5) {
		tmp = t_0;
	} else if (y <= 0.5) {
		tmp = (x / 2.0) + z;
	} else {
		tmp = t_0;
	}
	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 = (y * x) + z
    if (y <= (-0.5d0)) then
        tmp = t_0
    else if (y <= 0.5d0) then
        tmp = (x / 2.0d0) + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * x) + z;
	double tmp;
	if (y <= -0.5) {
		tmp = t_0;
	} else if (y <= 0.5) {
		tmp = (x / 2.0) + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * x) + z
	tmp = 0
	if y <= -0.5:
		tmp = t_0
	elif y <= 0.5:
		tmp = (x / 2.0) + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * x) + z)
	tmp = 0.0
	if (y <= -0.5)
		tmp = t_0;
	elseif (y <= 0.5)
		tmp = Float64(Float64(x / 2.0) + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * x) + z;
	tmp = 0.0;
	if (y <= -0.5)
		tmp = t_0;
	elseif (y <= 0.5)
		tmp = (x / 2.0) + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[y, -0.5], t$95$0, If[LessEqual[y, 0.5], N[(N[(x / 2.0), $MachinePrecision] + z), $MachinePrecision], t$95$0]]]

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. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{2} + y\right)} + z \]

   5. Applied rewrites 31.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \color{blue}{x} + z \]

   8. Applied rewrites 97.9%

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

   if -0.5 < y < 0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{2} + y\right)} + z \]

   5. Applied rewrites 98.8%

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

Alternative 4: 75.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ y \cdot x + z \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (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 = (y * x) + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x \cdot \left(\frac{1}{2} + y\right)} + z \]

5. Applied rewrites 64.5%

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

6. Taylor expanded in x around 0

   \[\leadsto \frac{1}{2} \cdot \color{blue}{x} + z \]

8. Applied rewrites 73.4%

   \[\leadsto y \cdot \color{blue}{x} + z \]
9. Add Preprocessing

Alternative 5: 36.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ y \cdot x \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = y * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{z + x \cdot \left(\frac{1}{2} + y\right)} \]

5. Applied rewrites 62.6%

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

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{z + \frac{1}{2} \cdot x} \]

8. Applied rewrites 36.5%

   \[\leadsto \color{blue}{y \cdot x} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  :pre (TRUE)
  (+ (+ (/ x 2.0) (* y x)) z))