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

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: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot x + z\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{2}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-195}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-210}:\\ \;\;\;\;\frac{x}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y x) z)))
   (if (<= y -6.2e-10)
     t_0
     (if (<= y -7.2e-139)
       (/ x 2.0)
       (if (<= y -6.2e-195) t_0 (if (<= y 5.5e-210) (/ x 2.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * x) + z;
	double tmp;
	if (y <= -6.2e-10) {
		tmp = t_0;
	} else if (y <= -7.2e-139) {
		tmp = x / 2.0;
	} else if (y <= -6.2e-195) {
		tmp = t_0;
	} else if (y <= 5.5e-210) {
		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 <= (-6.2d-10)) then
        tmp = t_0
    else if (y <= (-7.2d-139)) then
        tmp = x / 2.0d0
    else if (y <= (-6.2d-195)) then
        tmp = t_0
    else if (y <= 5.5d-210) 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 <= -6.2e-10) {
		tmp = t_0;
	} else if (y <= -7.2e-139) {
		tmp = x / 2.0;
	} else if (y <= -6.2e-195) {
		tmp = t_0;
	} else if (y <= 5.5e-210) {
		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 <= -6.2e-10:
		tmp = t_0
	elif y <= -7.2e-139:
		tmp = x / 2.0
	elif y <= -6.2e-195:
		tmp = t_0
	elif y <= 5.5e-210:
		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 <= -6.2e-10)
		tmp = t_0;
	elseif (y <= -7.2e-139)
		tmp = Float64(x / 2.0);
	elseif (y <= -6.2e-195)
		tmp = t_0;
	elseif (y <= 5.5e-210)
		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 <= -6.2e-10)
		tmp = t_0;
	elseif (y <= -7.2e-139)
		tmp = x / 2.0;
	elseif (y <= -6.2e-195)
		tmp = t_0;
	elseif (y <= 5.5e-210)
		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, -6.2e-10], t$95$0, If[LessEqual[y, -7.2e-139], N[(x / 2.0), $MachinePrecision], If[LessEqual[y, -6.2e-195], t$95$0, If[LessEqual[y, 5.5e-210], N[(x / 2.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000003e-10 or -7.20000000000000007e-139 < y < -6.20000000000000005e-195 or 5.50000000000000024e-210 < 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 47.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 91.2%

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

   if -6.2000000000000003e-10 < y < -7.20000000000000007e-139 or -6.20000000000000005e-195 < y < 5.50000000000000024e-210

   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 68.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 68.1%

      \[\leadsto \frac{x}{\color{blue}{2}} \]
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 30.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 97.5%

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

   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 99.1%

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

Alternative 4: 74.4% 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 62.2%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 74.5%

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

Alternative 5: 36.3% 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 63.6%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 38.9%

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

Reproduce

herbie shell --seed 2024313 
(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))