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

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 8

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 59.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.5:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-180}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-192}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-52}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-35}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+102}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.5)
   (* x y)
   (if (<= y -1.05e-180)
     (* x 0.5)
     (if (<= y 1.2e-192)
       z
       (if (<= y 3.5e-52)
         (* x 0.5)
         (if (<= y 6e-35)
           z
           (if (<= y 1.25e-7) (* x 0.5) (if (<= y 4.2e+102) z (* x y)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.5) {
		tmp = x * y;
	} else if (y <= -1.05e-180) {
		tmp = x * 0.5;
	} else if (y <= 1.2e-192) {
		tmp = z;
	} else if (y <= 3.5e-52) {
		tmp = x * 0.5;
	} else if (y <= 6e-35) {
		tmp = z;
	} else if (y <= 1.25e-7) {
		tmp = x * 0.5;
	} else if (y <= 4.2e+102) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	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 = x * y
    else if (y <= (-1.05d-180)) then
        tmp = x * 0.5d0
    else if (y <= 1.2d-192) then
        tmp = z
    else if (y <= 3.5d-52) then
        tmp = x * 0.5d0
    else if (y <= 6d-35) then
        tmp = z
    else if (y <= 1.25d-7) then
        tmp = x * 0.5d0
    else if (y <= 4.2d+102) then
        tmp = z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.5) {
		tmp = x * y;
	} else if (y <= -1.05e-180) {
		tmp = x * 0.5;
	} else if (y <= 1.2e-192) {
		tmp = z;
	} else if (y <= 3.5e-52) {
		tmp = x * 0.5;
	} else if (y <= 6e-35) {
		tmp = z;
	} else if (y <= 1.25e-7) {
		tmp = x * 0.5;
	} else if (y <= 4.2e+102) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.5:
		tmp = x * y
	elif y <= -1.05e-180:
		tmp = x * 0.5
	elif y <= 1.2e-192:
		tmp = z
	elif y <= 3.5e-52:
		tmp = x * 0.5
	elif y <= 6e-35:
		tmp = z
	elif y <= 1.25e-7:
		tmp = x * 0.5
	elif y <= 4.2e+102:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.5)
		tmp = Float64(x * y);
	elseif (y <= -1.05e-180)
		tmp = Float64(x * 0.5);
	elseif (y <= 1.2e-192)
		tmp = z;
	elseif (y <= 3.5e-52)
		tmp = Float64(x * 0.5);
	elseif (y <= 6e-35)
		tmp = z;
	elseif (y <= 1.25e-7)
		tmp = Float64(x * 0.5);
	elseif (y <= 4.2e+102)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.5)
		tmp = x * y;
	elseif (y <= -1.05e-180)
		tmp = x * 0.5;
	elseif (y <= 1.2e-192)
		tmp = z;
	elseif (y <= 3.5e-52)
		tmp = x * 0.5;
	elseif (y <= 6e-35)
		tmp = z;
	elseif (y <= 1.25e-7)
		tmp = x * 0.5;
	elseif (y <= 4.2e+102)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.5], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.05e-180], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 1.2e-192], z, If[LessEqual[y, 3.5e-52], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 6e-35], z, If[LessEqual[y, 1.25e-7], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 4.2e+102], z, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+190}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+137} \lor \neg \left(z \leq -0.032\right) \land z \leq 5.1 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.26e+190)
   z
   (if (or (<= z -5.2e+137) (and (not (<= z -0.032)) (<= z 5.1e+75)))
     (* x (+ y 0.5))
     z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.26e+190) {
		tmp = z;
	} else if ((z <= -5.2e+137) || (!(z <= -0.032) && (z <= 5.1e+75))) {
		tmp = x * (y + 0.5);
	} 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 <= (-1.26d+190)) then
        tmp = z
    else if ((z <= (-5.2d+137)) .or. (.not. (z <= (-0.032d0))) .and. (z <= 5.1d+75)) then
        tmp = x * (y + 0.5d0)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.26e+190) {
		tmp = z;
	} else if ((z <= -5.2e+137) || (!(z <= -0.032) && (z <= 5.1e+75))) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.26e+190:
		tmp = z
	elif (z <= -5.2e+137) or (not (z <= -0.032) and (z <= 5.1e+75)):
		tmp = x * (y + 0.5)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.26e+190)
		tmp = z;
	elseif ((z <= -5.2e+137) || (!(z <= -0.032) && (z <= 5.1e+75)))
		tmp = Float64(x * Float64(y + 0.5));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.26e+190)
		tmp = z;
	elseif ((z <= -5.2e+137) || (~((z <= -0.032)) && (z <= 5.1e+75)))
		tmp = x * (y + 0.5);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.26e+190], z, If[Or[LessEqual[z, -5.2e+137], And[N[Not[LessEqual[z, -0.032]], $MachinePrecision], LessEqual[z, 5.1e+75]]], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], z]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+15} \lor \neg \left(x \leq 1020000000000\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5e+15) (not (<= x 1020000000000.0)))
   (* x (+ y 0.5))
   (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e+15) || !(x <= 1020000000000.0)) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z + (x * y);
	}
	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 <= (-5d+15)) .or. (.not. (x <= 1020000000000.0d0))) then
        tmp = x * (y + 0.5d0)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e+15) || !(x <= 1020000000000.0)) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5e+15) or not (x <= 1020000000000.0):
		tmp = x * (y + 0.5)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5e+15) || !(x <= 1020000000000.0))
		tmp = Float64(x * Float64(y + 0.5));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5e+15) || ~((x <= 1020000000000.0)))
		tmp = x * (y + 0.5);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5e+15], N[Not[LessEqual[x, 1020000000000.0]], $MachinePrecision]], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 98.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 50.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+15} \lor \neg \left(x \leq 180000000000\right):\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.2e+15) (not (<= x 180000000000.0))) (* x 0.5) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e+15) || !(x <= 180000000000.0)) {
		tmp = x * 0.5;
	} 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 <= (-7.2d+15)) .or. (.not. (x <= 180000000000.0d0))) then
        tmp = x * 0.5d0
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e+15) || !(x <= 180000000000.0)) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.2e+15) or not (x <= 180000000000.0):
		tmp = x * 0.5
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.2e+15) || !(x <= 180000000000.0))
		tmp = Float64(x * 0.5);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.2e+15) || ~((x <= 180000000000.0)))
		tmp = x * 0.5;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.2e+15], N[Not[LessEqual[x, 180000000000.0]], $MachinePrecision]], N[(x * 0.5), $MachinePrecision], z]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023350 
(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))