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

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

Alternatives: 8

Speedup: 0.1×

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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

Alternative 2: 60.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -17000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-165}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-226}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-299}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-226}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -17000.0)
   (* y x)
   (if (<= y -3.7e-165)
     z
     (if (<= y -7e-226)
       (* x 0.5)
       (if (<= y 1.15e-299)
         z
         (if (<= y 6e-226) (* x 0.5) (if (<= y 2.2e+44) z (* y x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -17000.0) {
		tmp = y * x;
	} else if (y <= -3.7e-165) {
		tmp = z;
	} else if (y <= -7e-226) {
		tmp = x * 0.5;
	} else if (y <= 1.15e-299) {
		tmp = z;
	} else if (y <= 6e-226) {
		tmp = x * 0.5;
	} else if (y <= 2.2e+44) {
		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 <= (-17000.0d0)) then
        tmp = y * x
    else if (y <= (-3.7d-165)) then
        tmp = z
    else if (y <= (-7d-226)) then
        tmp = x * 0.5d0
    else if (y <= 1.15d-299) then
        tmp = z
    else if (y <= 6d-226) then
        tmp = x * 0.5d0
    else if (y <= 2.2d+44) 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 <= -17000.0) {
		tmp = y * x;
	} else if (y <= -3.7e-165) {
		tmp = z;
	} else if (y <= -7e-226) {
		tmp = x * 0.5;
	} else if (y <= 1.15e-299) {
		tmp = z;
	} else if (y <= 6e-226) {
		tmp = x * 0.5;
	} else if (y <= 2.2e+44) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -17000.0:
		tmp = y * x
	elif y <= -3.7e-165:
		tmp = z
	elif y <= -7e-226:
		tmp = x * 0.5
	elif y <= 1.15e-299:
		tmp = z
	elif y <= 6e-226:
		tmp = x * 0.5
	elif y <= 2.2e+44:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -17000.0)
		tmp = Float64(y * x);
	elseif (y <= -3.7e-165)
		tmp = z;
	elseif (y <= -7e-226)
		tmp = Float64(x * 0.5);
	elseif (y <= 1.15e-299)
		tmp = z;
	elseif (y <= 6e-226)
		tmp = Float64(x * 0.5);
	elseif (y <= 2.2e+44)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -17000.0)
		tmp = y * x;
	elseif (y <= -3.7e-165)
		tmp = z;
	elseif (y <= -7e-226)
		tmp = x * 0.5;
	elseif (y <= 1.15e-299)
		tmp = z;
	elseif (y <= 6e-226)
		tmp = x * 0.5;
	elseif (y <= 2.2e+44)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -17000.0], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.7e-165], z, If[LessEqual[y, -7e-226], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 1.15e-299], z, If[LessEqual[y, 6e-226], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 2.2e+44], z, N[(y * x), $MachinePrecision]]]]]]]

Derivation

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

Alternative 3: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.16 \lor \neg \left(y \leq 4.2 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.16) (not (<= y 4.2e+46))) (* x (+ y 0.5)) (- z (* x -0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.16) || !(y <= 4.2e+46)) {
		tmp = x * (y + 0.5);
	} 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 <= (-0.16d0)) .or. (.not. (y <= 4.2d+46))) then
        tmp = x * (y + 0.5d0)
    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 <= -0.16) || !(y <= 4.2e+46)) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z - (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.16) or not (y <= 4.2e+46):
		tmp = x * (y + 0.5)
	else:
		tmp = z - (x * -0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.16) || !(y <= 4.2e+46))
		tmp = Float64(x * Float64(y + 0.5));
	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 <= -0.16) || ~((y <= 4.2e+46)))
		tmp = x * (y + 0.5);
	else
		tmp = z - (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.16], N[Not[LessEqual[y, 4.2e+46]], $MachinePrecision]], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], N[(z - N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 4: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.5 \lor \neg \left(y \leq 2.2 \cdot 10^{-7}\right):\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.5) (not (<= y 2.2e-7))) (+ z (* y x)) (- z (* x -0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.5) || !(y <= 2.2e-7)) {
		tmp = z + (y * x);
	} 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 <= 2.2d-7))) then
        tmp = z + (y * x)
    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 <= 2.2e-7)) {
		tmp = z + (y * x);
	} else {
		tmp = z - (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.5) or not (y <= 2.2e-7):
		tmp = z + (y * x)
	else:
		tmp = z - (x * -0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.5) || !(y <= 2.2e-7))
		tmp = Float64(z + Float64(y * x));
	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 <= 2.2e-7)))
		tmp = z + (y * x);
	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, 2.2e-7]], $MachinePrecision]], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(z - N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+122}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 9000000:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.5e+122) z (if (<= z 9000000.0) (* x (+ y 0.5)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+122) {
		tmp = z;
	} else if (z <= 9000000.0) {
		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 <= (-4.5d+122)) then
        tmp = z
    else if (z <= 9000000.0d0) 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 <= -4.5e+122) {
		tmp = z;
	} else if (z <= 9000000.0) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.5e+122:
		tmp = z
	elif z <= 9000000.0:
		tmp = x * (y + 0.5)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.5e+122)
		tmp = z;
	elseif (z <= 9000000.0)
		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 <= -4.5e+122)
		tmp = z;
	elseif (z <= 9000000.0)
		tmp = x * (y + 0.5);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.5e+122], z, If[LessEqual[z, 9000000.0], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], z]]

Derivation

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

Alternative 6: 50.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-79}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-19}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5e-79) z (if (<= z 7e-19) (* x 0.5) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e-79) {
		tmp = z;
	} else if (z <= 7e-19) {
		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 (z <= (-9.5d-79)) then
        tmp = z
    else if (z <= 7d-19) 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 (z <= -9.5e-79) {
		tmp = z;
	} else if (z <= 7e-19) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.5e-79:
		tmp = z
	elif z <= 7e-19:
		tmp = x * 0.5
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5e-79)
		tmp = z;
	elseif (z <= 7e-19)
		tmp = Float64(x * 0.5);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.5e-79)
		tmp = z;
	elseif (z <= 7e-19)
		tmp = x * 0.5;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.5e-79], z, If[LessEqual[z, 7e-19], 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: 41.6% 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 2024008 
(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))