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

Percentage Accurate: 100.0% → 100.0%

Time: 1.5s

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(N[(x / 2.0), $MachinePrecision] + N[(x * y + z), $MachinePrecision]), $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. fma-def 100.0%

      \[\leadsto \frac{x}{2} + \color{blue}{\mathsf{fma}\left(x, y, z\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{x}{2} + \mathsf{fma}\left(x, y, z\right)} \]

4. Final simplification 100.0%

   \[\leadsto \frac{x}{2} + \mathsf{fma}\left(x, y, z\right) \]

Alternative 2: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.48 \cdot 10^{+57} \lor \neg \left(y \leq 1.55 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{x}{2} + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2} + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.48e+57) (not (<= y 1.55e+100)))
   (+ (/ x 2.0) (* x y))
   (+ (/ x 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.48e+57) || !(y <= 1.55e+100)) {
		tmp = (x / 2.0) + (x * y);
	} 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) :: tmp
    if ((y <= (-1.48d+57)) .or. (.not. (y <= 1.55d+100))) then
        tmp = (x / 2.0d0) + (x * y)
    else
        tmp = (x / 2.0d0) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.48e+57) || !(y <= 1.55e+100)) {
		tmp = (x / 2.0) + (x * y);
	} else {
		tmp = (x / 2.0) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.48e+57) or not (y <= 1.55e+100):
		tmp = (x / 2.0) + (x * y)
	else:
		tmp = (x / 2.0) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.48e+57) || !(y <= 1.55e+100))
		tmp = Float64(Float64(x / 2.0) + Float64(x * y));
	else
		tmp = Float64(Float64(x / 2.0) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.48e+57) || ~((y <= 1.55e+100)))
		tmp = (x / 2.0) + (x * y);
	else
		tmp = (x / 2.0) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.48e+57], N[Not[LessEqual[y, 1.55e+100]], $MachinePrecision]], N[(N[(x / 2.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(x / 2.0), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.47999999999999999e57 or 1.55000000000000003e100 < y

   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 84.9%

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

   if -1.47999999999999999e57 < y < 1.55000000000000003e100

   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 95.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.48 \cdot 10^{+57} \lor \neg \left(y \leq 1.55 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{x}{2} + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2} + z\\ \end{array} \]

Alternative 3: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return z + ((x / 2.0) + (x * 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 / 2.0d0) + (x * y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 4: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x / 2.0) + (z + (x * 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 = (x / 2.0d0) + (z + (x * y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x / 2.0), $MachinePrecision] + N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $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. Final simplification 100.0%

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

Alternative 5: 64.8% 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 66.1%

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

5. Final simplification 66.1%

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

Reproduce

herbie shell --seed 2023182 
(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))