Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Alternatives: 3

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) - x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) - x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(y + -1\right) \cdot x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (+ y -1.0) x))

C

double code(double x, double y) {
	return (y + -1.0) * x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + (-1.0d0)) * x
end function

Java

public static double code(double x, double y) {
	return (y + -1.0) * x;
}

Python

def code(x, y):
	return (y + -1.0) * x

Julia

function code(x, y)
	return Float64(Float64(y + -1.0) * x)
end

MATLAB

function tmp = code(x, y)
	tmp = (y + -1.0) * x;
end

Wolfram

code[x_, y_] := N[(N[(y + -1.0), $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot y - x \]
2. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. *-commutative 100.0%

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

   3. neg-mul-1 100.0%

      \[\leadsto y \cdot x + \color{blue}{-1 \cdot x} \]

   4. distribute-rgt-out 100.0%

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

   5. *-commutative 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \left(y + -1\right) \cdot x \]

Alternative 2: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (* y x) (if (<= y 1.0) (- x) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = y * x
    else if (y <= 1.0d0) then
        tmp = -x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = y * x
	elif y <= 1.0:
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(y * x);
	elseif (y <= 1.0)
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = y * x;
	elseif (y <= 1.0)
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.0], (-x), N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

      \[x \cdot y - x \]

   2. Taylor expanded in y around inf 98.2%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[x \cdot y - x \]

   2. Taylor expanded in y around 0 98.6%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. mul-1-neg 98.6%

         \[\leadsto \color{blue}{-x} \]

   4. Simplified 98.6%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 49.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -x
end function

Java

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

Python

def code(x, y):
	return -x

Julia

function code(x, y)
	return Float64(-x)
end

MATLAB

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

Wolfram

code[x_, y_] := (-x)

Derivation

1. Initial program 100.0%

   \[x \cdot y - x \]

2. Taylor expanded in y around 0 51.4%

   \[\leadsto \color{blue}{-1 \cdot x} \]
3. Step-by-step derivation

   1. mul-1-neg 51.4%

      \[\leadsto \color{blue}{-x} \]

4. Simplified 51.4%

   \[\leadsto \color{blue}{-x} \]

5. Final simplification 51.4%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))