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

Percentage Accurate: 100.0% → 100.0%

Time: 1.8s

Alternatives: 4

Speedup: 0.0×

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, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_] := N[(y * x + (-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%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{x \cdot \left(y + -1\right)} \]
4. Step-by-step derivation

   1. distribute-rgt-in 100.0%

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

   2. fma-def 100.0%

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

   3. neg-mul-1 100.0%

      \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{-x}\right) \]

5. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, -x\right)} \]

6. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, x, -x\right) \]

Alternative 2: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (* y x) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = -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)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * x
    else
        tmp = -x
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = y * x
	else:
		tmp = -x
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   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%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 98.5%

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

   if -1 < y < 1

   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%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 97.3%

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

      1. neg-mul-1 97.3%

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

   6. Simplified 97.3%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 4: 50.0% 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. 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%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around 0 49.4%

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

   1. neg-mul-1 49.4%

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

6. Simplified 49.4%

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

7. Final simplification 49.4%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023331 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))