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

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Alternatives: 4

Speedup: 1.0×

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, 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]

Derivation

1. Initial program 100.0%

   \[x \cdot y - x \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;0 - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (* x y) (if (<= y 1.0) (- 0.0 x) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 1.0) {
		tmp = 0.0 - x;
	} else {
		tmp = x * y;
	}
	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 = x * y
    else if (y <= 1.0d0) then
        tmp = 0.0d0 - x
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 1.0) {
		tmp = 0.0 - x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x * y
	elif y <= 1.0:
		tmp = 0.0 - x
	else:
		tmp = x * y
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 1.0], N[(0.0 - x), $MachinePrecision], N[(x * y), $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. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-mul-1 N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-out N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 + y\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{-1}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 99.5%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   7. Simplified 99.5%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-mul-1 N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-out N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 + y\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{-1}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x} \]

      3. --lowering--.f64 96.7%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

   7. Simplified 96.7%

      \[\leadsto \color{blue}{0 - x} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-lowering-neg.f64 96.7%

         \[\leadsto \mathsf{neg.f64}\left(x\right) \]

   9. Applied egg-rr 96.7%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;0 - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

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 N/A

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

   2. +-commutative N/A

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

   3. neg-mul-1 N/A

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

   4. *-commutative N/A

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

   5. distribute-rgt-out N/A

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

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 + y\right)}\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{-1}\right)\right) \]

   8. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{x \cdot \left(y + -1\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 4: 51.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ 0 - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 0.0 x))

C

double code(double x, double y) {
	return 0.0 - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0 - x
end function

Java

public static double code(double x, double y) {
	return 0.0 - x;
}

Python

def code(x, y):
	return 0.0 - x

Julia

function code(x, y)
	return Float64(0.0 - x)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0 - x;
end

Wolfram

code[x_, y_] := N[(0.0 - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. neg-mul-1 N/A

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

   4. *-commutative N/A

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

   5. distribute-rgt-out N/A

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

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 + y\right)}\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{-1}\right)\right) \]

   8. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(x\right) \]

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{x} \]

   3. --lowering--.f64 51.3%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

7. Simplified 51.3%

   \[\leadsto \color{blue}{0 - x} \]
8. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{neg}\left(x\right) \]

   2. neg-lowering-neg.f64 51.3%

      \[\leadsto \mathsf{neg.f64}\left(x\right) \]

9. Applied egg-rr 51.3%

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

10. Final simplification 51.3%

    \[\leadsto 0 - x \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024163 
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))