System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2

Percentage Accurate: 100.0% → 100.0%

Time: 1.6s

Alternatives: 4

Speedup: 1.0×

• 25.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x \cdot x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (- (* x x) y)))

C

double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * ((x * x) - y)
end function

Java

public static double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Python

def code(x, y):
	return 0.5 * ((x * x) - y)

Julia

function code(x, y)
	return Float64(0.5 * Float64(Float64(x * x) - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * ((x * x) - y);
end

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x \cdot x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (- (* x x) y)))

C

double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * ((x * x) - y)
end function

Java

public static double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Python

def code(x, y):
	return 0.5 * ((x * x) - y)

Julia

function code(x, y)
	return Float64(0.5 * Float64(Float64(x * x) - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * ((x * x) - y);
end

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (fma x x (- y))))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[0.5 \cdot \left(x \cdot x - y\right) \]
2. Step-by-step derivation

   1. fma-neg 100.0%

      \[\leadsto 0.5 \cdot \color{blue}{\mathsf{fma}\left(x, x, -y\right)} \]

3. Applied egg-rr 100.0%

   \[\leadsto 0.5 \cdot \color{blue}{\mathsf{fma}\left(x, x, -y\right)} \]

4. Final simplification 100.0%

   \[\leadsto 0.5 \cdot \mathsf{fma}\left(x, x, -y\right) \]

Alternative 2: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1150000000000:\\ \;\;\;\;0.5 \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* x x) 1150000000000.0) (* 0.5 (- y)) (* 0.5 (* x x))))

C

double code(double x, double y) {
	double tmp;
	if ((x * x) <= 1150000000000.0) {
		tmp = 0.5 * -y;
	} else {
		tmp = 0.5 * (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x * x) <= 1150000000000.0d0) then
        tmp = 0.5d0 * -y
    else
        tmp = 0.5d0 * (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x * x) <= 1150000000000.0) {
		tmp = 0.5 * -y;
	} else {
		tmp = 0.5 * (x * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x * x) <= 1150000000000.0:
		tmp = 0.5 * -y
	else:
		tmp = 0.5 * (x * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x * x) <= 1150000000000.0)
		tmp = Float64(0.5 * Float64(-y));
	else
		tmp = Float64(0.5 * Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x * x) <= 1150000000000.0)
		tmp = 0.5 * -y;
	else
		tmp = 0.5 * (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x * x), $MachinePrecision], 1150000000000.0], N[(0.5 * (-y)), $MachinePrecision], N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 1.15e12

   1. Initial program 100.0%

      \[0.5 \cdot \left(x \cdot x - y\right) \]

   2. Taylor expanded in x around 0 90.8%

      \[\leadsto 0.5 \cdot \color{blue}{\left(-1 \cdot y\right)} \]
   3. Step-by-step derivation

      1. neg-mul-1 90.8%

         \[\leadsto 0.5 \cdot \color{blue}{\left(-y\right)} \]

   4. Simplified 90.8%

      \[\leadsto 0.5 \cdot \color{blue}{\left(-y\right)} \]

   if 1.15e12 < (*.f64 x x)

   1. Initial program 100.0%

      \[0.5 \cdot \left(x \cdot x - y\right) \]

   2. Taylor expanded in x around inf 86.0%

      \[\leadsto 0.5 \cdot \color{blue}{{x}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 86.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot x\right)} \]

   4. Simplified 86.0%

      \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1150000000000:\\ \;\;\;\;0.5 \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \end{array} \]

Alternative 3: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x \cdot x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (- (* x x) y)))

C

double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * ((x * x) - y)
end function

Java

public static double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Python

def code(x, y):
	return 0.5 * ((x * x) - y)

Julia

function code(x, y)
	return Float64(0.5 * Float64(Float64(x * x) - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * ((x * x) - y);
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[0.5 \cdot \left(x \cdot x - y\right) \]

2. Final simplification 100.0%

   \[\leadsto 0.5 \cdot \left(x \cdot x - y\right) \]

Alternative 4: 50.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(-y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (- y)))

C

double code(double x, double y) {
	return 0.5 * -y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * -y
end function

Java

public static double code(double x, double y) {
	return 0.5 * -y;
}

Python

def code(x, y):
	return 0.5 * -y

Julia

function code(x, y)
	return Float64(0.5 * Float64(-y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * -y;
end

Wolfram

code[x_, y_] := N[(0.5 * (-y)), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[0.5 \cdot \left(x \cdot x - y\right) \]

2. Taylor expanded in x around 0 49.0%

   \[\leadsto 0.5 \cdot \color{blue}{\left(-1 \cdot y\right)} \]
3. Step-by-step derivation

   1. neg-mul-1 49.0%

      \[\leadsto 0.5 \cdot \color{blue}{\left(-y\right)} \]

4. Simplified 49.0%

   \[\leadsto 0.5 \cdot \color{blue}{\left(-y\right)} \]

5. Final simplification 49.0%

   \[\leadsto 0.5 \cdot \left(-y\right) \]

Reproduce

herbie shell --seed 2023208 
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  :precision binary64
  (* 0.5 (- (* x x) y)))