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

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 5

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: 86.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1.52 \cdot 10^{-93} \lor \neg \left(x \cdot x \leq 2.1 \cdot 10^{-50}\right) \land x \cdot x \leq 265000000:\\ \;\;\;\;0.5 \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (* x x) 1.52e-93)
         (and (not (<= (* x x) 2.1e-50)) (<= (* x x) 265000000.0)))
   (* 0.5 (- y))
   (* 0.5 (* x x))))

C

double code(double x, double y) {
	double tmp;
	if (((x * x) <= 1.52e-93) || (!((x * x) <= 2.1e-50) && ((x * x) <= 265000000.0))) {
		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) <= 1.52d-93) .or. (.not. ((x * x) <= 2.1d-50)) .and. ((x * x) <= 265000000.0d0)) 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) <= 1.52e-93) || (!((x * x) <= 2.1e-50) && ((x * x) <= 265000000.0))) {
		tmp = 0.5 * -y;
	} else {
		tmp = 0.5 * (x * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x * x) <= 1.52e-93) or (not ((x * x) <= 2.1e-50) and ((x * x) <= 265000000.0)):
		tmp = 0.5 * -y
	else:
		tmp = 0.5 * (x * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(x * x) <= 1.52e-93) || (!(Float64(x * x) <= 2.1e-50) && (Float64(x * x) <= 265000000.0)))
		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) <= 1.52e-93) || (~(((x * x) <= 2.1e-50)) && ((x * x) <= 265000000.0)))
		tmp = 0.5 * -y;
	else
		tmp = 0.5 * (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(x * x), $MachinePrecision], 1.52e-93], And[N[Not[LessEqual[N[(x * x), $MachinePrecision], 2.1e-50]], $MachinePrecision], LessEqual[N[(x * x), $MachinePrecision], 265000000.0]]], 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) < 1.52e-93 or 2.1000000000000001e-50 < (*.f64 x x) < 2.65e8

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.0%

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

      1. mul-1-neg 91.0%

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

   4. Simplified 91.0%

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

   if 1.52e-93 < (*.f64 x x) < 2.1000000000000001e-50 or 2.65e8 < (*.f64 x x)

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 92.0%

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

      1. unpow2 92.0%

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

   4. Simplified 92.0%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1.52 \cdot 10^{-93} \lor \neg \left(x \cdot x \leq 2.1 \cdot 10^{-50}\right) \land x \cdot x \leq 265000000:\\ \;\;\;\;0.5 \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \end{array} \]

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 51.1%

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

   1. mul-1-neg 51.1%

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

4. Simplified 51.1%

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

5. Final simplification 51.1%

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

Alternative 5: 3.9% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.5)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 0.5

Julia

function code(x, y)
	return 0.5
end

MATLAB

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

Wolfram

code[x_, y_] := 0.5

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around inf 51.6%

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

   1. unpow2 51.6%

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

4. Simplified 51.6%

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

6. Applied egg-rr 3.9%

   \[\leadsto \color{blue}{0.5} \]

7. Final simplification 3.9%

   \[\leadsto 0.5 \]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  :precision binary64
  (* 0.5 (- (* x x) y)))