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

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

Alternatives: 4

Speedup: 1.0×

• 25.5% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift--.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(x \cdot x - y\right)} \]

   2. sub-neg N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(x \cdot x + \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \left(\color{blue}{x \cdot x} + \left(\mathsf{neg}\left(y\right)\right)\right) \]

   4. lower-fma.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\mathsf{fma}\left(x, x, \mathsf{neg}\left(y\right)\right)} \]

   5. lower-neg.f64 100.0

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

4. Applied rewrites 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 7.4 \cdot 10^{-16}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* x x) 7.4e-16) (* -0.5 y) (* (* x x) 0.5)))

C

double code(double x, double y) {
	double tmp;
	if ((x * x) <= 7.4e-16) {
		tmp = -0.5 * y;
	} else {
		tmp = (x * x) * 0.5;
	}
	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) <= 7.4d-16) then
        tmp = (-0.5d0) * y
    else
        tmp = (x * x) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x * x) <= 7.4e-16) {
		tmp = -0.5 * y;
	} else {
		tmp = (x * x) * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x * x) <= 7.4e-16:
		tmp = -0.5 * y
	else:
		tmp = (x * x) * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x * x) <= 7.4e-16)
		tmp = Float64(-0.5 * y);
	else
		tmp = Float64(Float64(x * x) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x * x) <= 7.4e-16)
		tmp = -0.5 * y;
	else
		tmp = (x * x) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x * x), $MachinePrecision], 7.4e-16], N[(-0.5 * y), $MachinePrecision], N[(N[(x * x), $MachinePrecision] * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 7.3999999999999999e-16

   1. Initial program 100.0%

      \[0.5 \cdot \left(x \cdot x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot \frac{-1}{2}} \]

      2. lower-*.f64 91.4

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   5. Applied rewrites 91.4%

      \[\leadsto \color{blue}{y \cdot -0.5} \]

   if 7.3999999999999999e-16 < (*.f64 x x)

   1. Initial program 100.0%

      \[0.5 \cdot \left(x \cdot x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{1}{2} \cdot \color{blue}{{x}^{2}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(x \cdot x\right)} \]

      2. lower-*.f64 89.1

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

   5. Applied rewrites 89.1%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 7.4 \cdot 10^{-16}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[0.5 \cdot \left(x \cdot x - y\right) \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \left(x \cdot x - y\right) \cdot 0.5 \]
4. Add Preprocessing

Alternative 4: 51.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ -0.5 \cdot y \end{array} \]

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 * 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. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{\frac{-1}{2} \cdot y} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{y \cdot \frac{-1}{2}} \]

   2. lower-*.f64 48.9

      \[\leadsto \color{blue}{y \cdot -0.5} \]

5. Applied rewrites 48.9%

   \[\leadsto \color{blue}{y \cdot -0.5} \]

6. Final simplification 48.9%

   \[\leadsto -0.5 \cdot y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024244 
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  :precision binary64
  (* 0.5 (- (* x x) y)))