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

Percentage Accurate: 99.9% → 99.9%

Time: 1.6s

Alternatives: 4

Speedup: 1.0×

• 24.4% 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: 99.9% 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: 99.9% 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: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-38} \lor \neg \left(x \leq 1.75 \cdot 10^{-47}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.8e-38) (not (<= x 1.75e-47))) (* 0.5 (* x x)) (* 0.5 (- y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.8e-38) || !(x <= 1.75e-47)) {
		tmp = 0.5 * (x * x);
	} else {
		tmp = 0.5 * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.8d-38)) .or. (.not. (x <= 1.75d-47))) then
        tmp = 0.5d0 * (x * x)
    else
        tmp = 0.5d0 * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.8e-38) || !(x <= 1.75e-47)) {
		tmp = 0.5 * (x * x);
	} else {
		tmp = 0.5 * -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.8e-38) or not (x <= 1.75e-47):
		tmp = 0.5 * (x * x)
	else:
		tmp = 0.5 * -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.8e-38) || !(x <= 1.75e-47))
		tmp = Float64(0.5 * Float64(x * x));
	else
		tmp = Float64(0.5 * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.8e-38) || ~((x <= 1.75e-47)))
		tmp = 0.5 * (x * x);
	else
		tmp = 0.5 * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.8e-38], N[Not[LessEqual[x, 1.75e-47]], $MachinePrecision]], N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision], N[(0.5 * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e-38 or 1.7499999999999999e-47 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 84.8%

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

      1. unpow2 84.8%

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

   4. Simplified 84.8%

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

   if -1.8e-38 < x < 1.7499999999999999e-47

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.3%

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

      1. neg-mul-1 95.3%

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

   4. Simplified 95.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-38} \lor \neg \left(x \leq 1.75 \cdot 10^{-47}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 99.9% 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: 51.2% 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 48.3%

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

   1. neg-mul-1 48.3%

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

4. Simplified 48.3%

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

5. Final simplification 48.3%

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

Reproduce

herbie shell --seed 2023196 
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  :precision binary64
  (* 0.5 (- (* x x) y)))