Data.Random.Distribution.Normal:doubleStdNormalZ from random-fu-0.2.6.2

Percentage Accurate: 100.0% → 100.0%

Time: 1.2s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + x\right) - 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (+ x x) 1.0))

C

double code(double x) {
	return (x + x) - 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x + x) - 1.0d0
end function

Java

public static double code(double x) {
	return (x + x) - 1.0;
}

Python

def code(x):
	return (x + x) - 1.0

Julia

function code(x)
	return Float64(Float64(x + x) - 1.0)
end

MATLAB

function tmp = code(x)
	tmp = (x + x) - 1.0;
end

Wolfram

code[x_] := N[(N[(x + x), $MachinePrecision] - 1.0), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + x\right) - 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (+ x x) 1.0))

C

double code(double x) {
	return (x + x) - 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x + x) - 1.0d0
end function

Java

public static double code(double x) {
	return (x + x) - 1.0;
}

Python

def code(x):
	return (x + x) - 1.0

Julia

function code(x)
	return Float64(Float64(x + x) - 1.0)
end

MATLAB

function tmp = code(x)
	tmp = (x + x) - 1.0;
end

Wolfram

code[x_] := N[(N[(x + x), $MachinePrecision] - 1.0), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + x\right) + -1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ (+ x x) -1.0))

C

double code(double x) {
	return (x + x) + -1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x + x) + (-1.0d0)
end function

Java

public static double code(double x) {
	return (x + x) + -1.0;
}

Python

def code(x):
	return (x + x) + -1.0

Julia

function code(x)
	return Float64(Float64(x + x) + -1.0)
end

MATLAB

function tmp = code(x)
	tmp = (x + x) + -1.0;
end

Wolfram

code[x_] := N[(N[(x + x), $MachinePrecision] + -1.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + x\right) - 1 \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \left(x + x\right) + -1 \]
4. Add Preprocessing

Alternative 2: 97.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + x \leq -2:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x + x \leq 0.0005:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (+ x x) -2.0) (* x 2.0) (if (<= (+ x x) 0.0005) -1.0 (* x 2.0))))

C

double code(double x) {
	double tmp;
	if ((x + x) <= -2.0) {
		tmp = x * 2.0;
	} else if ((x + x) <= 0.0005) {
		tmp = -1.0;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x + x) <= (-2.0d0)) then
        tmp = x * 2.0d0
    else if ((x + x) <= 0.0005d0) then
        tmp = -1.0d0
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x + x) <= -2.0) {
		tmp = x * 2.0;
	} else if ((x + x) <= 0.0005) {
		tmp = -1.0;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x + x) <= -2.0:
		tmp = x * 2.0
	elif (x + x) <= 0.0005:
		tmp = -1.0
	else:
		tmp = x * 2.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(x + x) <= -2.0)
		tmp = Float64(x * 2.0);
	elseif (Float64(x + x) <= 0.0005)
		tmp = -1.0;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x + x) <= -2.0)
		tmp = x * 2.0;
	elseif ((x + x) <= 0.0005)
		tmp = -1.0;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(x + x), $MachinePrecision], -2.0], N[(x * 2.0), $MachinePrecision], If[LessEqual[N[(x + x), $MachinePrecision], 0.0005], -1.0, N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x x) < -2 or 5.0000000000000001e-4 < (+.f64 x x)

   1. Initial program 100.0%

      \[\left(x + x\right) - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 96.8

         \[\leadsto \color{blue}{2 \cdot x} \]

   5. Simplified 96.8%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -2 < (+.f64 x x) < 5.0000000000000001e-4

   1. Initial program 100.0%

      \[\left(x + x\right) - 1 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 97.2%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + x \leq -2:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x + x \leq 0.0005:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 -1.0)

C

double code(double x) {
	return -1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = -1.0d0
end function

Java

public static double code(double x) {
	return -1.0;
}

Python

def code(x):
	return -1.0

Julia

function code(x)
	return -1.0
end

MATLAB

function tmp = code(x)
	tmp = -1.0;
end

Wolfram

code[x_] := -1.0

Derivation

1. Initial program 100.0%

   \[\left(x + x\right) - 1 \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Simplified 46.4%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024204 
(FPCore (x)
  :name "Data.Random.Distribution.Normal:doubleStdNormalZ from random-fu-0.2.6.2"
  :precision binary64
  (- (+ x x) 1.0))