Main:bigenough1 from B

Percentage Accurate: 100.0% → 100.0%

Time: 2.0s

Alternatives: 3

Speedup: N/A×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + x \cdot x \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ x (* x x)))

C

double code(double x) {
	return x + (x * x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x + (x * x)
end function

Java

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

Python

def code(x):
	return x + (x * x)

Julia

function code(x)
	return Float64(x + Float64(x * x))
end

MATLAB

function tmp = code(x)
	tmp = x + (x * x);
end

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + x \cdot x \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ x (* x x)))

C

double code(double x) {
	return x + (x * x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x + (x * x)
end function

Java

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

Python

def code(x):
	return x + (x * x)

Julia

function code(x)
	return Float64(x + Float64(x * x))
end

MATLAB

function tmp = code(x)
	tmp = x + (x * x);
end

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

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(x * Float64(x + 1.0))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + x \cdot x \]
2. Step-by-step derivation

   1. distribute-rgt1-in 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\left(x + 1\right) \cdot x} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto x \cdot \left(x + 1\right) \]
6. Add Preprocessing

Alternative 2: 97.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0))) (* x x) x))

C

double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = x * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = x * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = x * x
	else:
		tmp = x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(x * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = x * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 100.0%

      \[x + x \cdot x \]
   2. Step-by-step derivation

      1. distribute-rgt1-in 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x + 1\right) \cdot x} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 97.3%

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

   if -1 < x < 1

   1. Initial program 100.0%

      \[x + x \cdot x \]
   2. Step-by-step derivation

      1. distribute-rgt1-in 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x + 1\right) \cdot x} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 96.7%

      \[\leadsto \color{blue}{1} \cdot x \]

   6. Taylor expanded in x around 0 96.7%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.5% accurate, 5.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 x)

C

double code(double x) {
	return x;
}

Fortran

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

Java

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

Python

def code(x):
	return x

Julia

function code(x)
	return x
end

MATLAB

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

Wolfram

code[x_] := x

Derivation

1. Initial program 100.0%

   \[x + x \cdot x \]
2. Step-by-step derivation

   1. distribute-rgt1-in 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\left(x + 1\right) \cdot x} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 41.8%

   \[\leadsto \color{blue}{1} \cdot x \]

6. Taylor expanded in x around 0 41.8%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024152 
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))