Numeric.Interval.Internal:bisect from intervals-0.7.1, A

Percentage Accurate: 100.0% → 100.0%

Time: 975.0ms

Alternatives: 5

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ x + \frac{y - x}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (- y x) 2.0)))

C

double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((y - x) / 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Python

def code(x, y):
	return x + ((y - x) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(Float64(y - x) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((y - x) / 2.0);
end

Wolfram

code[x_, y_] := N[(x + N[(N[(y - x), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (- y x) 2.0)))

C

double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((y - x) / 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Python

def code(x, y):
	return x + ((y - x) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(Float64(y - x) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((y - x) / 2.0);
end

Wolfram

code[x_, y_] := N[(x + N[(N[(y - x), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (- y x) 2.0)))

C

double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((y - x) / 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Python

def code(x, y):
	return x + ((y - x) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(Float64(y - x) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((y - x) / 2.0);
end

Wolfram

code[x_, y_] := N[(x + N[(N[(y - x), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{2} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+182}:\\ \;\;\;\;x + \left(x + \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.9e+182) (+ x (+ x (- y x))) (/ (- y x) 2.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.9e+182) {
		tmp = x + (x + (y - x));
	} else {
		tmp = (y - x) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.9d+182)) then
        tmp = x + (x + (y - x))
    else
        tmp = (y - x) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.9e+182) {
		tmp = x + (x + (y - x));
	} else {
		tmp = (y - x) / 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.9e+182:
		tmp = x + (x + (y - x))
	else:
		tmp = (y - x) / 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.9e+182)
		tmp = Float64(x + Float64(x + Float64(y - x)));
	else
		tmp = Float64(Float64(y - x) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.9e+182)
		tmp = x + (x + (y - x));
	else
		tmp = (y - x) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.9e+182], N[(x + N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8999999999999998e182

   1. Initial program 100.0%

      \[x + \frac{y - x}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 2.0%

      \[\leadsto x + \color{blue}{\left(y - x\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \]

   8. Applied rewrites 18.8%

      \[\leadsto x + \left(x + \color{blue}{\left(y - x\right)}\right) \]

   if -2.8999999999999998e182 < x

   1. Initial program 100.0%

      \[x + \frac{y - x}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 58.5%

      \[\leadsto \color{blue}{\frac{y - x}{2}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 18.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x + (x + (y - x))

Julia

function code(x, y)
	return Float64(x + Float64(x + Float64(y - x)))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 11.1%

   \[\leadsto x + \color{blue}{\left(y - x\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto x + y \]

8. Applied rewrites 18.8%

   \[\leadsto x + \left(x + \color{blue}{\left(y - x\right)}\right) \]
9. Add Preprocessing

Alternative 4: 10.8% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x + (y - x)

Julia

function code(x, y)
	return Float64(x + Float64(y - x))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 11.1%

   \[\leadsto x + \color{blue}{\left(y - x\right)} \]
6. Add Preprocessing

Alternative 5: 9.9% accurate, 4.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 51.3%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 10.2%

   \[\leadsto y - \color{blue}{x} \]
9. Add Preprocessing

Developer Target 1: 100.0% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024321 
(FPCore (x y)
  :name "Numeric.Interval.Internal:bisect from intervals-0.7.1, A"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (* 1/2 (+ x y)))

  (+ x (/ (- y x) 2.0)))