Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3

Percentage Accurate: 99.9% → 100.0%

Time: 12.4s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 1.5, \frac{y}{-2}\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x 1.5 (/ y -2.0)))

C

double code(double x, double y) {
	return fma(x, 1.5, (y / -2.0));
}

Julia

function code(x, y)
	return fma(x, 1.5, Float64(y / -2.0))
end

Wolfram

code[x_, y_] := N[(x * 1.5 + N[(y / -2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x + \frac{x - y}{2} \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]
7. Add Preprocessing

Alternative 2: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+79}:\\ \;\;\;\;1.5 \cdot x\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+28}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-46}:\\ \;\;\;\;\frac{-0.6666666666666666}{\frac{-0.4444444444444444}{x}}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-35}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8e+79)
   (* 1.5 x)
   (if (<= x -2.5e+28)
     (* -0.5 y)
     (if (<= x -1.15e-46)
       (/ -0.6666666666666666 (/ -0.4444444444444444 x))
       (if (<= x 6e-35) (* -0.5 y) (* 1.5 x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8e+79) {
		tmp = 1.5 * x;
	} else if (x <= -2.5e+28) {
		tmp = -0.5 * y;
	} else if (x <= -1.15e-46) {
		tmp = -0.6666666666666666 / (-0.4444444444444444 / x);
	} else if (x <= 6e-35) {
		tmp = -0.5 * y;
	} else {
		tmp = 1.5 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d+79)) then
        tmp = 1.5d0 * x
    else if (x <= (-2.5d+28)) then
        tmp = (-0.5d0) * y
    else if (x <= (-1.15d-46)) then
        tmp = (-0.6666666666666666d0) / ((-0.4444444444444444d0) / x)
    else if (x <= 6d-35) then
        tmp = (-0.5d0) * y
    else
        tmp = 1.5d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8e+79) {
		tmp = 1.5 * x;
	} else if (x <= -2.5e+28) {
		tmp = -0.5 * y;
	} else if (x <= -1.15e-46) {
		tmp = -0.6666666666666666 / (-0.4444444444444444 / x);
	} else if (x <= 6e-35) {
		tmp = -0.5 * y;
	} else {
		tmp = 1.5 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8e+79:
		tmp = 1.5 * x
	elif x <= -2.5e+28:
		tmp = -0.5 * y
	elif x <= -1.15e-46:
		tmp = -0.6666666666666666 / (-0.4444444444444444 / x)
	elif x <= 6e-35:
		tmp = -0.5 * y
	else:
		tmp = 1.5 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8e+79)
		tmp = Float64(1.5 * x);
	elseif (x <= -2.5e+28)
		tmp = Float64(-0.5 * y);
	elseif (x <= -1.15e-46)
		tmp = Float64(-0.6666666666666666 / Float64(-0.4444444444444444 / x));
	elseif (x <= 6e-35)
		tmp = Float64(-0.5 * y);
	else
		tmp = Float64(1.5 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8e+79)
		tmp = 1.5 * x;
	elseif (x <= -2.5e+28)
		tmp = -0.5 * y;
	elseif (x <= -1.15e-46)
		tmp = -0.6666666666666666 / (-0.4444444444444444 / x);
	elseif (x <= 6e-35)
		tmp = -0.5 * y;
	else
		tmp = 1.5 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8e+79], N[(1.5 * x), $MachinePrecision], If[LessEqual[x, -2.5e+28], N[(-0.5 * y), $MachinePrecision], If[LessEqual[x, -1.15e-46], N[(-0.6666666666666666 / N[(-0.4444444444444444 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-35], N[(-0.5 * y), $MachinePrecision], N[(1.5 * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.8000000000000002e79 or 5.99999999999999978e-35 < x

   1. Initial program 99.8%

      \[x + \frac{x - y}{2} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -3.8000000000000002e79 < x < -2.49999999999999979e28 or -1.15e-46 < x < 5.99999999999999978e-35

   1. Initial program 99.9%

      \[x + \frac{x - y}{2} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.49999999999999979e28 < x < -1.15e-46

   1. Initial program 99.6%

      \[x + \frac{x - y}{2} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]

   13. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+79}:\\ \;\;\;\;1.5 \cdot x\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{+30}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-48}:\\ \;\;\;\;1.5 \cdot x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-36}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4e+79)
   (* 1.5 x)
   (if (<= x -2.45e+30)
     (* -0.5 y)
     (if (<= x -2.1e-48) (* 1.5 x) (if (<= x 8.8e-36) (* -0.5 y) (* 1.5 x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4e+79) {
		tmp = 1.5 * x;
	} else if (x <= -2.45e+30) {
		tmp = -0.5 * y;
	} else if (x <= -2.1e-48) {
		tmp = 1.5 * x;
	} else if (x <= 8.8e-36) {
		tmp = -0.5 * y;
	} else {
		tmp = 1.5 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4d+79)) then
        tmp = 1.5d0 * x
    else if (x <= (-2.45d+30)) then
        tmp = (-0.5d0) * y
    else if (x <= (-2.1d-48)) then
        tmp = 1.5d0 * x
    else if (x <= 8.8d-36) then
        tmp = (-0.5d0) * y
    else
        tmp = 1.5d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4e+79) {
		tmp = 1.5 * x;
	} else if (x <= -2.45e+30) {
		tmp = -0.5 * y;
	} else if (x <= -2.1e-48) {
		tmp = 1.5 * x;
	} else if (x <= 8.8e-36) {
		tmp = -0.5 * y;
	} else {
		tmp = 1.5 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4e+79:
		tmp = 1.5 * x
	elif x <= -2.45e+30:
		tmp = -0.5 * y
	elif x <= -2.1e-48:
		tmp = 1.5 * x
	elif x <= 8.8e-36:
		tmp = -0.5 * y
	else:
		tmp = 1.5 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4e+79)
		tmp = Float64(1.5 * x);
	elseif (x <= -2.45e+30)
		tmp = Float64(-0.5 * y);
	elseif (x <= -2.1e-48)
		tmp = Float64(1.5 * x);
	elseif (x <= 8.8e-36)
		tmp = Float64(-0.5 * y);
	else
		tmp = Float64(1.5 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4e+79)
		tmp = 1.5 * x;
	elseif (x <= -2.45e+30)
		tmp = -0.5 * y;
	elseif (x <= -2.1e-48)
		tmp = 1.5 * x;
	elseif (x <= 8.8e-36)
		tmp = -0.5 * y;
	else
		tmp = 1.5 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4e+79], N[(1.5 * x), $MachinePrecision], If[LessEqual[x, -2.45e+30], N[(-0.5 * y), $MachinePrecision], If[LessEqual[x, -2.1e-48], N[(1.5 * x), $MachinePrecision], If[LessEqual[x, 8.8e-36], N[(-0.5 * y), $MachinePrecision], N[(1.5 * x), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999987e79 or -2.44999999999999992e30 < x < -2.09999999999999989e-48 or 8.7999999999999997e-36 < x

   1. Initial program 99.8%

      \[x + \frac{x - y}{2} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -3.99999999999999987e79 < x < -2.44999999999999992e30 or -2.09999999999999989e-48 < x < 8.7999999999999997e-36

   1. Initial program 99.9%

      \[x + \frac{x - y}{2} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{y}{-2} + x \cdot 1.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (/ y -2.0) (* x 1.5)))

C

double code(double x, double y) {
	return (y / -2.0) + (x * 1.5);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y / (-2.0d0)) + (x * 1.5d0)
end function

Java

public static double code(double x, double y) {
	return (y / -2.0) + (x * 1.5);
}

Python

def code(x, y):
	return (y / -2.0) + (x * 1.5)

Julia

function code(x, y)
	return Float64(Float64(y / -2.0) + Float64(x * 1.5))
end

MATLAB

function tmp = code(x, y)
	tmp = (y / -2.0) + (x * 1.5);
end

Wolfram

code[x_, y_] := N[(N[(y / -2.0), $MachinePrecision] + N[(x * 1.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x + \frac{x - y}{2} \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 6: 50.1% 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 99.9%

   \[x + \frac{x - y}{2} \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in y around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1.5 \cdot x - 0.5 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* 1.5 x) (* 0.5 y)))

C

double code(double x, double y) {
	return (1.5 * x) - (0.5 * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.5d0 * x) - (0.5d0 * y)
end function

Java

public static double code(double x, double y) {
	return (1.5 * x) - (0.5 * y);
}

Python

def code(x, y):
	return (1.5 * x) - (0.5 * y)

Julia

function code(x, y)
	return Float64(Float64(1.5 * x) - Float64(0.5 * y))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.5 * x) - (0.5 * y);
end

Wolfram

code[x_, y_] := N[(N[(1.5 * x), $MachinePrecision] - N[(0.5 * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
  :precision binary64

  :alt
  (- (* 1.5 x) (* 0.5 y))

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