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

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 3

Speedup: 1.0×

• could not determine a ground truth

  1. x = 5.666766523366997e-138
  2. y = 1.3478511034119486e-217

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: 100.0% 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, 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 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 71.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-19} \lor \neg \left(x \leq 9.5 \cdot 10^{-107} \lor \neg \left(x \leq 2 \cdot 10^{+134}\right) \land x \leq 3.4 \cdot 10^{+161}\right):\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.2e-19)
         (not (or (<= x 9.5e-107) (and (not (<= x 2e+134)) (<= x 3.4e+161)))))
   (* x 1.5)
   (* y -0.5)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.2e-19) || !((x <= 9.5e-107) || (!(x <= 2e+134) && (x <= 3.4e+161)))) {
		tmp = x * 1.5;
	} else {
		tmp = y * -0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-3.2d-19)) .or. (.not. (x <= 9.5d-107) .or. (.not. (x <= 2d+134)) .and. (x <= 3.4d+161))) then
        tmp = x * 1.5d0
    else
        tmp = y * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -3.2e-19) || !((x <= 9.5e-107) || (!(x <= 2e+134) && (x <= 3.4e+161)))) {
		tmp = x * 1.5;
	} else {
		tmp = y * -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.2e-19) or not ((x <= 9.5e-107) or (not (x <= 2e+134) and (x <= 3.4e+161))):
		tmp = x * 1.5
	else:
		tmp = y * -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.2e-19) || !((x <= 9.5e-107) || (!(x <= 2e+134) && (x <= 3.4e+161))))
		tmp = Float64(x * 1.5);
	else
		tmp = Float64(y * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.2e-19) || ~(((x <= 9.5e-107) || (~((x <= 2e+134)) && (x <= 3.4e+161)))))
		tmp = x * 1.5;
	else
		tmp = y * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.2e-19], N[Not[Or[LessEqual[x, 9.5e-107], And[N[Not[LessEqual[x, 2e+134]], $MachinePrecision], LessEqual[x, 3.4e+161]]]], $MachinePrecision]], N[(x * 1.5), $MachinePrecision], N[(y * -0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999982e-19 or 9.4999999999999999e-107 < x < 1.99999999999999984e134 or 3.39999999999999993e161 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.1%

      \[\leadsto \color{blue}{1.5 \cdot x} \]

   if -3.19999999999999982e-19 < x < 9.4999999999999999e-107 or 1.99999999999999984e134 < x < 3.39999999999999993e161

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.6%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-19} \lor \neg \left(x \leq 9.5 \cdot 10^{-107} \lor \neg \left(x \leq 2 \cdot 10^{+134}\right) \land x \leq 3.4 \cdot 10^{+161}\right):\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.3% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 49.8%

   \[\leadsto \color{blue}{-0.5 \cdot y} \]

4. Final simplification 49.8%

   \[\leadsto y \cdot -0.5 \]
5. Add Preprocessing

Developer target: 100.0% 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 2024031 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- (* 1.5 x) (* 0.5 y))

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