Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5

Percentage Accurate: 99.3% → 99.4%

Time: 42.9s

Alternatives: 26

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (+
   2.0
   (*
    (*
     (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
     (- (sin y) (/ (sin x) 16.0)))
    (- (cos x) (cos y))))
  (*
   3.0
   (+
    (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)))
    (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y))))))

C

double code(double x, double y) {
	return (2.0 + (((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))) * (sin(y) - (sin(x) / 16.0))) * (cos(x) - cos(y)))) / (3.0 * ((1.0 + (((sqrt(5.0) - 1.0) / 2.0) * cos(x))) + (((3.0 - sqrt(5.0)) / 2.0) * cos(y))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 + (((sqrt(2.0d0) * (sin(x) - (sin(y) / 16.0d0))) * (sin(y) - (sin(x) / 16.0d0))) * (cos(x) - cos(y)))) / (3.0d0 * ((1.0d0 + (((sqrt(5.0d0) - 1.0d0) / 2.0d0) * cos(x))) + (((3.0d0 - sqrt(5.0d0)) / 2.0d0) * cos(y))))
end function

Java

public static double code(double x, double y) {
	return (2.0 + (((Math.sqrt(2.0) * (Math.sin(x) - (Math.sin(y) / 16.0))) * (Math.sin(y) - (Math.sin(x) / 16.0))) * (Math.cos(x) - Math.cos(y)))) / (3.0 * ((1.0 + (((Math.sqrt(5.0) - 1.0) / 2.0) * Math.cos(x))) + (((3.0 - Math.sqrt(5.0)) / 2.0) * Math.cos(y))));
}

Python

def code(x, y):
	return (2.0 + (((math.sqrt(2.0) * (math.sin(x) - (math.sin(y) / 16.0))) * (math.sin(y) - (math.sin(x) / 16.0))) * (math.cos(x) - math.cos(y)))) / (3.0 * ((1.0 + (((math.sqrt(5.0) - 1.0) / 2.0) * math.cos(x))) + (((3.0 - math.sqrt(5.0)) / 2.0) * math.cos(y))))

Julia

function code(x, y)
	return Float64(Float64(2.0 + Float64(Float64(Float64(sqrt(2.0) * Float64(sin(x) - Float64(sin(y) / 16.0))) * Float64(sin(y) - Float64(sin(x) / 16.0))) * Float64(cos(x) - cos(y)))) / Float64(3.0 * Float64(Float64(1.0 + Float64(Float64(Float64(sqrt(5.0) - 1.0) / 2.0) * cos(x))) + Float64(Float64(Float64(3.0 - sqrt(5.0)) / 2.0) * cos(y)))))
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 + (((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))) * (sin(y) - (sin(x) / 16.0))) * (cos(x) - cos(y)))) / (3.0 * ((1.0 + (((sqrt(5.0) - 1.0) / 2.0) * cos(x))) + (((3.0 - sqrt(5.0)) / 2.0) * cos(y))));
end

Wolfram

code[x_, y_] := N[(N[(2.0 + N[(N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[(N[(N[Sqrt[5.0], $MachinePrecision] - 1.0), $MachinePrecision] / 2.0), $MachinePrecision] * N[Cos[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (+
   2.0
   (*
    (*
     (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
     (- (sin y) (/ (sin x) 16.0)))
    (- (cos x) (cos y))))
  (*
   3.0
   (+
    (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)))
    (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y))))))

C

double code(double x, double y) {
	return (2.0 + (((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))) * (sin(y) - (sin(x) / 16.0))) * (cos(x) - cos(y)))) / (3.0 * ((1.0 + (((sqrt(5.0) - 1.0) / 2.0) * cos(x))) + (((3.0 - sqrt(5.0)) / 2.0) * cos(y))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 + (((sqrt(2.0d0) * (sin(x) - (sin(y) / 16.0d0))) * (sin(y) - (sin(x) / 16.0d0))) * (cos(x) - cos(y)))) / (3.0d0 * ((1.0d0 + (((sqrt(5.0d0) - 1.0d0) / 2.0d0) * cos(x))) + (((3.0d0 - sqrt(5.0d0)) / 2.0d0) * cos(y))))
end function

Java

public static double code(double x, double y) {
	return (2.0 + (((Math.sqrt(2.0) * (Math.sin(x) - (Math.sin(y) / 16.0))) * (Math.sin(y) - (Math.sin(x) / 16.0))) * (Math.cos(x) - Math.cos(y)))) / (3.0 * ((1.0 + (((Math.sqrt(5.0) - 1.0) / 2.0) * Math.cos(x))) + (((3.0 - Math.sqrt(5.0)) / 2.0) * Math.cos(y))));
}

Python

def code(x, y):
	return (2.0 + (((math.sqrt(2.0) * (math.sin(x) - (math.sin(y) / 16.0))) * (math.sin(y) - (math.sin(x) / 16.0))) * (math.cos(x) - math.cos(y)))) / (3.0 * ((1.0 + (((math.sqrt(5.0) - 1.0) / 2.0) * math.cos(x))) + (((3.0 - math.sqrt(5.0)) / 2.0) * math.cos(y))))

Julia

function code(x, y)
	return Float64(Float64(2.0 + Float64(Float64(Float64(sqrt(2.0) * Float64(sin(x) - Float64(sin(y) / 16.0))) * Float64(sin(y) - Float64(sin(x) / 16.0))) * Float64(cos(x) - cos(y)))) / Float64(3.0 * Float64(Float64(1.0 + Float64(Float64(Float64(sqrt(5.0) - 1.0) / 2.0) * cos(x))) + Float64(Float64(Float64(3.0 - sqrt(5.0)) / 2.0) * cos(y)))))
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 + (((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))) * (sin(y) - (sin(x) / 16.0))) * (cos(x) - cos(y)))) / (3.0 * ((1.0 + (((sqrt(5.0) - 1.0) / 2.0) * cos(x))) + (((3.0 - sqrt(5.0)) / 2.0) * cos(y))));
end

Wolfram

code[x_, y_] := N[(N[(2.0 + N[(N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[(N[(N[Sqrt[5.0], $MachinePrecision] - 1.0), $MachinePrecision] / 2.0), $MachinePrecision] * N[Cos[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \frac{\mathsf{fma}\left(\sqrt{2}, \left(\sin x + -0.0625 \cdot \sin y\right) \cdot \left(\left(\sin y + \sin x \cdot -0.0625\right) \cdot \left(\cos x - \cos y\right)\right), 2\right)}{3 + 1.5 \cdot \left(4 \cdot \frac{\cos y}{3 + \sqrt{5}} + \cos x \cdot \left(\sqrt{5} + -1\right)\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (fma
   (sqrt 2.0)
   (*
    (+ (sin x) (* -0.0625 (sin y)))
    (* (+ (sin y) (* (sin x) -0.0625)) (- (cos x) (cos y))))
   2.0)
  (+
   3.0
   (*
    1.5
    (+
     (* 4.0 (/ (cos y) (+ 3.0 (sqrt 5.0))))
     (* (cos x) (+ (sqrt 5.0) -1.0)))))))

C

double code(double x, double y) {
	return fma(sqrt(2.0), ((sin(x) + (-0.0625 * sin(y))) * ((sin(y) + (sin(x) * -0.0625)) * (cos(x) - cos(y)))), 2.0) / (3.0 + (1.5 * ((4.0 * (cos(y) / (3.0 + sqrt(5.0)))) + (cos(x) * (sqrt(5.0) + -1.0)))));
}

Julia

function code(x, y)
	return Float64(fma(sqrt(2.0), Float64(Float64(sin(x) + Float64(-0.0625 * sin(y))) * Float64(Float64(sin(y) + Float64(sin(x) * -0.0625)) * Float64(cos(x) - cos(y)))), 2.0) / Float64(3.0 + Float64(1.5 * Float64(Float64(4.0 * Float64(cos(y) / Float64(3.0 + sqrt(5.0)))) + Float64(cos(x) * Float64(sqrt(5.0) + -1.0))))))
end

Wolfram

code[x_, y_] := N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(N[Sin[x], $MachinePrecision] + N[(-0.0625 * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sin[y], $MachinePrecision] + N[(N[Sin[x], $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(N[(4.0 * N[(N[Cos[y], $MachinePrecision] / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[x], $MachinePrecision] * N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2 + \left(\cos x - \cos y\right) \cdot \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (+
   2.0
   (*
    (- (cos x) (cos y))
    (*
     (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
     (- (sin y) (/ (sin x) 16.0)))))
  (*
   3.0
   (+
    (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))
    (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0))))))

C

double code(double x, double y) {
	return (2.0 + ((cos(x) - cos(y)) * ((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))) * (sin(y) - (sin(x) / 16.0))))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 + ((cos(x) - cos(y)) * ((sqrt(2.0d0) * (sin(x) - (sin(y) / 16.0d0))) * (sin(y) - (sin(x) / 16.0d0))))) / (3.0d0 * ((1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))) + (cos(y) * ((4.0d0 / (3.0d0 + sqrt(5.0d0))) / 2.0d0))))
end function

Java

public static double code(double x, double y) {
	return (2.0 + ((Math.cos(x) - Math.cos(y)) * ((Math.sqrt(2.0) * (Math.sin(x) - (Math.sin(y) / 16.0))) * (Math.sin(y) - (Math.sin(x) / 16.0))))) / (3.0 * ((1.0 + (Math.cos(x) * ((Math.sqrt(5.0) + -1.0) / 2.0))) + (Math.cos(y) * ((4.0 / (3.0 + Math.sqrt(5.0))) / 2.0))));
}

Python

def code(x, y):
	return (2.0 + ((math.cos(x) - math.cos(y)) * ((math.sqrt(2.0) * (math.sin(x) - (math.sin(y) / 16.0))) * (math.sin(y) - (math.sin(x) / 16.0))))) / (3.0 * ((1.0 + (math.cos(x) * ((math.sqrt(5.0) + -1.0) / 2.0))) + (math.cos(y) * ((4.0 / (3.0 + math.sqrt(5.0))) / 2.0))))

Julia

function code(x, y)
	return Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(Float64(sqrt(2.0) * Float64(sin(x) - Float64(sin(y) / 16.0))) * Float64(sin(y) - Float64(sin(x) / 16.0))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0))) + Float64(cos(y) * Float64(Float64(4.0 / Float64(3.0 + sqrt(5.0))) / 2.0)))))
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 + ((cos(x) - cos(y)) * ((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))) * (sin(y) - (sin(x) / 16.0))))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
end

Wolfram

code[x_, y_] := N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ \frac{2 + \left(\cos x - \cos y\right) \cdot \left(\sqrt{2} \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (sqrt 5.0) 2.0)))
   (/
    (+
     2.0
     (*
      (- (cos x) (cos y))
      (*
       (sqrt 2.0)
       (* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0))))))
    (* 3.0 (+ 1.0 (+ (* (cos x) (- t_0 0.5)) (* (cos y) (- 1.5 t_0))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) / 2.0;
	return (2.0 + ((cos(x) - cos(y)) * (sqrt(2.0) * ((sin(x) - (sin(y) / 16.0)) * (sin(y) - (sin(x) / 16.0)))))) / (3.0 * (1.0 + ((cos(x) * (t_0 - 0.5)) + (cos(y) * (1.5 - t_0)))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = sqrt(5.0d0) / 2.0d0
    code = (2.0d0 + ((cos(x) - cos(y)) * (sqrt(2.0d0) * ((sin(x) - (sin(y) / 16.0d0)) * (sin(y) - (sin(x) / 16.0d0)))))) / (3.0d0 * (1.0d0 + ((cos(x) * (t_0 - 0.5d0)) + (cos(y) * (1.5d0 - t_0)))))
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(5.0) / 2.0;
	return (2.0 + ((Math.cos(x) - Math.cos(y)) * (Math.sqrt(2.0) * ((Math.sin(x) - (Math.sin(y) / 16.0)) * (Math.sin(y) - (Math.sin(x) / 16.0)))))) / (3.0 * (1.0 + ((Math.cos(x) * (t_0 - 0.5)) + (Math.cos(y) * (1.5 - t_0)))));
}

Python

def code(x, y):
	t_0 = math.sqrt(5.0) / 2.0
	return (2.0 + ((math.cos(x) - math.cos(y)) * (math.sqrt(2.0) * ((math.sin(x) - (math.sin(y) / 16.0)) * (math.sin(y) - (math.sin(x) / 16.0)))))) / (3.0 * (1.0 + ((math.cos(x) * (t_0 - 0.5)) + (math.cos(y) * (1.5 - t_0)))))

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) / 2.0)
	return Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(sqrt(2.0) * Float64(Float64(sin(x) - Float64(sin(y) / 16.0)) * Float64(sin(y) - Float64(sin(x) / 16.0)))))) / Float64(3.0 * Float64(1.0 + Float64(Float64(cos(x) * Float64(t_0 - 0.5)) + Float64(cos(y) * Float64(1.5 - t_0))))))
end

MATLAB

function tmp = code(x, y)
	t_0 = sqrt(5.0) / 2.0;
	tmp = (2.0 + ((cos(x) - cos(y)) * (sqrt(2.0) * ((sin(x) - (sin(y) / 16.0)) * (sin(y) - (sin(x) / 16.0)))))) / (3.0 * (1.0 + ((cos(x) * (t_0 - 0.5)) + (cos(y) * (1.5 - t_0)))));
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[5.0], $MachinePrecision] / 2.0), $MachinePrecision]}, N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(N[Cos[x], $MachinePrecision] * N[(t$95$0 - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2 + \left(\left(\sin y + \sin x \cdot -0.0625\right) \cdot \left(\cos x - \cos y\right)\right) \cdot \left(\sqrt{2} \cdot \left(\sin x + -0.0625 \cdot \sin y\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (+
   2.0
   (*
    (* (+ (sin y) (* (sin x) -0.0625)) (- (cos x) (cos y)))
    (* (sqrt 2.0) (+ (sin x) (* -0.0625 (sin y))))))
  (*
   3.0
   (+
    (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))
    (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0))))))

C

double code(double x, double y) {
	return (2.0 + (((sin(y) + (sin(x) * -0.0625)) * (cos(x) - cos(y))) * (sqrt(2.0) * (sin(x) + (-0.0625 * sin(y)))))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 + (((sin(y) + (sin(x) * (-0.0625d0))) * (cos(x) - cos(y))) * (sqrt(2.0d0) * (sin(x) + ((-0.0625d0) * sin(y)))))) / (3.0d0 * ((1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))) + (cos(y) * ((3.0d0 - sqrt(5.0d0)) / 2.0d0))))
end function

Java

public static double code(double x, double y) {
	return (2.0 + (((Math.sin(y) + (Math.sin(x) * -0.0625)) * (Math.cos(x) - Math.cos(y))) * (Math.sqrt(2.0) * (Math.sin(x) + (-0.0625 * Math.sin(y)))))) / (3.0 * ((1.0 + (Math.cos(x) * ((Math.sqrt(5.0) + -1.0) / 2.0))) + (Math.cos(y) * ((3.0 - Math.sqrt(5.0)) / 2.0))));
}

Python

def code(x, y):
	return (2.0 + (((math.sin(y) + (math.sin(x) * -0.0625)) * (math.cos(x) - math.cos(y))) * (math.sqrt(2.0) * (math.sin(x) + (-0.0625 * math.sin(y)))))) / (3.0 * ((1.0 + (math.cos(x) * ((math.sqrt(5.0) + -1.0) / 2.0))) + (math.cos(y) * ((3.0 - math.sqrt(5.0)) / 2.0))))

Julia

function code(x, y)
	return Float64(Float64(2.0 + Float64(Float64(Float64(sin(y) + Float64(sin(x) * -0.0625)) * Float64(cos(x) - cos(y))) * Float64(sqrt(2.0) * Float64(sin(x) + Float64(-0.0625 * sin(y)))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0))) + Float64(cos(y) * Float64(Float64(3.0 - sqrt(5.0)) / 2.0)))))
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 + (((sin(y) + (sin(x) * -0.0625)) * (cos(x) - cos(y))) * (sqrt(2.0) * (sin(x) + (-0.0625 * sin(y)))))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
end

Wolfram

code[x_, y_] := N[(N[(2.0 + N[(N[(N[(N[Sin[y], $MachinePrecision] + N[(N[Sin[x], $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] + N[(-0.0625 * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2 + \left(\cos x - \cos y\right) \cdot \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (+
   2.0
   (*
    (- (cos x) (cos y))
    (*
     (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
     (- (sin y) (/ (sin x) 16.0)))))
  (*
   3.0
   (+
    (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))
    (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0))))))

C

double code(double x, double y) {
	return (2.0 + ((cos(x) - cos(y)) * ((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))) * (sin(y) - (sin(x) / 16.0))))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 + ((cos(x) - cos(y)) * ((sqrt(2.0d0) * (sin(x) - (sin(y) / 16.0d0))) * (sin(y) - (sin(x) / 16.0d0))))) / (3.0d0 * ((1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))) + (cos(y) * ((3.0d0 - sqrt(5.0d0)) / 2.0d0))))
end function

Java

public static double code(double x, double y) {
	return (2.0 + ((Math.cos(x) - Math.cos(y)) * ((Math.sqrt(2.0) * (Math.sin(x) - (Math.sin(y) / 16.0))) * (Math.sin(y) - (Math.sin(x) / 16.0))))) / (3.0 * ((1.0 + (Math.cos(x) * ((Math.sqrt(5.0) + -1.0) / 2.0))) + (Math.cos(y) * ((3.0 - Math.sqrt(5.0)) / 2.0))));
}

Python

def code(x, y):
	return (2.0 + ((math.cos(x) - math.cos(y)) * ((math.sqrt(2.0) * (math.sin(x) - (math.sin(y) / 16.0))) * (math.sin(y) - (math.sin(x) / 16.0))))) / (3.0 * ((1.0 + (math.cos(x) * ((math.sqrt(5.0) + -1.0) / 2.0))) + (math.cos(y) * ((3.0 - math.sqrt(5.0)) / 2.0))))

Julia

function code(x, y)
	return Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(Float64(sqrt(2.0) * Float64(sin(x) - Float64(sin(y) / 16.0))) * Float64(sin(y) - Float64(sin(x) / 16.0))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0))) + Float64(cos(y) * Float64(Float64(3.0 - sqrt(5.0)) / 2.0)))))
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 + ((cos(x) - cos(y)) * ((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))) * (sin(y) - (sin(x) / 16.0))))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
end

Wolfram

code[x_, y_] := N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 81.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{5} + -1\\ t_1 := \sin y - \frac{\sin x}{16}\\ t_2 := 3 - \sqrt{5}\\ t_3 := \cos x - \cos y\\ \mathbf{if}\;x \leq -0.037 \lor \neg \left(x \leq 0.022\right):\\ \;\;\;\;\frac{2 + t_3 \cdot \left(t_1 \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_0}{2}\right) + \cos y \cdot \frac{t_2}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_3 \cdot \left(t_1 \cdot \left(\sqrt{2} \cdot \left(x + -0.0625 \cdot \sin y\right)\right)\right)}{3 \cdot \left(1 + \left(\left(\cos x \cdot t_0\right) \cdot 0.5 + 0.5 \cdot \left(\cos y \cdot t_2\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (sqrt 5.0) -1.0))
        (t_1 (- (sin y) (/ (sin x) 16.0)))
        (t_2 (- 3.0 (sqrt 5.0)))
        (t_3 (- (cos x) (cos y))))
   (if (or (<= x -0.037) (not (<= x 0.022)))
     (/
      (+ 2.0 (* t_3 (* t_1 (* (sqrt 2.0) (sin x)))))
      (* 3.0 (+ (+ 1.0 (* (cos x) (/ t_0 2.0))) (* (cos y) (/ t_2 2.0)))))
     (/
      (+ 2.0 (* t_3 (* t_1 (* (sqrt 2.0) (+ x (* -0.0625 (sin y)))))))
      (* 3.0 (+ 1.0 (+ (* (* (cos x) t_0) 0.5) (* 0.5 (* (cos y) t_2)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) + -1.0;
	double t_1 = sin(y) - (sin(x) / 16.0);
	double t_2 = 3.0 - sqrt(5.0);
	double t_3 = cos(x) - cos(y);
	double tmp;
	if ((x <= -0.037) || !(x <= 0.022)) {
		tmp = (2.0 + (t_3 * (t_1 * (sqrt(2.0) * sin(x))))) / (3.0 * ((1.0 + (cos(x) * (t_0 / 2.0))) + (cos(y) * (t_2 / 2.0))));
	} else {
		tmp = (2.0 + (t_3 * (t_1 * (sqrt(2.0) * (x + (-0.0625 * sin(y))))))) / (3.0 * (1.0 + (((cos(x) * t_0) * 0.5) + (0.5 * (cos(y) * t_2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = sqrt(5.0d0) + (-1.0d0)
    t_1 = sin(y) - (sin(x) / 16.0d0)
    t_2 = 3.0d0 - sqrt(5.0d0)
    t_3 = cos(x) - cos(y)
    if ((x <= (-0.037d0)) .or. (.not. (x <= 0.022d0))) then
        tmp = (2.0d0 + (t_3 * (t_1 * (sqrt(2.0d0) * sin(x))))) / (3.0d0 * ((1.0d0 + (cos(x) * (t_0 / 2.0d0))) + (cos(y) * (t_2 / 2.0d0))))
    else
        tmp = (2.0d0 + (t_3 * (t_1 * (sqrt(2.0d0) * (x + ((-0.0625d0) * sin(y))))))) / (3.0d0 * (1.0d0 + (((cos(x) * t_0) * 0.5d0) + (0.5d0 * (cos(y) * t_2)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(5.0) + -1.0;
	double t_1 = Math.sin(y) - (Math.sin(x) / 16.0);
	double t_2 = 3.0 - Math.sqrt(5.0);
	double t_3 = Math.cos(x) - Math.cos(y);
	double tmp;
	if ((x <= -0.037) || !(x <= 0.022)) {
		tmp = (2.0 + (t_3 * (t_1 * (Math.sqrt(2.0) * Math.sin(x))))) / (3.0 * ((1.0 + (Math.cos(x) * (t_0 / 2.0))) + (Math.cos(y) * (t_2 / 2.0))));
	} else {
		tmp = (2.0 + (t_3 * (t_1 * (Math.sqrt(2.0) * (x + (-0.0625 * Math.sin(y))))))) / (3.0 * (1.0 + (((Math.cos(x) * t_0) * 0.5) + (0.5 * (Math.cos(y) * t_2)))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(5.0) + -1.0
	t_1 = math.sin(y) - (math.sin(x) / 16.0)
	t_2 = 3.0 - math.sqrt(5.0)
	t_3 = math.cos(x) - math.cos(y)
	tmp = 0
	if (x <= -0.037) or not (x <= 0.022):
		tmp = (2.0 + (t_3 * (t_1 * (math.sqrt(2.0) * math.sin(x))))) / (3.0 * ((1.0 + (math.cos(x) * (t_0 / 2.0))) + (math.cos(y) * (t_2 / 2.0))))
	else:
		tmp = (2.0 + (t_3 * (t_1 * (math.sqrt(2.0) * (x + (-0.0625 * math.sin(y))))))) / (3.0 * (1.0 + (((math.cos(x) * t_0) * 0.5) + (0.5 * (math.cos(y) * t_2)))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) + -1.0)
	t_1 = Float64(sin(y) - Float64(sin(x) / 16.0))
	t_2 = Float64(3.0 - sqrt(5.0))
	t_3 = Float64(cos(x) - cos(y))
	tmp = 0.0
	if ((x <= -0.037) || !(x <= 0.022))
		tmp = Float64(Float64(2.0 + Float64(t_3 * Float64(t_1 * Float64(sqrt(2.0) * sin(x))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(t_0 / 2.0))) + Float64(cos(y) * Float64(t_2 / 2.0)))));
	else
		tmp = Float64(Float64(2.0 + Float64(t_3 * Float64(t_1 * Float64(sqrt(2.0) * Float64(x + Float64(-0.0625 * sin(y))))))) / Float64(3.0 * Float64(1.0 + Float64(Float64(Float64(cos(x) * t_0) * 0.5) + Float64(0.5 * Float64(cos(y) * t_2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(5.0) + -1.0;
	t_1 = sin(y) - (sin(x) / 16.0);
	t_2 = 3.0 - sqrt(5.0);
	t_3 = cos(x) - cos(y);
	tmp = 0.0;
	if ((x <= -0.037) || ~((x <= 0.022)))
		tmp = (2.0 + (t_3 * (t_1 * (sqrt(2.0) * sin(x))))) / (3.0 * ((1.0 + (cos(x) * (t_0 / 2.0))) + (cos(y) * (t_2 / 2.0))));
	else
		tmp = (2.0 + (t_3 * (t_1 * (sqrt(2.0) * (x + (-0.0625 * sin(y))))))) / (3.0 * (1.0 + (((cos(x) * t_0) * 0.5) + (0.5 * (cos(y) * t_2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -0.037], N[Not[LessEqual[x, 0.022]], $MachinePrecision]], N[(N[(2.0 + N[(t$95$3 * N[(t$95$1 * N[(N[Sqrt[2.0], $MachinePrecision] * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(t$95$0 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(t$95$2 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(t$95$3 * N[(t$95$1 * N[(N[Sqrt[2.0], $MachinePrecision] * N[(x + N[(-0.0625 * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(N[(N[Cos[x], $MachinePrecision] * t$95$0), $MachinePrecision] * 0.5), $MachinePrecision] + N[(0.5 * N[(N[Cos[y], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 81.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := 3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)\\ t_2 := \cos x - \cos y\\ \mathbf{if}\;x \leq -0.02 \lor \neg \left(x \leq 0.034\right):\\ \;\;\;\;\frac{2 + t_2 \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \left(x + -0.0625 \cdot \sin y\right)\right)\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (sin y) (/ (sin x) 16.0)))
        (t_1
         (*
          3.0
          (+
           (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))
           (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))))
        (t_2 (- (cos x) (cos y))))
   (if (or (<= x -0.02) (not (<= x 0.034)))
     (/ (+ 2.0 (* t_2 (* t_0 (* (sqrt 2.0) (sin x))))) t_1)
     (/
      (+ 2.0 (* t_2 (* t_0 (* (sqrt 2.0) (+ x (* -0.0625 (sin y)))))))
      t_1))))

C

double code(double x, double y) {
	double t_0 = sin(y) - (sin(x) / 16.0);
	double t_1 = 3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0)));
	double t_2 = cos(x) - cos(y);
	double tmp;
	if ((x <= -0.02) || !(x <= 0.034)) {
		tmp = (2.0 + (t_2 * (t_0 * (sqrt(2.0) * sin(x))))) / t_1;
	} else {
		tmp = (2.0 + (t_2 * (t_0 * (sqrt(2.0) * (x + (-0.0625 * sin(y))))))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = sin(y) - (sin(x) / 16.0d0)
    t_1 = 3.0d0 * ((1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))) + (cos(y) * ((3.0d0 - sqrt(5.0d0)) / 2.0d0)))
    t_2 = cos(x) - cos(y)
    if ((x <= (-0.02d0)) .or. (.not. (x <= 0.034d0))) then
        tmp = (2.0d0 + (t_2 * (t_0 * (sqrt(2.0d0) * sin(x))))) / t_1
    else
        tmp = (2.0d0 + (t_2 * (t_0 * (sqrt(2.0d0) * (x + ((-0.0625d0) * sin(y))))))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sin(y) - (Math.sin(x) / 16.0);
	double t_1 = 3.0 * ((1.0 + (Math.cos(x) * ((Math.sqrt(5.0) + -1.0) / 2.0))) + (Math.cos(y) * ((3.0 - Math.sqrt(5.0)) / 2.0)));
	double t_2 = Math.cos(x) - Math.cos(y);
	double tmp;
	if ((x <= -0.02) || !(x <= 0.034)) {
		tmp = (2.0 + (t_2 * (t_0 * (Math.sqrt(2.0) * Math.sin(x))))) / t_1;
	} else {
		tmp = (2.0 + (t_2 * (t_0 * (Math.sqrt(2.0) * (x + (-0.0625 * Math.sin(y))))))) / t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sin(y) - (math.sin(x) / 16.0)
	t_1 = 3.0 * ((1.0 + (math.cos(x) * ((math.sqrt(5.0) + -1.0) / 2.0))) + (math.cos(y) * ((3.0 - math.sqrt(5.0)) / 2.0)))
	t_2 = math.cos(x) - math.cos(y)
	tmp = 0
	if (x <= -0.02) or not (x <= 0.034):
		tmp = (2.0 + (t_2 * (t_0 * (math.sqrt(2.0) * math.sin(x))))) / t_1
	else:
		tmp = (2.0 + (t_2 * (t_0 * (math.sqrt(2.0) * (x + (-0.0625 * math.sin(y))))))) / t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sin(y) - Float64(sin(x) / 16.0))
	t_1 = Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0))) + Float64(cos(y) * Float64(Float64(3.0 - sqrt(5.0)) / 2.0))))
	t_2 = Float64(cos(x) - cos(y))
	tmp = 0.0
	if ((x <= -0.02) || !(x <= 0.034))
		tmp = Float64(Float64(2.0 + Float64(t_2 * Float64(t_0 * Float64(sqrt(2.0) * sin(x))))) / t_1);
	else
		tmp = Float64(Float64(2.0 + Float64(t_2 * Float64(t_0 * Float64(sqrt(2.0) * Float64(x + Float64(-0.0625 * sin(y))))))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sin(y) - (sin(x) / 16.0);
	t_1 = 3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0)));
	t_2 = cos(x) - cos(y);
	tmp = 0.0;
	if ((x <= -0.02) || ~((x <= 0.034)))
		tmp = (2.0 + (t_2 * (t_0 * (sqrt(2.0) * sin(x))))) / t_1;
	else
		tmp = (2.0 + (t_2 * (t_0 * (sqrt(2.0) * (x + (-0.0625 * sin(y))))))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -0.02], N[Not[LessEqual[x, 0.034]], $MachinePrecision]], N[(N[(2.0 + N[(t$95$2 * N[(t$95$0 * N[(N[Sqrt[2.0], $MachinePrecision] * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(2.0 + N[(t$95$2 * N[(t$95$0 * N[(N[Sqrt[2.0], $MachinePrecision] * N[(x + N[(-0.0625 * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 81.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{5} + -1\\ t_1 := 3 - \sqrt{5}\\ \mathbf{if}\;x \leq -0.0052 \lor \neg \left(x \leq 0.0045\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_0}{2}\right) + \cos y \cdot \frac{t_1}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt{2}, \left(\sin x + -0.0625 \cdot \sin y\right) \cdot \left(\left(1 - \cos y\right) \cdot \left(\sin y + x \cdot -0.0625\right)\right), 2\right)}{3 + 1.5 \cdot \left(\cos x \cdot t_0 + \cos y \cdot t_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (sqrt 5.0) -1.0)) (t_1 (- 3.0 (sqrt 5.0))))
   (if (or (<= x -0.0052) (not (<= x 0.0045)))
     (/
      (+
       2.0
       (*
        (- (cos x) (cos y))
        (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (sin x)))))
      (* 3.0 (+ (+ 1.0 (* (cos x) (/ t_0 2.0))) (* (cos y) (/ t_1 2.0)))))
     (/
      (fma
       (sqrt 2.0)
       (*
        (+ (sin x) (* -0.0625 (sin y)))
        (* (- 1.0 (cos y)) (+ (sin y) (* x -0.0625))))
       2.0)
      (+ 3.0 (* 1.5 (+ (* (cos x) t_0) (* (cos y) t_1))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) + -1.0;
	double t_1 = 3.0 - sqrt(5.0);
	double tmp;
	if ((x <= -0.0052) || !(x <= 0.0045)) {
		tmp = (2.0 + ((cos(x) - cos(y)) * ((sin(y) - (sin(x) / 16.0)) * (sqrt(2.0) * sin(x))))) / (3.0 * ((1.0 + (cos(x) * (t_0 / 2.0))) + (cos(y) * (t_1 / 2.0))));
	} else {
		tmp = fma(sqrt(2.0), ((sin(x) + (-0.0625 * sin(y))) * ((1.0 - cos(y)) * (sin(y) + (x * -0.0625)))), 2.0) / (3.0 + (1.5 * ((cos(x) * t_0) + (cos(y) * t_1))));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) + -1.0)
	t_1 = Float64(3.0 - sqrt(5.0))
	tmp = 0.0
	if ((x <= -0.0052) || !(x <= 0.0045))
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(Float64(sin(y) - Float64(sin(x) / 16.0)) * Float64(sqrt(2.0) * sin(x))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(t_0 / 2.0))) + Float64(cos(y) * Float64(t_1 / 2.0)))));
	else
		tmp = Float64(fma(sqrt(2.0), Float64(Float64(sin(x) + Float64(-0.0625 * sin(y))) * Float64(Float64(1.0 - cos(y)) * Float64(sin(y) + Float64(x * -0.0625)))), 2.0) / Float64(3.0 + Float64(1.5 * Float64(Float64(cos(x) * t_0) + Float64(cos(y) * t_1)))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -0.0052], N[Not[LessEqual[x, 0.0045]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(t$95$0 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(t$95$1 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(N[Sin[x], $MachinePrecision] + N[(-0.0625 * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] + N[(x * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(N[(N[Cos[x], $MachinePrecision] * t$95$0), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 79.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.0023 \lor \neg \left(x \leq 23\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt{2}, \left(\sin x + -0.0625 \cdot \sin y\right) \cdot \left(\left(1 - \cos y\right) \cdot \left(\sin y + x \cdot -0.0625\right)\right), 2\right)}{3 + 1.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right) + \cos y \cdot \left(3 - \sqrt{5}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (sqrt 5.0) 2.0)))
   (if (or (<= x -0.0023) (not (<= x 23.0)))
     (/
      (+
       2.0
       (* (- (cos x) (cos y)) (* -0.0625 (* (sqrt 2.0) (pow (sin x) 2.0)))))
      (* 3.0 (+ 1.0 (+ (* (cos x) (- t_0 0.5)) (* (cos y) (- 1.5 t_0))))))
     (/
      (fma
       (sqrt 2.0)
       (*
        (+ (sin x) (* -0.0625 (sin y)))
        (* (- 1.0 (cos y)) (+ (sin y) (* x -0.0625))))
       2.0)
      (+
       3.0
       (*
        1.5
        (+
         (* (cos x) (+ (sqrt 5.0) -1.0))
         (* (cos y) (- 3.0 (sqrt 5.0))))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) / 2.0;
	double tmp;
	if ((x <= -0.0023) || !(x <= 23.0)) {
		tmp = (2.0 + ((cos(x) - cos(y)) * (-0.0625 * (sqrt(2.0) * pow(sin(x), 2.0))))) / (3.0 * (1.0 + ((cos(x) * (t_0 - 0.5)) + (cos(y) * (1.5 - t_0)))));
	} else {
		tmp = fma(sqrt(2.0), ((sin(x) + (-0.0625 * sin(y))) * ((1.0 - cos(y)) * (sin(y) + (x * -0.0625)))), 2.0) / (3.0 + (1.5 * ((cos(x) * (sqrt(5.0) + -1.0)) + (cos(y) * (3.0 - sqrt(5.0))))));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) / 2.0)
	tmp = 0.0
	if ((x <= -0.0023) || !(x <= 23.0))
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(-0.0625 * Float64(sqrt(2.0) * (sin(x) ^ 2.0))))) / Float64(3.0 * Float64(1.0 + Float64(Float64(cos(x) * Float64(t_0 - 0.5)) + Float64(cos(y) * Float64(1.5 - t_0))))));
	else
		tmp = Float64(fma(sqrt(2.0), Float64(Float64(sin(x) + Float64(-0.0625 * sin(y))) * Float64(Float64(1.0 - cos(y)) * Float64(sin(y) + Float64(x * -0.0625)))), 2.0) / Float64(3.0 + Float64(1.5 * Float64(Float64(cos(x) * Float64(sqrt(5.0) + -1.0)) + Float64(cos(y) * Float64(3.0 - sqrt(5.0)))))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[5.0], $MachinePrecision] / 2.0), $MachinePrecision]}, If[Or[LessEqual[x, -0.0023], N[Not[LessEqual[x, 23.0]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(N[Cos[x], $MachinePrecision] * N[(t$95$0 - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(N[Sin[x], $MachinePrecision] + N[(-0.0625 * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] + N[(x * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(N[(N[Cos[x], $MachinePrecision] * N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 79.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.0032 \lor \neg \left(x \leq 23\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{2} \cdot \left(x + -0.0625 \cdot \sin y\right)\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (sqrt 5.0) 2.0)))
   (if (or (<= x -0.0032) (not (<= x 23.0)))
     (/
      (+
       2.0
       (* (- (cos x) (cos y)) (* -0.0625 (* (sqrt 2.0) (pow (sin x) 2.0)))))
      (* 3.0 (+ 1.0 (+ (* (cos x) (- t_0 0.5)) (* (cos y) (- 1.5 t_0))))))
     (/
      (+
       2.0
       (*
        (*
         (- (sin y) (/ (sin x) 16.0))
         (* (sqrt 2.0) (+ x (* -0.0625 (sin y)))))
        (- 1.0 (cos y))))
      (*
       3.0
       (+
        (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))
        (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) / 2.0;
	double tmp;
	if ((x <= -0.0032) || !(x <= 23.0)) {
		tmp = (2.0 + ((cos(x) - cos(y)) * (-0.0625 * (sqrt(2.0) * pow(sin(x), 2.0))))) / (3.0 * (1.0 + ((cos(x) * (t_0 - 0.5)) + (cos(y) * (1.5 - t_0)))));
	} else {
		tmp = (2.0 + (((sin(y) - (sin(x) / 16.0)) * (sqrt(2.0) * (x + (-0.0625 * sin(y))))) * (1.0 - cos(y)))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(5.0d0) / 2.0d0
    if ((x <= (-0.0032d0)) .or. (.not. (x <= 23.0d0))) then
        tmp = (2.0d0 + ((cos(x) - cos(y)) * ((-0.0625d0) * (sqrt(2.0d0) * (sin(x) ** 2.0d0))))) / (3.0d0 * (1.0d0 + ((cos(x) * (t_0 - 0.5d0)) + (cos(y) * (1.5d0 - t_0)))))
    else
        tmp = (2.0d0 + (((sin(y) - (sin(x) / 16.0d0)) * (sqrt(2.0d0) * (x + ((-0.0625d0) * sin(y))))) * (1.0d0 - cos(y)))) / (3.0d0 * ((1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))) + (cos(y) * ((3.0d0 - sqrt(5.0d0)) / 2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(5.0) / 2.0;
	double tmp;
	if ((x <= -0.0032) || !(x <= 23.0)) {
		tmp = (2.0 + ((Math.cos(x) - Math.cos(y)) * (-0.0625 * (Math.sqrt(2.0) * Math.pow(Math.sin(x), 2.0))))) / (3.0 * (1.0 + ((Math.cos(x) * (t_0 - 0.5)) + (Math.cos(y) * (1.5 - t_0)))));
	} else {
		tmp = (2.0 + (((Math.sin(y) - (Math.sin(x) / 16.0)) * (Math.sqrt(2.0) * (x + (-0.0625 * Math.sin(y))))) * (1.0 - Math.cos(y)))) / (3.0 * ((1.0 + (Math.cos(x) * ((Math.sqrt(5.0) + -1.0) / 2.0))) + (Math.cos(y) * ((3.0 - Math.sqrt(5.0)) / 2.0))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(5.0) / 2.0
	tmp = 0
	if (x <= -0.0032) or not (x <= 23.0):
		tmp = (2.0 + ((math.cos(x) - math.cos(y)) * (-0.0625 * (math.sqrt(2.0) * math.pow(math.sin(x), 2.0))))) / (3.0 * (1.0 + ((math.cos(x) * (t_0 - 0.5)) + (math.cos(y) * (1.5 - t_0)))))
	else:
		tmp = (2.0 + (((math.sin(y) - (math.sin(x) / 16.0)) * (math.sqrt(2.0) * (x + (-0.0625 * math.sin(y))))) * (1.0 - math.cos(y)))) / (3.0 * ((1.0 + (math.cos(x) * ((math.sqrt(5.0) + -1.0) / 2.0))) + (math.cos(y) * ((3.0 - math.sqrt(5.0)) / 2.0))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) / 2.0)
	tmp = 0.0
	if ((x <= -0.0032) || !(x <= 23.0))
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(-0.0625 * Float64(sqrt(2.0) * (sin(x) ^ 2.0))))) / Float64(3.0 * Float64(1.0 + Float64(Float64(cos(x) * Float64(t_0 - 0.5)) + Float64(cos(y) * Float64(1.5 - t_0))))));
	else
		tmp = Float64(Float64(2.0 + Float64(Float64(Float64(sin(y) - Float64(sin(x) / 16.0)) * Float64(sqrt(2.0) * Float64(x + Float64(-0.0625 * sin(y))))) * Float64(1.0 - cos(y)))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0))) + Float64(cos(y) * Float64(Float64(3.0 - sqrt(5.0)) / 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(5.0) / 2.0;
	tmp = 0.0;
	if ((x <= -0.0032) || ~((x <= 23.0)))
		tmp = (2.0 + ((cos(x) - cos(y)) * (-0.0625 * (sqrt(2.0) * (sin(x) ^ 2.0))))) / (3.0 * (1.0 + ((cos(x) * (t_0 - 0.5)) + (cos(y) * (1.5 - t_0)))));
	else
		tmp = (2.0 + (((sin(y) - (sin(x) / 16.0)) * (sqrt(2.0) * (x + (-0.0625 * sin(y))))) * (1.0 - cos(y)))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[5.0], $MachinePrecision] / 2.0), $MachinePrecision]}, If[Or[LessEqual[x, -0.0032], N[Not[LessEqual[x, 23.0]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(N[Cos[x], $MachinePrecision] * N[(t$95$0 - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(N[(N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(x + N[(-0.0625 * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 79.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos x - \cos y\\ t_1 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{-5} \lor \neg \left(x \leq 0.00037\right):\\ \;\;\;\;\frac{2 + t_0 \cdot \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_1 - 0.5\right) + \cos y \cdot \left(1.5 - t_1\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_0 \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{2} \cdot \left(x + -0.0625 \cdot \sin y\right)\right)\right)}{3 \cdot \left(1 + 0.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right) + \left(\sqrt{5} + -1\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (cos x) (cos y))) (t_1 (/ (sqrt 5.0) 2.0)))
   (if (or (<= x -2.45e-5) (not (<= x 0.00037)))
     (/
      (+ 2.0 (* t_0 (* -0.0625 (* (sqrt 2.0) (pow (sin x) 2.0)))))
      (* 3.0 (+ 1.0 (+ (* (cos x) (- t_1 0.5)) (* (cos y) (- 1.5 t_1))))))
     (/
      (+
       2.0
       (*
        t_0
        (*
         (- (sin y) (/ (sin x) 16.0))
         (* (sqrt 2.0) (+ x (* -0.0625 (sin y)))))))
      (*
       3.0
       (+
        1.0
        (* 0.5 (+ (* (cos y) (- 3.0 (sqrt 5.0))) (+ (sqrt 5.0) -1.0)))))))))

C

double code(double x, double y) {
	double t_0 = cos(x) - cos(y);
	double t_1 = sqrt(5.0) / 2.0;
	double tmp;
	if ((x <= -2.45e-5) || !(x <= 0.00037)) {
		tmp = (2.0 + (t_0 * (-0.0625 * (sqrt(2.0) * pow(sin(x), 2.0))))) / (3.0 * (1.0 + ((cos(x) * (t_1 - 0.5)) + (cos(y) * (1.5 - t_1)))));
	} else {
		tmp = (2.0 + (t_0 * ((sin(y) - (sin(x) / 16.0)) * (sqrt(2.0) * (x + (-0.0625 * sin(y))))))) / (3.0 * (1.0 + (0.5 * ((cos(y) * (3.0 - sqrt(5.0))) + (sqrt(5.0) + -1.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos(x) - cos(y)
    t_1 = sqrt(5.0d0) / 2.0d0
    if ((x <= (-2.45d-5)) .or. (.not. (x <= 0.00037d0))) then
        tmp = (2.0d0 + (t_0 * ((-0.0625d0) * (sqrt(2.0d0) * (sin(x) ** 2.0d0))))) / (3.0d0 * (1.0d0 + ((cos(x) * (t_1 - 0.5d0)) + (cos(y) * (1.5d0 - t_1)))))
    else
        tmp = (2.0d0 + (t_0 * ((sin(y) - (sin(x) / 16.0d0)) * (sqrt(2.0d0) * (x + ((-0.0625d0) * sin(y))))))) / (3.0d0 * (1.0d0 + (0.5d0 * ((cos(y) * (3.0d0 - sqrt(5.0d0))) + (sqrt(5.0d0) + (-1.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.cos(x) - Math.cos(y);
	double t_1 = Math.sqrt(5.0) / 2.0;
	double tmp;
	if ((x <= -2.45e-5) || !(x <= 0.00037)) {
		tmp = (2.0 + (t_0 * (-0.0625 * (Math.sqrt(2.0) * Math.pow(Math.sin(x), 2.0))))) / (3.0 * (1.0 + ((Math.cos(x) * (t_1 - 0.5)) + (Math.cos(y) * (1.5 - t_1)))));
	} else {
		tmp = (2.0 + (t_0 * ((Math.sin(y) - (Math.sin(x) / 16.0)) * (Math.sqrt(2.0) * (x + (-0.0625 * Math.sin(y))))))) / (3.0 * (1.0 + (0.5 * ((Math.cos(y) * (3.0 - Math.sqrt(5.0))) + (Math.sqrt(5.0) + -1.0)))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.cos(x) - math.cos(y)
	t_1 = math.sqrt(5.0) / 2.0
	tmp = 0
	if (x <= -2.45e-5) or not (x <= 0.00037):
		tmp = (2.0 + (t_0 * (-0.0625 * (math.sqrt(2.0) * math.pow(math.sin(x), 2.0))))) / (3.0 * (1.0 + ((math.cos(x) * (t_1 - 0.5)) + (math.cos(y) * (1.5 - t_1)))))
	else:
		tmp = (2.0 + (t_0 * ((math.sin(y) - (math.sin(x) / 16.0)) * (math.sqrt(2.0) * (x + (-0.0625 * math.sin(y))))))) / (3.0 * (1.0 + (0.5 * ((math.cos(y) * (3.0 - math.sqrt(5.0))) + (math.sqrt(5.0) + -1.0)))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(cos(x) - cos(y))
	t_1 = Float64(sqrt(5.0) / 2.0)
	tmp = 0.0
	if ((x <= -2.45e-5) || !(x <= 0.00037))
		tmp = Float64(Float64(2.0 + Float64(t_0 * Float64(-0.0625 * Float64(sqrt(2.0) * (sin(x) ^ 2.0))))) / Float64(3.0 * Float64(1.0 + Float64(Float64(cos(x) * Float64(t_1 - 0.5)) + Float64(cos(y) * Float64(1.5 - t_1))))));
	else
		tmp = Float64(Float64(2.0 + Float64(t_0 * Float64(Float64(sin(y) - Float64(sin(x) / 16.0)) * Float64(sqrt(2.0) * Float64(x + Float64(-0.0625 * sin(y))))))) / Float64(3.0 * Float64(1.0 + Float64(0.5 * Float64(Float64(cos(y) * Float64(3.0 - sqrt(5.0))) + Float64(sqrt(5.0) + -1.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = cos(x) - cos(y);
	t_1 = sqrt(5.0) / 2.0;
	tmp = 0.0;
	if ((x <= -2.45e-5) || ~((x <= 0.00037)))
		tmp = (2.0 + (t_0 * (-0.0625 * (sqrt(2.0) * (sin(x) ^ 2.0))))) / (3.0 * (1.0 + ((cos(x) * (t_1 - 0.5)) + (cos(y) * (1.5 - t_1)))));
	else
		tmp = (2.0 + (t_0 * ((sin(y) - (sin(x) / 16.0)) * (sqrt(2.0) * (x + (-0.0625 * sin(y))))))) / (3.0 * (1.0 + (0.5 * ((cos(y) * (3.0 - sqrt(5.0))) + (sqrt(5.0) + -1.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[5.0], $MachinePrecision] / 2.0), $MachinePrecision]}, If[Or[LessEqual[x, -2.45e-5], N[Not[LessEqual[x, 0.00037]], $MachinePrecision]], N[(N[(2.0 + N[(t$95$0 * N[(-0.0625 * N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(N[Cos[x], $MachinePrecision] * N[(t$95$1 - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(t$95$0 * N[(N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(x + N[(-0.0625 * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(0.5 * N[(N[(N[Cos[y], $MachinePrecision] * N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 12: 79.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\sin y}^{2}\\ t_1 := \sqrt{5} + -1\\ t_2 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(-0.0625 \cdot \left(\sqrt{2} \cdot t_0\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_2 - 0.5\right) + \cos y \cdot \left(1.5 - t_2\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt{2}, \left(\sin x + -0.0625 \cdot \sin y\right) \cdot \left(\left(\cos x + -1\right) \cdot \left(y + \sin x \cdot -0.0625\right)\right), 2\right)}{3 + \left(1.5 \cdot \left(\cos x \cdot t_1\right) + 1.5 \cdot \left(3 - \sqrt{5}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (pow (sin y) 2.0))
        (t_1 (+ (sqrt 5.0) -1.0))
        (t_2 (/ (sqrt 5.0) 2.0)))
   (if (<= y -6.8e-5)
     (/
      (+ 2.0 (* (- (cos x) (cos y)) (* -0.0625 (* (sqrt 2.0) t_0))))
      (* 3.0 (+ 1.0 (+ (* (cos x) (- t_2 0.5)) (* (cos y) (- 1.5 t_2))))))
     (if (<= y 4.2e-17)
       (/
        (fma
         (sqrt 2.0)
         (*
          (+ (sin x) (* -0.0625 (sin y)))
          (* (+ (cos x) -1.0) (+ y (* (sin x) -0.0625))))
         2.0)
        (+ 3.0 (+ (* 1.5 (* (cos x) t_1)) (* 1.5 (- 3.0 (sqrt 5.0))))))
       (/
        (+ 2.0 (* -0.0625 (* t_0 (* (sqrt 2.0) (- 1.0 (cos y))))))
        (*
         3.0
         (+
          (+ 1.0 (* (cos x) (/ t_1 2.0)))
          (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0)))))))))

C

double code(double x, double y) {
	double t_0 = pow(sin(y), 2.0);
	double t_1 = sqrt(5.0) + -1.0;
	double t_2 = sqrt(5.0) / 2.0;
	double tmp;
	if (y <= -6.8e-5) {
		tmp = (2.0 + ((cos(x) - cos(y)) * (-0.0625 * (sqrt(2.0) * t_0)))) / (3.0 * (1.0 + ((cos(x) * (t_2 - 0.5)) + (cos(y) * (1.5 - t_2)))));
	} else if (y <= 4.2e-17) {
		tmp = fma(sqrt(2.0), ((sin(x) + (-0.0625 * sin(y))) * ((cos(x) + -1.0) * (y + (sin(x) * -0.0625)))), 2.0) / (3.0 + ((1.5 * (cos(x) * t_1)) + (1.5 * (3.0 - sqrt(5.0)))));
	} else {
		tmp = (2.0 + (-0.0625 * (t_0 * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * ((1.0 + (cos(x) * (t_1 / 2.0))) + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = sin(y) ^ 2.0
	t_1 = Float64(sqrt(5.0) + -1.0)
	t_2 = Float64(sqrt(5.0) / 2.0)
	tmp = 0.0
	if (y <= -6.8e-5)
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(-0.0625 * Float64(sqrt(2.0) * t_0)))) / Float64(3.0 * Float64(1.0 + Float64(Float64(cos(x) * Float64(t_2 - 0.5)) + Float64(cos(y) * Float64(1.5 - t_2))))));
	elseif (y <= 4.2e-17)
		tmp = Float64(fma(sqrt(2.0), Float64(Float64(sin(x) + Float64(-0.0625 * sin(y))) * Float64(Float64(cos(x) + -1.0) * Float64(y + Float64(sin(x) * -0.0625)))), 2.0) / Float64(3.0 + Float64(Float64(1.5 * Float64(cos(x) * t_1)) + Float64(1.5 * Float64(3.0 - sqrt(5.0))))));
	else
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(t_0 * Float64(sqrt(2.0) * Float64(1.0 - cos(y)))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(t_1 / 2.0))) + Float64(cos(y) * Float64(Float64(4.0 / Float64(3.0 + sqrt(5.0))) / 2.0)))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[5.0], $MachinePrecision] / 2.0), $MachinePrecision]}, If[LessEqual[y, -6.8e-5], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[(N[Sqrt[2.0], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(N[Cos[x], $MachinePrecision] * N[(t$95$2 - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-17], N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(N[Sin[x], $MachinePrecision] + N[(-0.0625 * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision] * N[(y + N[(N[Sin[x], $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 + N[(N[(1.5 * N[(N[Cos[x], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(1.5 * N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(-0.0625 * N[(t$95$0 * N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(t$95$1 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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1. Add Preprocessing

Alternative 13: 79.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.0034 \lor \neg \left(x \leq 23\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left({\sin y}^{2} \cdot \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (sqrt 5.0) 2.0)))
   (if (or (<= x -0.0034) (not (<= x 23.0)))
     (/
      (+
       2.0
       (* (- (cos x) (cos y)) (* -0.0625 (* (sqrt 2.0) (pow (sin x) 2.0)))))
      (* 3.0 (+ 1.0 (+ (* (cos x) (- t_0 0.5)) (* (cos y) (- 1.5 t_0))))))
     (/
      (+ 2.0 (* -0.0625 (* (pow (sin y) 2.0) (* (sqrt 2.0) (- 1.0 (cos y))))))
      (*
       3.0
       (+
        (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))
        (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) / 2.0;
	double tmp;
	if ((x <= -0.0034) || !(x <= 23.0)) {
		tmp = (2.0 + ((cos(x) - cos(y)) * (-0.0625 * (sqrt(2.0) * pow(sin(x), 2.0))))) / (3.0 * (1.0 + ((cos(x) * (t_0 - 0.5)) + (cos(y) * (1.5 - t_0)))));
	} else {
		tmp = (2.0 + (-0.0625 * (pow(sin(y), 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(5.0d0) / 2.0d0
    if ((x <= (-0.0034d0)) .or. (.not. (x <= 23.0d0))) then
        tmp = (2.0d0 + ((cos(x) - cos(y)) * ((-0.0625d0) * (sqrt(2.0d0) * (sin(x) ** 2.0d0))))) / (3.0d0 * (1.0d0 + ((cos(x) * (t_0 - 0.5d0)) + (cos(y) * (1.5d0 - t_0)))))
    else
        tmp = (2.0d0 + ((-0.0625d0) * ((sin(y) ** 2.0d0) * (sqrt(2.0d0) * (1.0d0 - cos(y)))))) / (3.0d0 * ((1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))) + (cos(y) * ((4.0d0 / (3.0d0 + sqrt(5.0d0))) / 2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(5.0) / 2.0;
	double tmp;
	if ((x <= -0.0034) || !(x <= 23.0)) {
		tmp = (2.0 + ((Math.cos(x) - Math.cos(y)) * (-0.0625 * (Math.sqrt(2.0) * Math.pow(Math.sin(x), 2.0))))) / (3.0 * (1.0 + ((Math.cos(x) * (t_0 - 0.5)) + (Math.cos(y) * (1.5 - t_0)))));
	} else {
		tmp = (2.0 + (-0.0625 * (Math.pow(Math.sin(y), 2.0) * (Math.sqrt(2.0) * (1.0 - Math.cos(y)))))) / (3.0 * ((1.0 + (Math.cos(x) * ((Math.sqrt(5.0) + -1.0) / 2.0))) + (Math.cos(y) * ((4.0 / (3.0 + Math.sqrt(5.0))) / 2.0))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(5.0) / 2.0
	tmp = 0
	if (x <= -0.0034) or not (x <= 23.0):
		tmp = (2.0 + ((math.cos(x) - math.cos(y)) * (-0.0625 * (math.sqrt(2.0) * math.pow(math.sin(x), 2.0))))) / (3.0 * (1.0 + ((math.cos(x) * (t_0 - 0.5)) + (math.cos(y) * (1.5 - t_0)))))
	else:
		tmp = (2.0 + (-0.0625 * (math.pow(math.sin(y), 2.0) * (math.sqrt(2.0) * (1.0 - math.cos(y)))))) / (3.0 * ((1.0 + (math.cos(x) * ((math.sqrt(5.0) + -1.0) / 2.0))) + (math.cos(y) * ((4.0 / (3.0 + math.sqrt(5.0))) / 2.0))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) / 2.0)
	tmp = 0.0
	if ((x <= -0.0034) || !(x <= 23.0))
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(-0.0625 * Float64(sqrt(2.0) * (sin(x) ^ 2.0))))) / Float64(3.0 * Float64(1.0 + Float64(Float64(cos(x) * Float64(t_0 - 0.5)) + Float64(cos(y) * Float64(1.5 - t_0))))));
	else
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64((sin(y) ^ 2.0) * Float64(sqrt(2.0) * Float64(1.0 - cos(y)))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0))) + Float64(cos(y) * Float64(Float64(4.0 / Float64(3.0 + sqrt(5.0))) / 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(5.0) / 2.0;
	tmp = 0.0;
	if ((x <= -0.0034) || ~((x <= 23.0)))
		tmp = (2.0 + ((cos(x) - cos(y)) * (-0.0625 * (sqrt(2.0) * (sin(x) ^ 2.0))))) / (3.0 * (1.0 + ((cos(x) * (t_0 - 0.5)) + (cos(y) * (1.5 - t_0)))));
	else
		tmp = (2.0 + (-0.0625 * ((sin(y) ^ 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[5.0], $MachinePrecision] / 2.0), $MachinePrecision]}, If[Or[LessEqual[x, -0.0034], N[Not[LessEqual[x, 23.0]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(N[Cos[x], $MachinePrecision] * N[(t$95$0 - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(-0.0625 * N[(N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 79.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\sin y}^{2}\\ t_1 := 3 + \sqrt{5}\\ t_2 := \sqrt{5} + -1\\ t_3 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;y \leq -0.00054:\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(-0.0625 \cdot \left(\sqrt{2} \cdot t_0\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_3 - 0.5\right) + \cos y \cdot \left(1.5 - t_3\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt{2}, \left(\cos x + -1\right) \cdot \left(-0.0625 \cdot {\sin x}^{2}\right), 2\right)}{3 + 1.5 \cdot \left(4 \cdot \frac{\cos y}{t_1} + \cos x \cdot t_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_2}{2}\right) + \cos y \cdot \frac{\frac{4}{t_1}}{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (pow (sin y) 2.0))
        (t_1 (+ 3.0 (sqrt 5.0)))
        (t_2 (+ (sqrt 5.0) -1.0))
        (t_3 (/ (sqrt 5.0) 2.0)))
   (if (<= y -0.00054)
     (/
      (+ 2.0 (* (- (cos x) (cos y)) (* -0.0625 (* (sqrt 2.0) t_0))))
      (* 3.0 (+ 1.0 (+ (* (cos x) (- t_3 0.5)) (* (cos y) (- 1.5 t_3))))))
     (if (<= y 4.2e-17)
       (/
        (fma (sqrt 2.0) (* (+ (cos x) -1.0) (* -0.0625 (pow (sin x) 2.0))) 2.0)
        (+ 3.0 (* 1.5 (+ (* 4.0 (/ (cos y) t_1)) (* (cos x) t_2)))))
       (/
        (+ 2.0 (* -0.0625 (* t_0 (* (sqrt 2.0) (- 1.0 (cos y))))))
        (*
         3.0
         (+
          (+ 1.0 (* (cos x) (/ t_2 2.0)))
          (* (cos y) (/ (/ 4.0 t_1) 2.0)))))))))

C

double code(double x, double y) {
	double t_0 = pow(sin(y), 2.0);
	double t_1 = 3.0 + sqrt(5.0);
	double t_2 = sqrt(5.0) + -1.0;
	double t_3 = sqrt(5.0) / 2.0;
	double tmp;
	if (y <= -0.00054) {
		tmp = (2.0 + ((cos(x) - cos(y)) * (-0.0625 * (sqrt(2.0) * t_0)))) / (3.0 * (1.0 + ((cos(x) * (t_3 - 0.5)) + (cos(y) * (1.5 - t_3)))));
	} else if (y <= 4.2e-17) {
		tmp = fma(sqrt(2.0), ((cos(x) + -1.0) * (-0.0625 * pow(sin(x), 2.0))), 2.0) / (3.0 + (1.5 * ((4.0 * (cos(y) / t_1)) + (cos(x) * t_2))));
	} else {
		tmp = (2.0 + (-0.0625 * (t_0 * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * ((1.0 + (cos(x) * (t_2 / 2.0))) + (cos(y) * ((4.0 / t_1) / 2.0))));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = sin(y) ^ 2.0
	t_1 = Float64(3.0 + sqrt(5.0))
	t_2 = Float64(sqrt(5.0) + -1.0)
	t_3 = Float64(sqrt(5.0) / 2.0)
	tmp = 0.0
	if (y <= -0.00054)
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(-0.0625 * Float64(sqrt(2.0) * t_0)))) / Float64(3.0 * Float64(1.0 + Float64(Float64(cos(x) * Float64(t_3 - 0.5)) + Float64(cos(y) * Float64(1.5 - t_3))))));
	elseif (y <= 4.2e-17)
		tmp = Float64(fma(sqrt(2.0), Float64(Float64(cos(x) + -1.0) * Float64(-0.0625 * (sin(x) ^ 2.0))), 2.0) / Float64(3.0 + Float64(1.5 * Float64(Float64(4.0 * Float64(cos(y) / t_1)) + Float64(cos(x) * t_2)))));
	else
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(t_0 * Float64(sqrt(2.0) * Float64(1.0 - cos(y)))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(t_2 / 2.0))) + Float64(cos(y) * Float64(Float64(4.0 / t_1) / 2.0)))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$1 = N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[Sqrt[5.0], $MachinePrecision] / 2.0), $MachinePrecision]}, If[LessEqual[y, -0.00054], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[(N[Sqrt[2.0], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(N[Cos[x], $MachinePrecision] * N[(t$95$3 - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-17], N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision] * N[(-0.0625 * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(N[(4.0 * N[(N[Cos[y], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[x], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(-0.0625 * N[(t$95$0 * N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(t$95$2 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(4.0 / t$95$1), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 15: 79.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 + \sqrt{5}\\ t_1 := \sqrt{5} + -1\\ \mathbf{if}\;y \leq -0.00054 \lor \neg \left(y \leq 4.2 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left({\sin y}^{2} \cdot \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_1}{2}\right) + \cos y \cdot \frac{\frac{4}{t_0}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt{2}, \left(\cos x + -1\right) \cdot \left(-0.0625 \cdot {\sin x}^{2}\right), 2\right)}{3 + 1.5 \cdot \left(4 \cdot \frac{\cos y}{t_0} + \cos x \cdot t_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 3.0 (sqrt 5.0))) (t_1 (+ (sqrt 5.0) -1.0)))
   (if (or (<= y -0.00054) (not (<= y 4.2e-17)))
     (/
      (+ 2.0 (* -0.0625 (* (pow (sin y) 2.0) (* (sqrt 2.0) (- 1.0 (cos y))))))
      (*
       3.0
       (+ (+ 1.0 (* (cos x) (/ t_1 2.0))) (* (cos y) (/ (/ 4.0 t_0) 2.0)))))
     (/
      (fma (sqrt 2.0) (* (+ (cos x) -1.0) (* -0.0625 (pow (sin x) 2.0))) 2.0)
      (+ 3.0 (* 1.5 (+ (* 4.0 (/ (cos y) t_0)) (* (cos x) t_1))))))))

C

double code(double x, double y) {
	double t_0 = 3.0 + sqrt(5.0);
	double t_1 = sqrt(5.0) + -1.0;
	double tmp;
	if ((y <= -0.00054) || !(y <= 4.2e-17)) {
		tmp = (2.0 + (-0.0625 * (pow(sin(y), 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * ((1.0 + (cos(x) * (t_1 / 2.0))) + (cos(y) * ((4.0 / t_0) / 2.0))));
	} else {
		tmp = fma(sqrt(2.0), ((cos(x) + -1.0) * (-0.0625 * pow(sin(x), 2.0))), 2.0) / (3.0 + (1.5 * ((4.0 * (cos(y) / t_0)) + (cos(x) * t_1))));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(3.0 + sqrt(5.0))
	t_1 = Float64(sqrt(5.0) + -1.0)
	tmp = 0.0
	if ((y <= -0.00054) || !(y <= 4.2e-17))
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64((sin(y) ^ 2.0) * Float64(sqrt(2.0) * Float64(1.0 - cos(y)))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(t_1 / 2.0))) + Float64(cos(y) * Float64(Float64(4.0 / t_0) / 2.0)))));
	else
		tmp = Float64(fma(sqrt(2.0), Float64(Float64(cos(x) + -1.0) * Float64(-0.0625 * (sin(x) ^ 2.0))), 2.0) / Float64(3.0 + Float64(1.5 * Float64(Float64(4.0 * Float64(cos(y) / t_0)) + Float64(cos(x) * t_1)))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]}, If[Or[LessEqual[y, -0.00054], N[Not[LessEqual[y, 4.2e-17]], $MachinePrecision]], N[(N[(2.0 + N[(-0.0625 * N[(N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(t$95$1 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(4.0 / t$95$0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision] * N[(-0.0625 * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(N[(4.0 * N[(N[Cos[y], $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[x], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 16: 79.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{5} + -1\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-6} \lor \neg \left(y \leq 4.2 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left({\sin y}^{2} \cdot \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_0}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(\sqrt{2} \cdot {\sin x}^{2}\right) \cdot \left(\cos x + -1\right)\right)}{3 + 1.5 \cdot \left(3 + \left(\cos x \cdot t_0 - \sqrt{5}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (sqrt 5.0) -1.0)))
   (if (or (<= y -6.5e-6) (not (<= y 4.2e-17)))
     (/
      (+ 2.0 (* -0.0625 (* (pow (sin y) 2.0) (* (sqrt 2.0) (- 1.0 (cos y))))))
      (*
       3.0
       (+
        (+ 1.0 (* (cos x) (/ t_0 2.0)))
        (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0)))))
     (/
      (+ 2.0 (* -0.0625 (* (* (sqrt 2.0) (pow (sin x) 2.0)) (+ (cos x) -1.0))))
      (+ 3.0 (* 1.5 (+ 3.0 (- (* (cos x) t_0) (sqrt 5.0)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) + -1.0;
	double tmp;
	if ((y <= -6.5e-6) || !(y <= 4.2e-17)) {
		tmp = (2.0 + (-0.0625 * (pow(sin(y), 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * ((1.0 + (cos(x) * (t_0 / 2.0))) + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	} else {
		tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * pow(sin(x), 2.0)) * (cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((cos(x) * t_0) - sqrt(5.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(5.0d0) + (-1.0d0)
    if ((y <= (-6.5d-6)) .or. (.not. (y <= 4.2d-17))) then
        tmp = (2.0d0 + ((-0.0625d0) * ((sin(y) ** 2.0d0) * (sqrt(2.0d0) * (1.0d0 - cos(y)))))) / (3.0d0 * ((1.0d0 + (cos(x) * (t_0 / 2.0d0))) + (cos(y) * ((4.0d0 / (3.0d0 + sqrt(5.0d0))) / 2.0d0))))
    else
        tmp = (2.0d0 + ((-0.0625d0) * ((sqrt(2.0d0) * (sin(x) ** 2.0d0)) * (cos(x) + (-1.0d0))))) / (3.0d0 + (1.5d0 * (3.0d0 + ((cos(x) * t_0) - sqrt(5.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(5.0) + -1.0;
	double tmp;
	if ((y <= -6.5e-6) || !(y <= 4.2e-17)) {
		tmp = (2.0 + (-0.0625 * (Math.pow(Math.sin(y), 2.0) * (Math.sqrt(2.0) * (1.0 - Math.cos(y)))))) / (3.0 * ((1.0 + (Math.cos(x) * (t_0 / 2.0))) + (Math.cos(y) * ((4.0 / (3.0 + Math.sqrt(5.0))) / 2.0))));
	} else {
		tmp = (2.0 + (-0.0625 * ((Math.sqrt(2.0) * Math.pow(Math.sin(x), 2.0)) * (Math.cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((Math.cos(x) * t_0) - Math.sqrt(5.0)))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(5.0) + -1.0
	tmp = 0
	if (y <= -6.5e-6) or not (y <= 4.2e-17):
		tmp = (2.0 + (-0.0625 * (math.pow(math.sin(y), 2.0) * (math.sqrt(2.0) * (1.0 - math.cos(y)))))) / (3.0 * ((1.0 + (math.cos(x) * (t_0 / 2.0))) + (math.cos(y) * ((4.0 / (3.0 + math.sqrt(5.0))) / 2.0))))
	else:
		tmp = (2.0 + (-0.0625 * ((math.sqrt(2.0) * math.pow(math.sin(x), 2.0)) * (math.cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((math.cos(x) * t_0) - math.sqrt(5.0)))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) + -1.0)
	tmp = 0.0
	if ((y <= -6.5e-6) || !(y <= 4.2e-17))
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64((sin(y) ^ 2.0) * Float64(sqrt(2.0) * Float64(1.0 - cos(y)))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(t_0 / 2.0))) + Float64(cos(y) * Float64(Float64(4.0 / Float64(3.0 + sqrt(5.0))) / 2.0)))));
	else
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(Float64(sqrt(2.0) * (sin(x) ^ 2.0)) * Float64(cos(x) + -1.0)))) / Float64(3.0 + Float64(1.5 * Float64(3.0 + Float64(Float64(cos(x) * t_0) - sqrt(5.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(5.0) + -1.0;
	tmp = 0.0;
	if ((y <= -6.5e-6) || ~((y <= 4.2e-17)))
		tmp = (2.0 + (-0.0625 * ((sin(y) ^ 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * ((1.0 + (cos(x) * (t_0 / 2.0))) + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	else
		tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * (sin(x) ^ 2.0)) * (cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((cos(x) * t_0) - sqrt(5.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]}, If[Or[LessEqual[y, -6.5e-6], N[Not[LessEqual[y, 4.2e-17]], $MachinePrecision]], N[(N[(2.0 + N[(-0.0625 * N[(N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(t$95$0 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(-0.0625 * N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(3.0 + N[(N[(N[Cos[x], $MachinePrecision] * t$95$0), $MachinePrecision] - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 17: 79.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{5} + -1\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{-5} \lor \neg \left(y \leq 4.2 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos y\right) \cdot {\sin y}^{2}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_0}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(\sqrt{2} \cdot {\sin x}^{2}\right) \cdot \left(\cos x + -1\right)\right)}{3 + 1.5 \cdot \left(3 + \left(\cos x \cdot t_0 - \sqrt{5}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (sqrt 5.0) -1.0)))
   (if (or (<= y -1.06e-5) (not (<= y 4.2e-17)))
     (/
      (+ 2.0 (* -0.0625 (* (sqrt 2.0) (* (- 1.0 (cos y)) (pow (sin y) 2.0)))))
      (*
       3.0
       (+
        (+ 1.0 (* (cos x) (/ t_0 2.0)))
        (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))))
     (/
      (+ 2.0 (* -0.0625 (* (* (sqrt 2.0) (pow (sin x) 2.0)) (+ (cos x) -1.0))))
      (+ 3.0 (* 1.5 (+ 3.0 (- (* (cos x) t_0) (sqrt 5.0)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) + -1.0;
	double tmp;
	if ((y <= -1.06e-5) || !(y <= 4.2e-17)) {
		tmp = (2.0 + (-0.0625 * (sqrt(2.0) * ((1.0 - cos(y)) * pow(sin(y), 2.0))))) / (3.0 * ((1.0 + (cos(x) * (t_0 / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
	} else {
		tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * pow(sin(x), 2.0)) * (cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((cos(x) * t_0) - sqrt(5.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(5.0d0) + (-1.0d0)
    if ((y <= (-1.06d-5)) .or. (.not. (y <= 4.2d-17))) then
        tmp = (2.0d0 + ((-0.0625d0) * (sqrt(2.0d0) * ((1.0d0 - cos(y)) * (sin(y) ** 2.0d0))))) / (3.0d0 * ((1.0d0 + (cos(x) * (t_0 / 2.0d0))) + (cos(y) * ((3.0d0 - sqrt(5.0d0)) / 2.0d0))))
    else
        tmp = (2.0d0 + ((-0.0625d0) * ((sqrt(2.0d0) * (sin(x) ** 2.0d0)) * (cos(x) + (-1.0d0))))) / (3.0d0 + (1.5d0 * (3.0d0 + ((cos(x) * t_0) - sqrt(5.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(5.0) + -1.0;
	double tmp;
	if ((y <= -1.06e-5) || !(y <= 4.2e-17)) {
		tmp = (2.0 + (-0.0625 * (Math.sqrt(2.0) * ((1.0 - Math.cos(y)) * Math.pow(Math.sin(y), 2.0))))) / (3.0 * ((1.0 + (Math.cos(x) * (t_0 / 2.0))) + (Math.cos(y) * ((3.0 - Math.sqrt(5.0)) / 2.0))));
	} else {
		tmp = (2.0 + (-0.0625 * ((Math.sqrt(2.0) * Math.pow(Math.sin(x), 2.0)) * (Math.cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((Math.cos(x) * t_0) - Math.sqrt(5.0)))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(5.0) + -1.0
	tmp = 0
	if (y <= -1.06e-5) or not (y <= 4.2e-17):
		tmp = (2.0 + (-0.0625 * (math.sqrt(2.0) * ((1.0 - math.cos(y)) * math.pow(math.sin(y), 2.0))))) / (3.0 * ((1.0 + (math.cos(x) * (t_0 / 2.0))) + (math.cos(y) * ((3.0 - math.sqrt(5.0)) / 2.0))))
	else:
		tmp = (2.0 + (-0.0625 * ((math.sqrt(2.0) * math.pow(math.sin(x), 2.0)) * (math.cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((math.cos(x) * t_0) - math.sqrt(5.0)))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) + -1.0)
	tmp = 0.0
	if ((y <= -1.06e-5) || !(y <= 4.2e-17))
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(sqrt(2.0) * Float64(Float64(1.0 - cos(y)) * (sin(y) ^ 2.0))))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(t_0 / 2.0))) + Float64(cos(y) * Float64(Float64(3.0 - sqrt(5.0)) / 2.0)))));
	else
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(Float64(sqrt(2.0) * (sin(x) ^ 2.0)) * Float64(cos(x) + -1.0)))) / Float64(3.0 + Float64(1.5 * Float64(3.0 + Float64(Float64(cos(x) * t_0) - sqrt(5.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(5.0) + -1.0;
	tmp = 0.0;
	if ((y <= -1.06e-5) || ~((y <= 4.2e-17)))
		tmp = (2.0 + (-0.0625 * (sqrt(2.0) * ((1.0 - cos(y)) * (sin(y) ^ 2.0))))) / (3.0 * ((1.0 + (cos(x) * (t_0 / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
	else
		tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * (sin(x) ^ 2.0)) * (cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((cos(x) * t_0) - sqrt(5.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]}, If[Or[LessEqual[y, -1.06e-5], N[Not[LessEqual[y, 4.2e-17]], $MachinePrecision]], N[(N[(2.0 + N[(-0.0625 * N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(t$95$0 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(-0.0625 * N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(3.0 + N[(N[(N[Cos[x], $MachinePrecision] * t$95$0), $MachinePrecision] - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 18: 78.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos x + -1\\ t_1 := \sqrt{5} + -1\\ t_2 := \cos x \cdot t_1\\ t_3 := {\sin x}^{2}\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(t_3 \cdot \left(\sqrt{2} \cdot t_0\right)\right)}{3 + 1.5 \cdot \left(\left(3 + t_2\right) - \sqrt{5}\right)}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left({\sin y}^{2} \cdot \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 \cdot \left(1 + 0.5 \cdot \left(t_1 + \cos y \cdot \frac{4}{3 + \sqrt{5}}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt{2}, t_0 \cdot \left(-0.0625 \cdot t_3\right), 2\right)}{3 + \left(1.5 \cdot t_2 + 1.5 \cdot \left(3 - \sqrt{5}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (cos x) -1.0))
        (t_1 (+ (sqrt 5.0) -1.0))
        (t_2 (* (cos x) t_1))
        (t_3 (pow (sin x) 2.0)))
   (if (<= x -7.5e-6)
     (/
      (+ 2.0 (* -0.0625 (* t_3 (* (sqrt 2.0) t_0))))
      (+ 3.0 (* 1.5 (- (+ 3.0 t_2) (sqrt 5.0)))))
     (if (<= x 8.5e-7)
       (/
        (+
         2.0
         (* -0.0625 (* (pow (sin y) 2.0) (* (sqrt 2.0) (- 1.0 (cos y))))))
        (* 3.0 (+ 1.0 (* 0.5 (+ t_1 (* (cos y) (/ 4.0 (+ 3.0 (sqrt 5.0)))))))))
       (/
        (fma (sqrt 2.0) (* t_0 (* -0.0625 t_3)) 2.0)
        (+ 3.0 (+ (* 1.5 t_2) (* 1.5 (- 3.0 (sqrt 5.0))))))))))

C

double code(double x, double y) {
	double t_0 = cos(x) + -1.0;
	double t_1 = sqrt(5.0) + -1.0;
	double t_2 = cos(x) * t_1;
	double t_3 = pow(sin(x), 2.0);
	double tmp;
	if (x <= -7.5e-6) {
		tmp = (2.0 + (-0.0625 * (t_3 * (sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_2) - sqrt(5.0))));
	} else if (x <= 8.5e-7) {
		tmp = (2.0 + (-0.0625 * (pow(sin(y), 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * (1.0 + (0.5 * (t_1 + (cos(y) * (4.0 / (3.0 + sqrt(5.0))))))));
	} else {
		tmp = fma(sqrt(2.0), (t_0 * (-0.0625 * t_3)), 2.0) / (3.0 + ((1.5 * t_2) + (1.5 * (3.0 - sqrt(5.0)))));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(cos(x) + -1.0)
	t_1 = Float64(sqrt(5.0) + -1.0)
	t_2 = Float64(cos(x) * t_1)
	t_3 = sin(x) ^ 2.0
	tmp = 0.0
	if (x <= -7.5e-6)
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(t_3 * Float64(sqrt(2.0) * t_0)))) / Float64(3.0 + Float64(1.5 * Float64(Float64(3.0 + t_2) - sqrt(5.0)))));
	elseif (x <= 8.5e-7)
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64((sin(y) ^ 2.0) * Float64(sqrt(2.0) * Float64(1.0 - cos(y)))))) / Float64(3.0 * Float64(1.0 + Float64(0.5 * Float64(t_1 + Float64(cos(y) * Float64(4.0 / Float64(3.0 + sqrt(5.0)))))))));
	else
		tmp = Float64(fma(sqrt(2.0), Float64(t_0 * Float64(-0.0625 * t_3)), 2.0) / Float64(3.0 + Float64(Float64(1.5 * t_2) + Float64(1.5 * Float64(3.0 - sqrt(5.0))))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[Cos[x], $MachinePrecision] * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[x, -7.5e-6], N[(N[(2.0 + N[(-0.0625 * N[(t$95$3 * N[(N[Sqrt[2.0], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(N[(3.0 + t$95$2), $MachinePrecision] - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-7], N[(N[(2.0 + N[(-0.0625 * N[(N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(0.5 * N[(t$95$1 + N[(N[Cos[y], $MachinePrecision] * N[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(t$95$0 * N[(-0.0625 * t$95$3), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 + N[(N[(1.5 * t$95$2), $MachinePrecision] + N[(1.5 * N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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1. Add Preprocessing

Alternative 19: 78.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos x + -1\\ t_1 := \sqrt{5} + -1\\ t_2 := \cos x \cdot t_1\\ t_3 := {\sin x}^{2}\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(t_3 \cdot \left(\sqrt{2} \cdot t_0\right)\right)}{3 + 1.5 \cdot \left(\left(3 + t_2\right) - \sqrt{5}\right)}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left({\sin y}^{2} \cdot \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 \cdot \left(1 + 0.5 \cdot \left(t_1 + \cos y \cdot \frac{4}{3 + \sqrt{5}}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(\sqrt{2} \cdot t_3\right) \cdot t_0\right)}{3 + 1.5 \cdot \left(3 + \left(t_2 - \sqrt{5}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (cos x) -1.0))
        (t_1 (+ (sqrt 5.0) -1.0))
        (t_2 (* (cos x) t_1))
        (t_3 (pow (sin x) 2.0)))
   (if (<= x -2.9e-5)
     (/
      (+ 2.0 (* -0.0625 (* t_3 (* (sqrt 2.0) t_0))))
      (+ 3.0 (* 1.5 (- (+ 3.0 t_2) (sqrt 5.0)))))
     (if (<= x 8.5e-7)
       (/
        (+
         2.0
         (* -0.0625 (* (pow (sin y) 2.0) (* (sqrt 2.0) (- 1.0 (cos y))))))
        (* 3.0 (+ 1.0 (* 0.5 (+ t_1 (* (cos y) (/ 4.0 (+ 3.0 (sqrt 5.0)))))))))
       (/
        (+ 2.0 (* -0.0625 (* (* (sqrt 2.0) t_3) t_0)))
        (+ 3.0 (* 1.5 (+ 3.0 (- t_2 (sqrt 5.0))))))))))

C

double code(double x, double y) {
	double t_0 = cos(x) + -1.0;
	double t_1 = sqrt(5.0) + -1.0;
	double t_2 = cos(x) * t_1;
	double t_3 = pow(sin(x), 2.0);
	double tmp;
	if (x <= -2.9e-5) {
		tmp = (2.0 + (-0.0625 * (t_3 * (sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_2) - sqrt(5.0))));
	} else if (x <= 8.5e-7) {
		tmp = (2.0 + (-0.0625 * (pow(sin(y), 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * (1.0 + (0.5 * (t_1 + (cos(y) * (4.0 / (3.0 + sqrt(5.0))))))));
	} else {
		tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * t_3) * t_0))) / (3.0 + (1.5 * (3.0 + (t_2 - sqrt(5.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = cos(x) + (-1.0d0)
    t_1 = sqrt(5.0d0) + (-1.0d0)
    t_2 = cos(x) * t_1
    t_3 = sin(x) ** 2.0d0
    if (x <= (-2.9d-5)) then
        tmp = (2.0d0 + ((-0.0625d0) * (t_3 * (sqrt(2.0d0) * t_0)))) / (3.0d0 + (1.5d0 * ((3.0d0 + t_2) - sqrt(5.0d0))))
    else if (x <= 8.5d-7) then
        tmp = (2.0d0 + ((-0.0625d0) * ((sin(y) ** 2.0d0) * (sqrt(2.0d0) * (1.0d0 - cos(y)))))) / (3.0d0 * (1.0d0 + (0.5d0 * (t_1 + (cos(y) * (4.0d0 / (3.0d0 + sqrt(5.0d0))))))))
    else
        tmp = (2.0d0 + ((-0.0625d0) * ((sqrt(2.0d0) * t_3) * t_0))) / (3.0d0 + (1.5d0 * (3.0d0 + (t_2 - sqrt(5.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.cos(x) + -1.0;
	double t_1 = Math.sqrt(5.0) + -1.0;
	double t_2 = Math.cos(x) * t_1;
	double t_3 = Math.pow(Math.sin(x), 2.0);
	double tmp;
	if (x <= -2.9e-5) {
		tmp = (2.0 + (-0.0625 * (t_3 * (Math.sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_2) - Math.sqrt(5.0))));
	} else if (x <= 8.5e-7) {
		tmp = (2.0 + (-0.0625 * (Math.pow(Math.sin(y), 2.0) * (Math.sqrt(2.0) * (1.0 - Math.cos(y)))))) / (3.0 * (1.0 + (0.5 * (t_1 + (Math.cos(y) * (4.0 / (3.0 + Math.sqrt(5.0))))))));
	} else {
		tmp = (2.0 + (-0.0625 * ((Math.sqrt(2.0) * t_3) * t_0))) / (3.0 + (1.5 * (3.0 + (t_2 - Math.sqrt(5.0)))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.cos(x) + -1.0
	t_1 = math.sqrt(5.0) + -1.0
	t_2 = math.cos(x) * t_1
	t_3 = math.pow(math.sin(x), 2.0)
	tmp = 0
	if x <= -2.9e-5:
		tmp = (2.0 + (-0.0625 * (t_3 * (math.sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_2) - math.sqrt(5.0))))
	elif x <= 8.5e-7:
		tmp = (2.0 + (-0.0625 * (math.pow(math.sin(y), 2.0) * (math.sqrt(2.0) * (1.0 - math.cos(y)))))) / (3.0 * (1.0 + (0.5 * (t_1 + (math.cos(y) * (4.0 / (3.0 + math.sqrt(5.0))))))))
	else:
		tmp = (2.0 + (-0.0625 * ((math.sqrt(2.0) * t_3) * t_0))) / (3.0 + (1.5 * (3.0 + (t_2 - math.sqrt(5.0)))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(cos(x) + -1.0)
	t_1 = Float64(sqrt(5.0) + -1.0)
	t_2 = Float64(cos(x) * t_1)
	t_3 = sin(x) ^ 2.0
	tmp = 0.0
	if (x <= -2.9e-5)
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(t_3 * Float64(sqrt(2.0) * t_0)))) / Float64(3.0 + Float64(1.5 * Float64(Float64(3.0 + t_2) - sqrt(5.0)))));
	elseif (x <= 8.5e-7)
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64((sin(y) ^ 2.0) * Float64(sqrt(2.0) * Float64(1.0 - cos(y)))))) / Float64(3.0 * Float64(1.0 + Float64(0.5 * Float64(t_1 + Float64(cos(y) * Float64(4.0 / Float64(3.0 + sqrt(5.0)))))))));
	else
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(Float64(sqrt(2.0) * t_3) * t_0))) / Float64(3.0 + Float64(1.5 * Float64(3.0 + Float64(t_2 - sqrt(5.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = cos(x) + -1.0;
	t_1 = sqrt(5.0) + -1.0;
	t_2 = cos(x) * t_1;
	t_3 = sin(x) ^ 2.0;
	tmp = 0.0;
	if (x <= -2.9e-5)
		tmp = (2.0 + (-0.0625 * (t_3 * (sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_2) - sqrt(5.0))));
	elseif (x <= 8.5e-7)
		tmp = (2.0 + (-0.0625 * ((sin(y) ^ 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * (1.0 + (0.5 * (t_1 + (cos(y) * (4.0 / (3.0 + sqrt(5.0))))))));
	else
		tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * t_3) * t_0))) / (3.0 + (1.5 * (3.0 + (t_2 - sqrt(5.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[Cos[x], $MachinePrecision] * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[x, -2.9e-5], N[(N[(2.0 + N[(-0.0625 * N[(t$95$3 * N[(N[Sqrt[2.0], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(N[(3.0 + t$95$2), $MachinePrecision] - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-7], N[(N[(2.0 + N[(-0.0625 * N[(N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(0.5 * N[(t$95$1 + N[(N[Cos[y], $MachinePrecision] * N[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(-0.0625 * N[(N[(N[Sqrt[2.0], $MachinePrecision] * t$95$3), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(3.0 + N[(t$95$2 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 20: 78.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos x + -1\\ t_1 := \sqrt{5} + -1\\ t_2 := \cos x \cdot t_1\\ t_3 := {\sin x}^{2}\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(t_3 \cdot \left(\sqrt{2} \cdot t_0\right)\right)}{3 + 1.5 \cdot \left(\left(3 + t_2\right) - \sqrt{5}\right)}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left({\sin y}^{2} \cdot \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 \cdot \left(1 + 0.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right) + t_1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(\sqrt{2} \cdot t_3\right) \cdot t_0\right)}{3 + 1.5 \cdot \left(3 + \left(t_2 - \sqrt{5}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (cos x) -1.0))
        (t_1 (+ (sqrt 5.0) -1.0))
        (t_2 (* (cos x) t_1))
        (t_3 (pow (sin x) 2.0)))
   (if (<= x -5.5e-5)
     (/
      (+ 2.0 (* -0.0625 (* t_3 (* (sqrt 2.0) t_0))))
      (+ 3.0 (* 1.5 (- (+ 3.0 t_2) (sqrt 5.0)))))
     (if (<= x 8.5e-7)
       (/
        (+
         2.0
         (* -0.0625 (* (pow (sin y) 2.0) (* (sqrt 2.0) (- 1.0 (cos y))))))
        (* 3.0 (+ 1.0 (* 0.5 (+ (* (cos y) (- 3.0 (sqrt 5.0))) t_1)))))
       (/
        (+ 2.0 (* -0.0625 (* (* (sqrt 2.0) t_3) t_0)))
        (+ 3.0 (* 1.5 (+ 3.0 (- t_2 (sqrt 5.0))))))))))

C

double code(double x, double y) {
	double t_0 = cos(x) + -1.0;
	double t_1 = sqrt(5.0) + -1.0;
	double t_2 = cos(x) * t_1;
	double t_3 = pow(sin(x), 2.0);
	double tmp;
	if (x <= -5.5e-5) {
		tmp = (2.0 + (-0.0625 * (t_3 * (sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_2) - sqrt(5.0))));
	} else if (x <= 8.5e-7) {
		tmp = (2.0 + (-0.0625 * (pow(sin(y), 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * (1.0 + (0.5 * ((cos(y) * (3.0 - sqrt(5.0))) + t_1))));
	} else {
		tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * t_3) * t_0))) / (3.0 + (1.5 * (3.0 + (t_2 - sqrt(5.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = cos(x) + (-1.0d0)
    t_1 = sqrt(5.0d0) + (-1.0d0)
    t_2 = cos(x) * t_1
    t_3 = sin(x) ** 2.0d0
    if (x <= (-5.5d-5)) then
        tmp = (2.0d0 + ((-0.0625d0) * (t_3 * (sqrt(2.0d0) * t_0)))) / (3.0d0 + (1.5d0 * ((3.0d0 + t_2) - sqrt(5.0d0))))
    else if (x <= 8.5d-7) then
        tmp = (2.0d0 + ((-0.0625d0) * ((sin(y) ** 2.0d0) * (sqrt(2.0d0) * (1.0d0 - cos(y)))))) / (3.0d0 * (1.0d0 + (0.5d0 * ((cos(y) * (3.0d0 - sqrt(5.0d0))) + t_1))))
    else
        tmp = (2.0d0 + ((-0.0625d0) * ((sqrt(2.0d0) * t_3) * t_0))) / (3.0d0 + (1.5d0 * (3.0d0 + (t_2 - sqrt(5.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.cos(x) + -1.0;
	double t_1 = Math.sqrt(5.0) + -1.0;
	double t_2 = Math.cos(x) * t_1;
	double t_3 = Math.pow(Math.sin(x), 2.0);
	double tmp;
	if (x <= -5.5e-5) {
		tmp = (2.0 + (-0.0625 * (t_3 * (Math.sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_2) - Math.sqrt(5.0))));
	} else if (x <= 8.5e-7) {
		tmp = (2.0 + (-0.0625 * (Math.pow(Math.sin(y), 2.0) * (Math.sqrt(2.0) * (1.0 - Math.cos(y)))))) / (3.0 * (1.0 + (0.5 * ((Math.cos(y) * (3.0 - Math.sqrt(5.0))) + t_1))));
	} else {
		tmp = (2.0 + (-0.0625 * ((Math.sqrt(2.0) * t_3) * t_0))) / (3.0 + (1.5 * (3.0 + (t_2 - Math.sqrt(5.0)))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.cos(x) + -1.0
	t_1 = math.sqrt(5.0) + -1.0
	t_2 = math.cos(x) * t_1
	t_3 = math.pow(math.sin(x), 2.0)
	tmp = 0
	if x <= -5.5e-5:
		tmp = (2.0 + (-0.0625 * (t_3 * (math.sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_2) - math.sqrt(5.0))))
	elif x <= 8.5e-7:
		tmp = (2.0 + (-0.0625 * (math.pow(math.sin(y), 2.0) * (math.sqrt(2.0) * (1.0 - math.cos(y)))))) / (3.0 * (1.0 + (0.5 * ((math.cos(y) * (3.0 - math.sqrt(5.0))) + t_1))))
	else:
		tmp = (2.0 + (-0.0625 * ((math.sqrt(2.0) * t_3) * t_0))) / (3.0 + (1.5 * (3.0 + (t_2 - math.sqrt(5.0)))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(cos(x) + -1.0)
	t_1 = Float64(sqrt(5.0) + -1.0)
	t_2 = Float64(cos(x) * t_1)
	t_3 = sin(x) ^ 2.0
	tmp = 0.0
	if (x <= -5.5e-5)
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(t_3 * Float64(sqrt(2.0) * t_0)))) / Float64(3.0 + Float64(1.5 * Float64(Float64(3.0 + t_2) - sqrt(5.0)))));
	elseif (x <= 8.5e-7)
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64((sin(y) ^ 2.0) * Float64(sqrt(2.0) * Float64(1.0 - cos(y)))))) / Float64(3.0 * Float64(1.0 + Float64(0.5 * Float64(Float64(cos(y) * Float64(3.0 - sqrt(5.0))) + t_1)))));
	else
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(Float64(sqrt(2.0) * t_3) * t_0))) / Float64(3.0 + Float64(1.5 * Float64(3.0 + Float64(t_2 - sqrt(5.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = cos(x) + -1.0;
	t_1 = sqrt(5.0) + -1.0;
	t_2 = cos(x) * t_1;
	t_3 = sin(x) ^ 2.0;
	tmp = 0.0;
	if (x <= -5.5e-5)
		tmp = (2.0 + (-0.0625 * (t_3 * (sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_2) - sqrt(5.0))));
	elseif (x <= 8.5e-7)
		tmp = (2.0 + (-0.0625 * ((sin(y) ^ 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * (1.0 + (0.5 * ((cos(y) * (3.0 - sqrt(5.0))) + t_1))));
	else
		tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * t_3) * t_0))) / (3.0 + (1.5 * (3.0 + (t_2 - sqrt(5.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[Cos[x], $MachinePrecision] * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[x, -5.5e-5], N[(N[(2.0 + N[(-0.0625 * N[(t$95$3 * N[(N[Sqrt[2.0], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(N[(3.0 + t$95$2), $MachinePrecision] - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-7], N[(N[(2.0 + N[(-0.0625 * N[(N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(0.5 * N[(N[(N[Cos[y], $MachinePrecision] * N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(-0.0625 * N[(N[(N[Sqrt[2.0], $MachinePrecision] * t$95$3), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(3.0 + N[(t$95$2 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 21: 78.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos x + -1\\ t_1 := \cos x \cdot \left(\sqrt{5} + -1\right)\\ t_2 := {\sin x}^{2}\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(t_2 \cdot \left(\sqrt{2} \cdot t_0\right)\right)}{3 + 1.5 \cdot \left(\left(3 + t_1\right) - \sqrt{5}\right)}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-7}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left({\sin y}^{2} \cdot \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 \cdot \left(1 + 0.5 \cdot \left(-1 + \left(\sqrt{5} + \cos y \cdot \left(3 - \sqrt{5}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(\sqrt{2} \cdot t_2\right) \cdot t_0\right)}{3 + 1.5 \cdot \left(3 + \left(t_1 - \sqrt{5}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (cos x) -1.0))
        (t_1 (* (cos x) (+ (sqrt 5.0) -1.0)))
        (t_2 (pow (sin x) 2.0)))
   (if (<= x -4.6e-5)
     (/
      (+ 2.0 (* -0.0625 (* t_2 (* (sqrt 2.0) t_0))))
      (+ 3.0 (* 1.5 (- (+ 3.0 t_1) (sqrt 5.0)))))
     (if (<= x 8e-7)
       (/
        (+
         2.0
         (* -0.0625 (* (pow (sin y) 2.0) (* (sqrt 2.0) (- 1.0 (cos y))))))
        (*
         3.0
         (+
          1.0
          (* 0.5 (+ -1.0 (+ (sqrt 5.0) (* (cos y) (- 3.0 (sqrt 5.0)))))))))
       (/
        (+ 2.0 (* -0.0625 (* (* (sqrt 2.0) t_2) t_0)))
        (+ 3.0 (* 1.5 (+ 3.0 (- t_1 (sqrt 5.0))))))))))

C

double code(double x, double y) {
	double t_0 = cos(x) + -1.0;
	double t_1 = cos(x) * (sqrt(5.0) + -1.0);
	double t_2 = pow(sin(x), 2.0);
	double tmp;
	if (x <= -4.6e-5) {
		tmp = (2.0 + (-0.0625 * (t_2 * (sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_1) - sqrt(5.0))));
	} else if (x <= 8e-7) {
		tmp = (2.0 + (-0.0625 * (pow(sin(y), 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * (1.0 + (0.5 * (-1.0 + (sqrt(5.0) + (cos(y) * (3.0 - sqrt(5.0))))))));
	} else {
		tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * t_2) * t_0))) / (3.0 + (1.5 * (3.0 + (t_1 - sqrt(5.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = cos(x) + (-1.0d0)
    t_1 = cos(x) * (sqrt(5.0d0) + (-1.0d0))
    t_2 = sin(x) ** 2.0d0
    if (x <= (-4.6d-5)) then
        tmp = (2.0d0 + ((-0.0625d0) * (t_2 * (sqrt(2.0d0) * t_0)))) / (3.0d0 + (1.5d0 * ((3.0d0 + t_1) - sqrt(5.0d0))))
    else if (x <= 8d-7) then
        tmp = (2.0d0 + ((-0.0625d0) * ((sin(y) ** 2.0d0) * (sqrt(2.0d0) * (1.0d0 - cos(y)))))) / (3.0d0 * (1.0d0 + (0.5d0 * ((-1.0d0) + (sqrt(5.0d0) + (cos(y) * (3.0d0 - sqrt(5.0d0))))))))
    else
        tmp = (2.0d0 + ((-0.0625d0) * ((sqrt(2.0d0) * t_2) * t_0))) / (3.0d0 + (1.5d0 * (3.0d0 + (t_1 - sqrt(5.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.cos(x) + -1.0;
	double t_1 = Math.cos(x) * (Math.sqrt(5.0) + -1.0);
	double t_2 = Math.pow(Math.sin(x), 2.0);
	double tmp;
	if (x <= -4.6e-5) {
		tmp = (2.0 + (-0.0625 * (t_2 * (Math.sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_1) - Math.sqrt(5.0))));
	} else if (x <= 8e-7) {
		tmp = (2.0 + (-0.0625 * (Math.pow(Math.sin(y), 2.0) * (Math.sqrt(2.0) * (1.0 - Math.cos(y)))))) / (3.0 * (1.0 + (0.5 * (-1.0 + (Math.sqrt(5.0) + (Math.cos(y) * (3.0 - Math.sqrt(5.0))))))));
	} else {
		tmp = (2.0 + (-0.0625 * ((Math.sqrt(2.0) * t_2) * t_0))) / (3.0 + (1.5 * (3.0 + (t_1 - Math.sqrt(5.0)))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.cos(x) + -1.0
	t_1 = math.cos(x) * (math.sqrt(5.0) + -1.0)
	t_2 = math.pow(math.sin(x), 2.0)
	tmp = 0
	if x <= -4.6e-5:
		tmp = (2.0 + (-0.0625 * (t_2 * (math.sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_1) - math.sqrt(5.0))))
	elif x <= 8e-7:
		tmp = (2.0 + (-0.0625 * (math.pow(math.sin(y), 2.0) * (math.sqrt(2.0) * (1.0 - math.cos(y)))))) / (3.0 * (1.0 + (0.5 * (-1.0 + (math.sqrt(5.0) + (math.cos(y) * (3.0 - math.sqrt(5.0))))))))
	else:
		tmp = (2.0 + (-0.0625 * ((math.sqrt(2.0) * t_2) * t_0))) / (3.0 + (1.5 * (3.0 + (t_1 - math.sqrt(5.0)))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(cos(x) + -1.0)
	t_1 = Float64(cos(x) * Float64(sqrt(5.0) + -1.0))
	t_2 = sin(x) ^ 2.0
	tmp = 0.0
	if (x <= -4.6e-5)
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(t_2 * Float64(sqrt(2.0) * t_0)))) / Float64(3.0 + Float64(1.5 * Float64(Float64(3.0 + t_1) - sqrt(5.0)))));
	elseif (x <= 8e-7)
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64((sin(y) ^ 2.0) * Float64(sqrt(2.0) * Float64(1.0 - cos(y)))))) / Float64(3.0 * Float64(1.0 + Float64(0.5 * Float64(-1.0 + Float64(sqrt(5.0) + Float64(cos(y) * Float64(3.0 - sqrt(5.0)))))))));
	else
		tmp = Float64(Float64(2.0 + Float64(-0.0625 * Float64(Float64(sqrt(2.0) * t_2) * t_0))) / Float64(3.0 + Float64(1.5 * Float64(3.0 + Float64(t_1 - sqrt(5.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = cos(x) + -1.0;
	t_1 = cos(x) * (sqrt(5.0) + -1.0);
	t_2 = sin(x) ^ 2.0;
	tmp = 0.0;
	if (x <= -4.6e-5)
		tmp = (2.0 + (-0.0625 * (t_2 * (sqrt(2.0) * t_0)))) / (3.0 + (1.5 * ((3.0 + t_1) - sqrt(5.0))));
	elseif (x <= 8e-7)
		tmp = (2.0 + (-0.0625 * ((sin(y) ^ 2.0) * (sqrt(2.0) * (1.0 - cos(y)))))) / (3.0 * (1.0 + (0.5 * (-1.0 + (sqrt(5.0) + (cos(y) * (3.0 - sqrt(5.0))))))));
	else
		tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * t_2) * t_0))) / (3.0 + (1.5 * (3.0 + (t_1 - sqrt(5.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[x], $MachinePrecision] * N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[x, -4.6e-5], N[(N[(2.0 + N[(-0.0625 * N[(t$95$2 * N[(N[Sqrt[2.0], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(N[(3.0 + t$95$1), $MachinePrecision] - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-7], N[(N[(2.0 + N[(-0.0625 * N[(N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(0.5 * N[(-1.0 + N[(N[Sqrt[5.0], $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(-0.0625 * N[(N[(N[Sqrt[2.0], $MachinePrecision] * t$95$2), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(3.0 + N[(t$95$1 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 22: 60.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \frac{2 + -0.0625 \cdot \left(\left(\sqrt{2} \cdot {\sin x}^{2}\right) \cdot \left(\cos x + -1\right)\right)}{3 + 1.5 \cdot \left(3 + \left(\cos x \cdot \left(\sqrt{5} + -1\right) - \sqrt{5}\right)\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (+ 2.0 (* -0.0625 (* (* (sqrt 2.0) (pow (sin x) 2.0)) (+ (cos x) -1.0))))
  (+ 3.0 (* 1.5 (+ 3.0 (- (* (cos x) (+ (sqrt 5.0) -1.0)) (sqrt 5.0)))))))

C

double code(double x, double y) {
	return (2.0 + (-0.0625 * ((sqrt(2.0) * pow(sin(x), 2.0)) * (cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((cos(x) * (sqrt(5.0) + -1.0)) - sqrt(5.0)))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 + ((-0.0625d0) * ((sqrt(2.0d0) * (sin(x) ** 2.0d0)) * (cos(x) + (-1.0d0))))) / (3.0d0 + (1.5d0 * (3.0d0 + ((cos(x) * (sqrt(5.0d0) + (-1.0d0))) - sqrt(5.0d0)))))
end function

Java

public static double code(double x, double y) {
	return (2.0 + (-0.0625 * ((Math.sqrt(2.0) * Math.pow(Math.sin(x), 2.0)) * (Math.cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((Math.cos(x) * (Math.sqrt(5.0) + -1.0)) - Math.sqrt(5.0)))));
}

Python

def code(x, y):
	return (2.0 + (-0.0625 * ((math.sqrt(2.0) * math.pow(math.sin(x), 2.0)) * (math.cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((math.cos(x) * (math.sqrt(5.0) + -1.0)) - math.sqrt(5.0)))))

Julia

function code(x, y)
	return Float64(Float64(2.0 + Float64(-0.0625 * Float64(Float64(sqrt(2.0) * (sin(x) ^ 2.0)) * Float64(cos(x) + -1.0)))) / Float64(3.0 + Float64(1.5 * Float64(3.0 + Float64(Float64(cos(x) * Float64(sqrt(5.0) + -1.0)) - sqrt(5.0))))))
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 + (-0.0625 * ((sqrt(2.0) * (sin(x) ^ 2.0)) * (cos(x) + -1.0)))) / (3.0 + (1.5 * (3.0 + ((cos(x) * (sqrt(5.0) + -1.0)) - sqrt(5.0)))));
end

Wolfram

code[x_, y_] := N[(N[(2.0 + N[(-0.0625 * N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(1.5 * N[(3.0 + N[(N[(N[Cos[x], $MachinePrecision] * N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 23: 42.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \frac{2}{3 + 1.5 \cdot \mathsf{expm1}\left(\log \left(\mathsf{fma}\left(\cos y, 3 - \sqrt{5}, \sqrt{5}\right)\right)\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  2.0
  (+ 3.0 (* 1.5 (expm1 (log (fma (cos y) (- 3.0 (sqrt 5.0)) (sqrt 5.0))))))))

C

double code(double x, double y) {
	return 2.0 / (3.0 + (1.5 * expm1(log(fma(cos(y), (3.0 - sqrt(5.0)), sqrt(5.0))))));
}

Julia

function code(x, y)
	return Float64(2.0 / Float64(3.0 + Float64(1.5 * expm1(log(fma(cos(y), Float64(3.0 - sqrt(5.0)), sqrt(5.0)))))))
end

Wolfram

code[x_, y_] := N[(2.0 / N[(3.0 + N[(1.5 * N[(Exp[N[Log[N[(N[Cos[y], $MachinePrecision] * N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 24: 42.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \frac{2}{3 + 1.5 \cdot \left(-1 + \left(\sqrt{5} + \cos y \cdot \frac{4}{3 + \sqrt{5}}\right)\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  2.0
  (+
   3.0
   (* 1.5 (+ -1.0 (+ (sqrt 5.0) (* (cos y) (/ 4.0 (+ 3.0 (sqrt 5.0))))))))))

C

double code(double x, double y) {
	return 2.0 / (3.0 + (1.5 * (-1.0 + (sqrt(5.0) + (cos(y) * (4.0 / (3.0 + sqrt(5.0))))))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 2.0d0 / (3.0d0 + (1.5d0 * ((-1.0d0) + (sqrt(5.0d0) + (cos(y) * (4.0d0 / (3.0d0 + sqrt(5.0d0))))))))
end function

Java

public static double code(double x, double y) {
	return 2.0 / (3.0 + (1.5 * (-1.0 + (Math.sqrt(5.0) + (Math.cos(y) * (4.0 / (3.0 + Math.sqrt(5.0))))))));
}

Python

def code(x, y):
	return 2.0 / (3.0 + (1.5 * (-1.0 + (math.sqrt(5.0) + (math.cos(y) * (4.0 / (3.0 + math.sqrt(5.0))))))))

Julia

function code(x, y)
	return Float64(2.0 / Float64(3.0 + Float64(1.5 * Float64(-1.0 + Float64(sqrt(5.0) + Float64(cos(y) * Float64(4.0 / Float64(3.0 + sqrt(5.0)))))))))
end

MATLAB

function tmp = code(x, y)
	tmp = 2.0 / (3.0 + (1.5 * (-1.0 + (sqrt(5.0) + (cos(y) * (4.0 / (3.0 + sqrt(5.0))))))));
end

Wolfram

code[x_, y_] := N[(2.0 / N[(3.0 + N[(1.5 * N[(-1.0 + N[(N[Sqrt[5.0], $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 25: 42.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \frac{2}{3 + 1.5 \cdot \left(-1 + \left(\sqrt{5} + \cos y \cdot \left(3 - \sqrt{5}\right)\right)\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  2.0
  (+ 3.0 (* 1.5 (+ -1.0 (+ (sqrt 5.0) (* (cos y) (- 3.0 (sqrt 5.0)))))))))

C

double code(double x, double y) {
	return 2.0 / (3.0 + (1.5 * (-1.0 + (sqrt(5.0) + (cos(y) * (3.0 - sqrt(5.0)))))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 2.0d0 / (3.0d0 + (1.5d0 * ((-1.0d0) + (sqrt(5.0d0) + (cos(y) * (3.0d0 - sqrt(5.0d0)))))))
end function

Java

public static double code(double x, double y) {
	return 2.0 / (3.0 + (1.5 * (-1.0 + (Math.sqrt(5.0) + (Math.cos(y) * (3.0 - Math.sqrt(5.0)))))));
}

Python

def code(x, y):
	return 2.0 / (3.0 + (1.5 * (-1.0 + (math.sqrt(5.0) + (math.cos(y) * (3.0 - math.sqrt(5.0)))))))

Julia

function code(x, y)
	return Float64(2.0 / Float64(3.0 + Float64(1.5 * Float64(-1.0 + Float64(sqrt(5.0) + Float64(cos(y) * Float64(3.0 - sqrt(5.0))))))))
end

MATLAB

function tmp = code(x, y)
	tmp = 2.0 / (3.0 + (1.5 * (-1.0 + (sqrt(5.0) + (cos(y) * (3.0 - sqrt(5.0)))))));
end

Wolfram

code[x_, y_] := N[(2.0 / N[(3.0 + N[(1.5 * N[(-1.0 + N[(N[Sqrt[5.0], $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 26: 40.2% accurate, 1139.0× speedup

Math

\[\begin{array}{l} \\ 0.3333333333333333 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.3333333333333333)

C

double code(double x, double y) {
	return 0.3333333333333333;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.3333333333333333d0
end function

Java

public static double code(double x, double y) {
	return 0.3333333333333333;
}

Python

def code(x, y):
	return 0.3333333333333333

Julia

function code(x, y)
	return 0.3333333333333333
end

MATLAB

function tmp = code(x, y)
	tmp = 0.3333333333333333;
end

Wolfram

code[x_, y_] := 0.3333333333333333

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2024003 
(FPCore (x y)
  :name "Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5"
  :precision binary64
  (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y))))))