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

Percentage Accurate: 99.3% → 99.3%

Time: 41.9s

Alternatives: 18

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: 99.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \frac{2 + \left(\sqrt{2} \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \cos y \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(1.5 - \sqrt{1.25}\right)\right)\right)\right)} \end{array} \]

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
    (+
     (* (cos x) (- (/ (sqrt 5.0) 2.0) 0.5))
     (* (cos y) (expm1 (log1p (- 1.5 (sqrt 1.25))))))))))

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 + ((cos(x) * ((sqrt(5.0) / 2.0) - 0.5)) + (cos(y) * expm1(log1p((1.5 - sqrt(1.25))))))));
}

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.cos(x) * ((Math.sqrt(5.0) / 2.0) - 0.5)) + (Math.cos(y) * Math.expm1(Math.log1p((1.5 - Math.sqrt(1.25))))))));
}

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.cos(x) * ((math.sqrt(5.0) / 2.0) - 0.5)) + (math.cos(y) * math.expm1(math.log1p((1.5 - math.sqrt(1.25))))))))

Julia

function code(x, y)
	return Float64(Float64(2.0 + Float64(Float64(sqrt(2.0) * Float64(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(1.0 + Float64(Float64(cos(x) * Float64(Float64(sqrt(5.0) / 2.0) - 0.5)) + Float64(cos(y) * expm1(log1p(Float64(1.5 - sqrt(1.25)))))))))
end

Wolfram

code[x_, y_] := N[(N[(2.0 + N[(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] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] / 2.0), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(Exp[N[Log[1 + N[(1.5 - N[Sqrt[1.25], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 99.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (+
   2.0
   (*
    (- (cos x) (cos y))
    (*
     (- (sin y) (/ (sin x) 16.0))
     (* (sqrt 2.0) (- (sin x) (/ (sin y) 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)) * ((sin(y) - (sin(x) / 16.0)) * (sqrt(2.0) * (sin(x) - (sin(y) / 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)) * ((sin(y) - (sin(x) / 16.0d0)) * (sqrt(2.0d0) * (sin(x) - (sin(y) / 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.sin(y) - (Math.sin(x) / 16.0)) * (Math.sqrt(2.0) * (Math.sin(x) - (Math.sin(y) / 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.sin(y) - (math.sin(x) / 16.0)) * (math.sqrt(2.0) * (math.sin(x) - (math.sin(y) / 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(sin(y) - Float64(sin(x) / 16.0)) * Float64(sqrt(2.0) * Float64(sin(x) - Float64(sin(y) / 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)) * ((sin(y) - (sin(x) / 16.0)) * (sqrt(2.0) * (sin(x) - (sin(y) / 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[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $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 3: 99.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (+
   2.0
   (*
    (- (cos x) (cos y))
    (*
     (sqrt 2.0)
     (* (- (sin y) (* (sin x) 0.0625)) (+ (sin x) (* (sin y) -0.0625))))))
  (*
   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(y) - (sin(x) * 0.0625)) * (sin(x) + (sin(y) * -0.0625)))))) / (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(y) - (sin(x) * 0.0625d0)) * (sin(x) + (sin(y) * (-0.0625d0))))))) / (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(y) - (Math.sin(x) * 0.0625)) * (Math.sin(x) + (Math.sin(y) * -0.0625)))))) / (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(y) - (math.sin(x) * 0.0625)) * (math.sin(x) + (math.sin(y) * -0.0625)))))) / (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(sqrt(2.0) * Float64(Float64(sin(y) - Float64(sin(x) * 0.0625)) * Float64(sin(x) + Float64(sin(y) * -0.0625)))))) / 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(y) - (sin(x) * 0.0625)) * (sin(x) + (sin(y) * -0.0625)))))) / (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[Sqrt[2.0], $MachinePrecision] * N[(N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * -0.0625), $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 4: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2 + \left(\sqrt{2} \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\sqrt{5} \cdot 0.5 - 0.5\right) + \cos y \cdot \left(1.5 - \sqrt{1.25}\right)\right)\right)} \end{array} \]

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
    (+
     (* (cos x) (- (* (sqrt 5.0) 0.5) 0.5))
     (* (cos y) (- 1.5 (sqrt 1.25))))))))

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 + ((cos(x) * ((sqrt(5.0) * 0.5) - 0.5)) + (cos(y) * (1.5 - sqrt(1.25))))));
}

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 + ((cos(x) * ((sqrt(5.0d0) * 0.5d0) - 0.5d0)) + (cos(y) * (1.5d0 - sqrt(1.25d0))))))
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.cos(x) * ((Math.sqrt(5.0) * 0.5) - 0.5)) + (Math.cos(y) * (1.5 - Math.sqrt(1.25))))));
}

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.cos(x) * ((math.sqrt(5.0) * 0.5) - 0.5)) + (math.cos(y) * (1.5 - math.sqrt(1.25))))))

Julia

function code(x, y)
	return Float64(Float64(2.0 + Float64(Float64(sqrt(2.0) * Float64(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(1.0 + Float64(Float64(cos(x) * Float64(Float64(sqrt(5.0) * 0.5) - 0.5)) + Float64(cos(y) * Float64(1.5 - sqrt(1.25)))))))
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 + ((cos(x) * ((sqrt(5.0) * 0.5) - 0.5)) + (cos(y) * (1.5 - sqrt(1.25))))));
end

Wolfram

code[x_, y_] := N[(N[(2.0 + N[(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] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] * 0.5), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - N[Sqrt[1.25], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 5: 81.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ t_2 := \cos x - \cos y\\ \mathbf{if}\;x \leq -0.04 \lor \neg \left(x \leq 0.042\right):\\ \;\;\;\;\frac{2 + t_2 \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \left(x + \sin y \cdot -0.0625\right)\right)\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (sin y) (/ (sin x) 16.0)))
        (t_1 (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0))))
        (t_2 (- (cos x) (cos y))))
   (if (or (<= x -0.04) (not (<= x 0.042)))
     (/
      (+ 2.0 (* t_2 (* t_0 (* (sqrt 2.0) (sin x)))))
      (* 3.0 (+ t_1 (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0)))))
     (/
      (+ 2.0 (* t_2 (* t_0 (* (sqrt 2.0) (+ x (* (sin y) -0.0625))))))
      (* 3.0 (+ t_1 (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0))))))))

C

double code(double x, double y) {
	double t_0 = sin(y) - (sin(x) / 16.0);
	double t_1 = 1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0));
	double t_2 = cos(x) - cos(y);
	double tmp;
	if ((x <= -0.04) || !(x <= 0.042)) {
		tmp = (2.0 + (t_2 * (t_0 * (sqrt(2.0) * sin(x))))) / (3.0 * (t_1 + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	} else {
		tmp = (2.0 + (t_2 * (t_0 * (sqrt(2.0) * (x + (sin(y) * -0.0625)))))) / (3.0 * (t_1 + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = sin(y) - (sin(x) / 16.0d0)
    t_1 = 1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))
    t_2 = cos(x) - cos(y)
    if ((x <= (-0.04d0)) .or. (.not. (x <= 0.042d0))) then
        tmp = (2.0d0 + (t_2 * (t_0 * (sqrt(2.0d0) * sin(x))))) / (3.0d0 * (t_1 + (cos(y) * ((4.0d0 / (3.0d0 + sqrt(5.0d0))) / 2.0d0))))
    else
        tmp = (2.0d0 + (t_2 * (t_0 * (sqrt(2.0d0) * (x + (sin(y) * (-0.0625d0))))))) / (3.0d0 * (t_1 + (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.sin(y) - (Math.sin(x) / 16.0);
	double t_1 = 1.0 + (Math.cos(x) * ((Math.sqrt(5.0) + -1.0) / 2.0));
	double t_2 = Math.cos(x) - Math.cos(y);
	double tmp;
	if ((x <= -0.04) || !(x <= 0.042)) {
		tmp = (2.0 + (t_2 * (t_0 * (Math.sqrt(2.0) * Math.sin(x))))) / (3.0 * (t_1 + (Math.cos(y) * ((4.0 / (3.0 + Math.sqrt(5.0))) / 2.0))));
	} else {
		tmp = (2.0 + (t_2 * (t_0 * (Math.sqrt(2.0) * (x + (Math.sin(y) * -0.0625)))))) / (3.0 * (t_1 + (Math.cos(y) * ((3.0 - Math.sqrt(5.0)) / 2.0))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sin(y) - (math.sin(x) / 16.0)
	t_1 = 1.0 + (math.cos(x) * ((math.sqrt(5.0) + -1.0) / 2.0))
	t_2 = math.cos(x) - math.cos(y)
	tmp = 0
	if (x <= -0.04) or not (x <= 0.042):
		tmp = (2.0 + (t_2 * (t_0 * (math.sqrt(2.0) * math.sin(x))))) / (3.0 * (t_1 + (math.cos(y) * ((4.0 / (3.0 + math.sqrt(5.0))) / 2.0))))
	else:
		tmp = (2.0 + (t_2 * (t_0 * (math.sqrt(2.0) * (x + (math.sin(y) * -0.0625)))))) / (3.0 * (t_1 + (math.cos(y) * ((3.0 - math.sqrt(5.0)) / 2.0))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sin(y) - Float64(sin(x) / 16.0))
	t_1 = Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0)))
	t_2 = Float64(cos(x) - cos(y))
	tmp = 0.0
	if ((x <= -0.04) || !(x <= 0.042))
		tmp = Float64(Float64(2.0 + Float64(t_2 * Float64(t_0 * Float64(sqrt(2.0) * sin(x))))) / Float64(3.0 * Float64(t_1 + Float64(cos(y) * Float64(Float64(4.0 / Float64(3.0 + sqrt(5.0))) / 2.0)))));
	else
		tmp = Float64(Float64(2.0 + Float64(t_2 * Float64(t_0 * Float64(sqrt(2.0) * Float64(x + Float64(sin(y) * -0.0625)))))) / Float64(3.0 * Float64(t_1 + 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 = sin(y) - (sin(x) / 16.0);
	t_1 = 1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0));
	t_2 = cos(x) - cos(y);
	tmp = 0.0;
	if ((x <= -0.04) || ~((x <= 0.042)))
		tmp = (2.0 + (t_2 * (t_0 * (sqrt(2.0) * sin(x))))) / (3.0 * (t_1 + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	else
		tmp = (2.0 + (t_2 * (t_0 * (sqrt(2.0) * (x + (sin(y) * -0.0625)))))) / (3.0 * (t_1 + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
	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[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -0.04], N[Not[LessEqual[x, 0.042]], $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] / N[(3.0 * N[(t$95$1 + 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[(t$95$2 * N[(t$95$0 * N[(N[Sqrt[2.0], $MachinePrecision] * N[(x + N[(N[Sin[y], $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(t$95$1 + 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: 81.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ \mathbf{if}\;x \leq -0.0064 \lor \neg \left(x \leq 0.0265\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(t_0 \cdot \left(\sqrt{2} \cdot \left(x + \sin y \cdot -0.0625\right)\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (sin y) (/ (sin x) 16.0)))
        (t_1 (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))))
   (if (or (<= x -0.0064) (not (<= x 0.0265)))
     (/
      (+ 2.0 (* (- (cos x) (cos y)) (* t_0 (* (sqrt 2.0) (sin x)))))
      (* 3.0 (+ t_1 (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0)))))
     (/
      (+
       2.0
       (* (* t_0 (* (sqrt 2.0) (+ x (* (sin y) -0.0625)))) (- 1.0 (cos y))))
      (* 3.0 (+ t_1 (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0))))))))

C

double code(double x, double y) {
	double t_0 = sin(y) - (sin(x) / 16.0);
	double t_1 = 1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0));
	double tmp;
	if ((x <= -0.0064) || !(x <= 0.0265)) {
		tmp = (2.0 + ((cos(x) - cos(y)) * (t_0 * (sqrt(2.0) * sin(x))))) / (3.0 * (t_1 + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	} else {
		tmp = (2.0 + ((t_0 * (sqrt(2.0) * (x + (sin(y) * -0.0625)))) * (1.0 - cos(y)))) / (3.0 * (t_1 + (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) :: t_1
    real(8) :: tmp
    t_0 = sin(y) - (sin(x) / 16.0d0)
    t_1 = 1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))
    if ((x <= (-0.0064d0)) .or. (.not. (x <= 0.0265d0))) then
        tmp = (2.0d0 + ((cos(x) - cos(y)) * (t_0 * (sqrt(2.0d0) * sin(x))))) / (3.0d0 * (t_1 + (cos(y) * ((4.0d0 / (3.0d0 + sqrt(5.0d0))) / 2.0d0))))
    else
        tmp = (2.0d0 + ((t_0 * (sqrt(2.0d0) * (x + (sin(y) * (-0.0625d0))))) * (1.0d0 - cos(y)))) / (3.0d0 * (t_1 + (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.sin(y) - (Math.sin(x) / 16.0);
	double t_1 = 1.0 + (Math.cos(x) * ((Math.sqrt(5.0) + -1.0) / 2.0));
	double tmp;
	if ((x <= -0.0064) || !(x <= 0.0265)) {
		tmp = (2.0 + ((Math.cos(x) - Math.cos(y)) * (t_0 * (Math.sqrt(2.0) * Math.sin(x))))) / (3.0 * (t_1 + (Math.cos(y) * ((4.0 / (3.0 + Math.sqrt(5.0))) / 2.0))));
	} else {
		tmp = (2.0 + ((t_0 * (Math.sqrt(2.0) * (x + (Math.sin(y) * -0.0625)))) * (1.0 - Math.cos(y)))) / (3.0 * (t_1 + (Math.cos(y) * ((3.0 - Math.sqrt(5.0)) / 2.0))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sin(y) - (math.sin(x) / 16.0)
	t_1 = 1.0 + (math.cos(x) * ((math.sqrt(5.0) + -1.0) / 2.0))
	tmp = 0
	if (x <= -0.0064) or not (x <= 0.0265):
		tmp = (2.0 + ((math.cos(x) - math.cos(y)) * (t_0 * (math.sqrt(2.0) * math.sin(x))))) / (3.0 * (t_1 + (math.cos(y) * ((4.0 / (3.0 + math.sqrt(5.0))) / 2.0))))
	else:
		tmp = (2.0 + ((t_0 * (math.sqrt(2.0) * (x + (math.sin(y) * -0.0625)))) * (1.0 - math.cos(y)))) / (3.0 * (t_1 + (math.cos(y) * ((3.0 - math.sqrt(5.0)) / 2.0))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sin(y) - Float64(sin(x) / 16.0))
	t_1 = Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0)))
	tmp = 0.0
	if ((x <= -0.0064) || !(x <= 0.0265))
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(t_0 * Float64(sqrt(2.0) * sin(x))))) / Float64(3.0 * Float64(t_1 + Float64(cos(y) * Float64(Float64(4.0 / Float64(3.0 + sqrt(5.0))) / 2.0)))));
	else
		tmp = Float64(Float64(2.0 + Float64(Float64(t_0 * Float64(sqrt(2.0) * Float64(x + Float64(sin(y) * -0.0625)))) * Float64(1.0 - cos(y)))) / Float64(3.0 * Float64(t_1 + 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 = sin(y) - (sin(x) / 16.0);
	t_1 = 1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0));
	tmp = 0.0;
	if ((x <= -0.0064) || ~((x <= 0.0265)))
		tmp = (2.0 + ((cos(x) - cos(y)) * (t_0 * (sqrt(2.0) * sin(x))))) / (3.0 * (t_1 + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	else
		tmp = (2.0 + ((t_0 * (sqrt(2.0) * (x + (sin(y) * -0.0625)))) * (1.0 - cos(y)))) / (3.0 * (t_1 + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
	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[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -0.0064], N[Not[LessEqual[x, 0.0265]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(N[Sqrt[2.0], $MachinePrecision] * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(t$95$1 + 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[(N[(t$95$0 * N[(N[Sqrt[2.0], $MachinePrecision] * N[(x + N[(N[Sin[y], $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(t$95$1 + 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 7: 81.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := 3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)\\ \mathbf{if}\;x \leq -0.00125 \lor \neg \left(x \leq 0.0265\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(t_0 \cdot \left(\sqrt{2} \cdot \left(x + \sin y \cdot -0.0625\right)\right)\right) \cdot \left(1 - \cos y\right)}{t_1}\\ \end{array} \end{array} \]

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))))))
   (if (or (<= x -0.00125) (not (<= x 0.0265)))
     (/ (+ 2.0 (* (- (cos x) (cos y)) (* t_0 (* (sqrt 2.0) (sin x))))) t_1)
     (/
      (+
       2.0
       (* (* t_0 (* (sqrt 2.0) (+ x (* (sin y) -0.0625)))) (- 1.0 (cos 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 tmp;
	if ((x <= -0.00125) || !(x <= 0.0265)) {
		tmp = (2.0 + ((cos(x) - cos(y)) * (t_0 * (sqrt(2.0) * sin(x))))) / t_1;
	} else {
		tmp = (2.0 + ((t_0 * (sqrt(2.0) * (x + (sin(y) * -0.0625)))) * (1.0 - cos(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) :: 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)))
    if ((x <= (-0.00125d0)) .or. (.not. (x <= 0.0265d0))) then
        tmp = (2.0d0 + ((cos(x) - cos(y)) * (t_0 * (sqrt(2.0d0) * sin(x))))) / t_1
    else
        tmp = (2.0d0 + ((t_0 * (sqrt(2.0d0) * (x + (sin(y) * (-0.0625d0))))) * (1.0d0 - cos(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 tmp;
	if ((x <= -0.00125) || !(x <= 0.0265)) {
		tmp = (2.0 + ((Math.cos(x) - Math.cos(y)) * (t_0 * (Math.sqrt(2.0) * Math.sin(x))))) / t_1;
	} else {
		tmp = (2.0 + ((t_0 * (Math.sqrt(2.0) * (x + (Math.sin(y) * -0.0625)))) * (1.0 - Math.cos(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)))
	tmp = 0
	if (x <= -0.00125) or not (x <= 0.0265):
		tmp = (2.0 + ((math.cos(x) - math.cos(y)) * (t_0 * (math.sqrt(2.0) * math.sin(x))))) / t_1
	else:
		tmp = (2.0 + ((t_0 * (math.sqrt(2.0) * (x + (math.sin(y) * -0.0625)))) * (1.0 - math.cos(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))))
	tmp = 0.0
	if ((x <= -0.00125) || !(x <= 0.0265))
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(t_0 * Float64(sqrt(2.0) * sin(x))))) / t_1);
	else
		tmp = Float64(Float64(2.0 + Float64(Float64(t_0 * Float64(sqrt(2.0) * Float64(x + Float64(sin(y) * -0.0625)))) * Float64(1.0 - cos(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)));
	tmp = 0.0;
	if ((x <= -0.00125) || ~((x <= 0.0265)))
		tmp = (2.0 + ((cos(x) - cos(y)) * (t_0 * (sqrt(2.0) * sin(x))))) / t_1;
	else
		tmp = (2.0 + ((t_0 * (sqrt(2.0) * (x + (sin(y) * -0.0625)))) * (1.0 - cos(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]}, If[Or[LessEqual[x, -0.00125], N[Not[LessEqual[x, 0.0265]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * 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[(N[(t$95$0 * N[(N[Sqrt[2.0], $MachinePrecision] * N[(x + N[(N[Sin[y], $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

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

Alternative 8: 80.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ t_1 := 3 \cdot \left(t_0 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)\\ t_2 := \sin y - \frac{\sin x}{16}\\ \mathbf{if}\;x \leq -0.0122:\\ \;\;\;\;\frac{2 + \left(t_2 \cdot \left(\sqrt{2} \cdot \sin x\right)\right) \cdot \left(\cos x + -1\right)}{t_1}\\ \mathbf{elif}\;x \leq 0.0265:\\ \;\;\;\;\frac{2 + \left(t_2 \cdot \left(\sqrt{2} \cdot \left(x + \sin y \cdot -0.0625\right)\right)\right) \cdot \left(1 - \cos y\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left({\sin x}^{2} \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{3 \cdot \left(t_0 + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0))))
        (t_1 (* 3.0 (+ t_0 (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))))
        (t_2 (- (sin y) (/ (sin x) 16.0))))
   (if (<= x -0.0122)
     (/ (+ 2.0 (* (* t_2 (* (sqrt 2.0) (sin x))) (+ (cos x) -1.0))) t_1)
     (if (<= x 0.0265)
       (/
        (+
         2.0
         (* (* t_2 (* (sqrt 2.0) (+ x (* (sin y) -0.0625)))) (- 1.0 (cos y))))
        t_1)
       (/
        (+
         2.0
         (* (- (cos x) (cos y)) (* (pow (sin x) 2.0) (* (sqrt 2.0) -0.0625))))
        (* 3.0 (+ t_0 (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0)))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0));
	double t_1 = 3.0 * (t_0 + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0)));
	double t_2 = sin(y) - (sin(x) / 16.0);
	double tmp;
	if (x <= -0.0122) {
		tmp = (2.0 + ((t_2 * (sqrt(2.0) * sin(x))) * (cos(x) + -1.0))) / t_1;
	} else if (x <= 0.0265) {
		tmp = (2.0 + ((t_2 * (sqrt(2.0) * (x + (sin(y) * -0.0625)))) * (1.0 - cos(y)))) / t_1;
	} else {
		tmp = (2.0 + ((cos(x) - cos(y)) * (pow(sin(x), 2.0) * (sqrt(2.0) * -0.0625)))) / (3.0 * (t_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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))
    t_1 = 3.0d0 * (t_0 + (cos(y) * ((3.0d0 - sqrt(5.0d0)) / 2.0d0)))
    t_2 = sin(y) - (sin(x) / 16.0d0)
    if (x <= (-0.0122d0)) then
        tmp = (2.0d0 + ((t_2 * (sqrt(2.0d0) * sin(x))) * (cos(x) + (-1.0d0)))) / t_1
    else if (x <= 0.0265d0) then
        tmp = (2.0d0 + ((t_2 * (sqrt(2.0d0) * (x + (sin(y) * (-0.0625d0))))) * (1.0d0 - cos(y)))) / t_1
    else
        tmp = (2.0d0 + ((cos(x) - cos(y)) * ((sin(x) ** 2.0d0) * (sqrt(2.0d0) * (-0.0625d0))))) / (3.0d0 * (t_0 + (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 = 1.0 + (Math.cos(x) * ((Math.sqrt(5.0) + -1.0) / 2.0));
	double t_1 = 3.0 * (t_0 + (Math.cos(y) * ((3.0 - Math.sqrt(5.0)) / 2.0)));
	double t_2 = Math.sin(y) - (Math.sin(x) / 16.0);
	double tmp;
	if (x <= -0.0122) {
		tmp = (2.0 + ((t_2 * (Math.sqrt(2.0) * Math.sin(x))) * (Math.cos(x) + -1.0))) / t_1;
	} else if (x <= 0.0265) {
		tmp = (2.0 + ((t_2 * (Math.sqrt(2.0) * (x + (Math.sin(y) * -0.0625)))) * (1.0 - Math.cos(y)))) / t_1;
	} else {
		tmp = (2.0 + ((Math.cos(x) - Math.cos(y)) * (Math.pow(Math.sin(x), 2.0) * (Math.sqrt(2.0) * -0.0625)))) / (3.0 * (t_0 + (Math.cos(y) * ((4.0 / (3.0 + Math.sqrt(5.0))) / 2.0))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (math.cos(x) * ((math.sqrt(5.0) + -1.0) / 2.0))
	t_1 = 3.0 * (t_0 + (math.cos(y) * ((3.0 - math.sqrt(5.0)) / 2.0)))
	t_2 = math.sin(y) - (math.sin(x) / 16.0)
	tmp = 0
	if x <= -0.0122:
		tmp = (2.0 + ((t_2 * (math.sqrt(2.0) * math.sin(x))) * (math.cos(x) + -1.0))) / t_1
	elif x <= 0.0265:
		tmp = (2.0 + ((t_2 * (math.sqrt(2.0) * (x + (math.sin(y) * -0.0625)))) * (1.0 - math.cos(y)))) / t_1
	else:
		tmp = (2.0 + ((math.cos(x) - math.cos(y)) * (math.pow(math.sin(x), 2.0) * (math.sqrt(2.0) * -0.0625)))) / (3.0 * (t_0 + (math.cos(y) * ((4.0 / (3.0 + math.sqrt(5.0))) / 2.0))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0)))
	t_1 = Float64(3.0 * Float64(t_0 + Float64(cos(y) * Float64(Float64(3.0 - sqrt(5.0)) / 2.0))))
	t_2 = Float64(sin(y) - Float64(sin(x) / 16.0))
	tmp = 0.0
	if (x <= -0.0122)
		tmp = Float64(Float64(2.0 + Float64(Float64(t_2 * Float64(sqrt(2.0) * sin(x))) * Float64(cos(x) + -1.0))) / t_1);
	elseif (x <= 0.0265)
		tmp = Float64(Float64(2.0 + Float64(Float64(t_2 * Float64(sqrt(2.0) * Float64(x + Float64(sin(y) * -0.0625)))) * Float64(1.0 - cos(y)))) / t_1);
	else
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64((sin(x) ^ 2.0) * Float64(sqrt(2.0) * -0.0625)))) / Float64(3.0 * Float64(t_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 = 1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0));
	t_1 = 3.0 * (t_0 + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0)));
	t_2 = sin(y) - (sin(x) / 16.0);
	tmp = 0.0;
	if (x <= -0.0122)
		tmp = (2.0 + ((t_2 * (sqrt(2.0) * sin(x))) * (cos(x) + -1.0))) / t_1;
	elseif (x <= 0.0265)
		tmp = (2.0 + ((t_2 * (sqrt(2.0) * (x + (sin(y) * -0.0625)))) * (1.0 - cos(y)))) / t_1;
	else
		tmp = (2.0 + ((cos(x) - cos(y)) * ((sin(x) ^ 2.0) * (sqrt(2.0) * -0.0625)))) / (3.0 * (t_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[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(t$95$0 + 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[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.0122], N[(N[(2.0 + N[(N[(t$95$2 * N[(N[Sqrt[2.0], $MachinePrecision] * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x, 0.0265], N[(N[(2.0 + N[(N[(t$95$2 * N[(N[Sqrt[2.0], $MachinePrecision] * N[(x + N[(N[Sin[y], $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(t$95$0 + 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 9: 78.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\sin x}^{2}\\ t_1 := 3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)\\ t_2 := \sqrt{5} \cdot 0.5\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\cos x + -1\right)\right) \cdot \left(-0.0625 \cdot t_0\right)}{t_1}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+22}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sin x - \frac{\sin y}{16}, \left(1 - \cos y\right) \cdot \left(\sqrt{2} \cdot \sin y\right), 2\right)}{3 \cdot \left(0.5 + \left(t_2 + \cos y \cdot \left(1.5 - t_2\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (pow (sin x) 2.0))
        (t_1
         (*
          3.0
          (+
           (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))
           (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0)))))
        (t_2 (* (sqrt 5.0) 0.5)))
   (if (<= x -4.6e-8)
     (/ (+ 2.0 (* (* (sqrt 2.0) (+ (cos x) -1.0)) (* -0.0625 t_0))) t_1)
     (if (<= x 1.15e+22)
       (/
        (fma
         (- (sin x) (/ (sin y) 16.0))
         (* (- 1.0 (cos y)) (* (sqrt 2.0) (sin y)))
         2.0)
        (* 3.0 (+ 0.5 (+ t_2 (* (cos y) (- 1.5 t_2))))))
       (/
        (+ 2.0 (* (- (cos x) (cos y)) (* t_0 (* (sqrt 2.0) -0.0625))))
        t_1)))))

C

double code(double x, double y) {
	double t_0 = pow(sin(x), 2.0);
	double t_1 = 3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0)));
	double t_2 = sqrt(5.0) * 0.5;
	double tmp;
	if (x <= -4.6e-8) {
		tmp = (2.0 + ((sqrt(2.0) * (cos(x) + -1.0)) * (-0.0625 * t_0))) / t_1;
	} else if (x <= 1.15e+22) {
		tmp = fma((sin(x) - (sin(y) / 16.0)), ((1.0 - cos(y)) * (sqrt(2.0) * sin(y))), 2.0) / (3.0 * (0.5 + (t_2 + (cos(y) * (1.5 - t_2)))));
	} else {
		tmp = (2.0 + ((cos(x) - cos(y)) * (t_0 * (sqrt(2.0) * -0.0625)))) / t_1;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = sin(x) ^ 2.0
	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(4.0 / Float64(3.0 + sqrt(5.0))) / 2.0))))
	t_2 = Float64(sqrt(5.0) * 0.5)
	tmp = 0.0
	if (x <= -4.6e-8)
		tmp = Float64(Float64(2.0 + Float64(Float64(sqrt(2.0) * Float64(cos(x) + -1.0)) * Float64(-0.0625 * t_0))) / t_1);
	elseif (x <= 1.15e+22)
		tmp = Float64(fma(Float64(sin(x) - Float64(sin(y) / 16.0)), Float64(Float64(1.0 - cos(y)) * Float64(sqrt(2.0) * sin(y))), 2.0) / Float64(3.0 * Float64(0.5 + Float64(t_2 + Float64(cos(y) * Float64(1.5 - t_2))))));
	else
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(t_0 * Float64(sqrt(2.0) * -0.0625)))) / t_1);
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[Power[N[Sin[x], $MachinePrecision], 2.0], $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[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[5.0], $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[x, -4.6e-8], N[(N[(2.0 + N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x, 1.15e+22], N[(N[(N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 * N[(0.5 + N[(t$95$2 + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(N[Sqrt[2.0], $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]

Derivation

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

Alternative 10: 78.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ t_1 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{2 + \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{2} \cdot \sin x\right)\right) \cdot \left(\cos x + -1\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+22}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sin x - \frac{\sin y}{16}, \left(1 - \cos y\right) \cdot \left(\sqrt{2} \cdot \sin y\right), 2\right)}{3 \cdot \left(0.5 + \left(t_0 + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left({\sin x}^{2} \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt 5.0) 0.5))
        (t_1 (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))))
   (if (<= x -4.6e-8)
     (/
      (+
       2.0
       (*
        (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (sin x)))
        (+ (cos x) -1.0)))
      (* 3.0 (+ t_1 (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))))
     (if (<= x 1.15e+22)
       (/
        (fma
         (- (sin x) (/ (sin y) 16.0))
         (* (- 1.0 (cos y)) (* (sqrt 2.0) (sin y)))
         2.0)
        (* 3.0 (+ 0.5 (+ t_0 (* (cos y) (- 1.5 t_0))))))
       (/
        (+
         2.0
         (* (- (cos x) (cos y)) (* (pow (sin x) 2.0) (* (sqrt 2.0) -0.0625))))
        (* 3.0 (+ t_1 (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) * 0.5;
	double t_1 = 1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0));
	double tmp;
	if (x <= -4.6e-8) {
		tmp = (2.0 + (((sin(y) - (sin(x) / 16.0)) * (sqrt(2.0) * sin(x))) * (cos(x) + -1.0))) / (3.0 * (t_1 + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
	} else if (x <= 1.15e+22) {
		tmp = fma((sin(x) - (sin(y) / 16.0)), ((1.0 - cos(y)) * (sqrt(2.0) * sin(y))), 2.0) / (3.0 * (0.5 + (t_0 + (cos(y) * (1.5 - t_0)))));
	} else {
		tmp = (2.0 + ((cos(x) - cos(y)) * (pow(sin(x), 2.0) * (sqrt(2.0) * -0.0625)))) / (3.0 * (t_1 + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) * 0.5)
	t_1 = Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0)))
	tmp = 0.0
	if (x <= -4.6e-8)
		tmp = Float64(Float64(2.0 + Float64(Float64(Float64(sin(y) - Float64(sin(x) / 16.0)) * Float64(sqrt(2.0) * sin(x))) * Float64(cos(x) + -1.0))) / Float64(3.0 * Float64(t_1 + Float64(cos(y) * Float64(Float64(3.0 - sqrt(5.0)) / 2.0)))));
	elseif (x <= 1.15e+22)
		tmp = Float64(fma(Float64(sin(x) - Float64(sin(y) / 16.0)), Float64(Float64(1.0 - cos(y)) * Float64(sqrt(2.0) * sin(y))), 2.0) / Float64(3.0 * Float64(0.5 + Float64(t_0 + Float64(cos(y) * Float64(1.5 - t_0))))));
	else
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64((sin(x) ^ 2.0) * Float64(sqrt(2.0) * -0.0625)))) / Float64(3.0 * Float64(t_1 + 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[(N[Sqrt[5.0], $MachinePrecision] * 0.5), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6e-8], 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[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(t$95$1 + N[(N[Cos[y], $MachinePrecision] * N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+22], N[(N[(N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 * N[(0.5 + N[(t$95$0 + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(t$95$1 + 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 11: 78.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-8} \lor \neg \left(x \leq 1.15 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\cos x + -1\right)\right) \cdot \left(-0.0625 \cdot {\sin x}^{2}\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sin x - \frac{\sin y}{16}, \left(1 - \cos y\right) \cdot \left(\sqrt{2} \cdot \sin y\right), 2\right)}{3 \cdot \left(0.5 + \left(t_0 + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt 5.0) 0.5)))
   (if (or (<= x -4.6e-8) (not (<= x 1.15e+22)))
     (/
      (+ 2.0 (* (* (sqrt 2.0) (+ (cos x) -1.0)) (* -0.0625 (pow (sin x) 2.0))))
      (*
       3.0
       (+
        (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))
        (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0)))))
     (/
      (fma
       (- (sin x) (/ (sin y) 16.0))
       (* (- 1.0 (cos y)) (* (sqrt 2.0) (sin y)))
       2.0)
      (* 3.0 (+ 0.5 (+ t_0 (* (cos y) (- 1.5 t_0)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) * 0.5;
	double tmp;
	if ((x <= -4.6e-8) || !(x <= 1.15e+22)) {
		tmp = (2.0 + ((sqrt(2.0) * (cos(x) + -1.0)) * (-0.0625 * pow(sin(x), 2.0)))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	} else {
		tmp = fma((sin(x) - (sin(y) / 16.0)), ((1.0 - cos(y)) * (sqrt(2.0) * sin(y))), 2.0) / (3.0 * (0.5 + (t_0 + (cos(y) * (1.5 - t_0)))));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) * 0.5)
	tmp = 0.0
	if ((x <= -4.6e-8) || !(x <= 1.15e+22))
		tmp = Float64(Float64(2.0 + Float64(Float64(sqrt(2.0) * Float64(cos(x) + -1.0)) * Float64(-0.0625 * (sin(x) ^ 2.0)))) / 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)))));
	else
		tmp = Float64(fma(Float64(sin(x) - Float64(sin(y) / 16.0)), Float64(Float64(1.0 - cos(y)) * Float64(sqrt(2.0) * sin(y))), 2.0) / Float64(3.0 * Float64(0.5 + Float64(t_0 + Float64(cos(y) * Float64(1.5 - t_0))))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[5.0], $MachinePrecision] * 0.5), $MachinePrecision]}, If[Or[LessEqual[x, -4.6e-8], N[Not[LessEqual[x, 1.15e+22]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[Power[N[Sin[x], $MachinePrecision], 2.0], $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], N[(N[(N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 * N[(0.5 + N[(t$95$0 + 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 12: 79.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ \mathbf{if}\;x \leq -0.00092 \lor \neg \left(x \leq 5.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\cos x + -1\right)\right) \cdot \left(-0.0625 \cdot {\sin x}^{2}\right)}{3 \cdot \left(t_0 + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right) \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)}{3 \cdot \left(t_0 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))))
   (if (or (<= x -0.00092) (not (<= x 5.5e+19)))
     (/
      (+ 2.0 (* (* (sqrt 2.0) (+ (cos x) -1.0)) (* -0.0625 (pow (sin x) 2.0))))
      (* 3.0 (+ t_0 (* (cos y) (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0)))))
     (/
      (+ 2.0 (* (* (sqrt 2.0) (- 1.0 (cos y))) (* -0.0625 (pow (sin y) 2.0))))
      (* 3.0 (+ t_0 (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0));
	double tmp;
	if ((x <= -0.00092) || !(x <= 5.5e+19)) {
		tmp = (2.0 + ((sqrt(2.0) * (cos(x) + -1.0)) * (-0.0625 * pow(sin(x), 2.0)))) / (3.0 * (t_0 + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	} else {
		tmp = (2.0 + ((sqrt(2.0) * (1.0 - cos(y))) * (-0.0625 * pow(sin(y), 2.0)))) / (3.0 * (t_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 = 1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))
    if ((x <= (-0.00092d0)) .or. (.not. (x <= 5.5d+19))) then
        tmp = (2.0d0 + ((sqrt(2.0d0) * (cos(x) + (-1.0d0))) * ((-0.0625d0) * (sin(x) ** 2.0d0)))) / (3.0d0 * (t_0 + (cos(y) * ((4.0d0 / (3.0d0 + sqrt(5.0d0))) / 2.0d0))))
    else
        tmp = (2.0d0 + ((sqrt(2.0d0) * (1.0d0 - cos(y))) * ((-0.0625d0) * (sin(y) ** 2.0d0)))) / (3.0d0 * (t_0 + (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 = 1.0 + (Math.cos(x) * ((Math.sqrt(5.0) + -1.0) / 2.0));
	double tmp;
	if ((x <= -0.00092) || !(x <= 5.5e+19)) {
		tmp = (2.0 + ((Math.sqrt(2.0) * (Math.cos(x) + -1.0)) * (-0.0625 * Math.pow(Math.sin(x), 2.0)))) / (3.0 * (t_0 + (Math.cos(y) * ((4.0 / (3.0 + Math.sqrt(5.0))) / 2.0))));
	} else {
		tmp = (2.0 + ((Math.sqrt(2.0) * (1.0 - Math.cos(y))) * (-0.0625 * Math.pow(Math.sin(y), 2.0)))) / (3.0 * (t_0 + (Math.cos(y) * ((3.0 - Math.sqrt(5.0)) / 2.0))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (math.cos(x) * ((math.sqrt(5.0) + -1.0) / 2.0))
	tmp = 0
	if (x <= -0.00092) or not (x <= 5.5e+19):
		tmp = (2.0 + ((math.sqrt(2.0) * (math.cos(x) + -1.0)) * (-0.0625 * math.pow(math.sin(x), 2.0)))) / (3.0 * (t_0 + (math.cos(y) * ((4.0 / (3.0 + math.sqrt(5.0))) / 2.0))))
	else:
		tmp = (2.0 + ((math.sqrt(2.0) * (1.0 - math.cos(y))) * (-0.0625 * math.pow(math.sin(y), 2.0)))) / (3.0 * (t_0 + (math.cos(y) * ((3.0 - math.sqrt(5.0)) / 2.0))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(cos(x) * Float64(Float64(sqrt(5.0) + -1.0) / 2.0)))
	tmp = 0.0
	if ((x <= -0.00092) || !(x <= 5.5e+19))
		tmp = Float64(Float64(2.0 + Float64(Float64(sqrt(2.0) * Float64(cos(x) + -1.0)) * Float64(-0.0625 * (sin(x) ^ 2.0)))) / Float64(3.0 * Float64(t_0 + Float64(cos(y) * Float64(Float64(4.0 / Float64(3.0 + sqrt(5.0))) / 2.0)))));
	else
		tmp = Float64(Float64(2.0 + Float64(Float64(sqrt(2.0) * Float64(1.0 - cos(y))) * Float64(-0.0625 * (sin(y) ^ 2.0)))) / Float64(3.0 * Float64(t_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 = 1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0));
	tmp = 0.0;
	if ((x <= -0.00092) || ~((x <= 5.5e+19)))
		tmp = (2.0 + ((sqrt(2.0) * (cos(x) + -1.0)) * (-0.0625 * (sin(x) ^ 2.0)))) / (3.0 * (t_0 + (cos(y) * ((4.0 / (3.0 + sqrt(5.0))) / 2.0))));
	else
		tmp = (2.0 + ((sqrt(2.0) * (1.0 - cos(y))) * (-0.0625 * (sin(y) ^ 2.0)))) / (3.0 * (t_0 + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -0.00092], N[Not[LessEqual[x, 5.5e+19]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(t$95$0 + 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[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(t$95$0 + 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 13: 79.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)\\ \mathbf{if}\;x \leq -0.00075 \lor \neg \left(x \leq 5.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\cos x + -1\right)\right) \cdot \left(-0.0625 \cdot {\sin x}^{2}\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right) \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)}{t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_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))))))
   (if (or (<= x -0.00075) (not (<= x 5.5e+19)))
     (/
      (+ 2.0 (* (* (sqrt 2.0) (+ (cos x) -1.0)) (* -0.0625 (pow (sin x) 2.0))))
      t_0)
     (/
      (+ 2.0 (* (* (sqrt 2.0) (- 1.0 (cos y))) (* -0.0625 (pow (sin y) 2.0))))
      t_0))))

C

double code(double x, double y) {
	double t_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)));
	double tmp;
	if ((x <= -0.00075) || !(x <= 5.5e+19)) {
		tmp = (2.0 + ((sqrt(2.0) * (cos(x) + -1.0)) * (-0.0625 * pow(sin(x), 2.0)))) / t_0;
	} else {
		tmp = (2.0 + ((sqrt(2.0) * (1.0 - cos(y))) * (-0.0625 * pow(sin(y), 2.0)))) / t_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 = 3.0d0 * ((1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))) + (cos(y) * ((4.0d0 / (3.0d0 + sqrt(5.0d0))) / 2.0d0)))
    if ((x <= (-0.00075d0)) .or. (.not. (x <= 5.5d+19))) then
        tmp = (2.0d0 + ((sqrt(2.0d0) * (cos(x) + (-1.0d0))) * ((-0.0625d0) * (sin(x) ** 2.0d0)))) / t_0
    else
        tmp = (2.0d0 + ((sqrt(2.0d0) * (1.0d0 - cos(y))) * ((-0.0625d0) * (sin(y) ** 2.0d0)))) / t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_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)));
	double tmp;
	if ((x <= -0.00075) || !(x <= 5.5e+19)) {
		tmp = (2.0 + ((Math.sqrt(2.0) * (Math.cos(x) + -1.0)) * (-0.0625 * Math.pow(Math.sin(x), 2.0)))) / t_0;
	} else {
		tmp = (2.0 + ((Math.sqrt(2.0) * (1.0 - Math.cos(y))) * (-0.0625 * Math.pow(Math.sin(y), 2.0)))) / t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_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)))
	tmp = 0
	if (x <= -0.00075) or not (x <= 5.5e+19):
		tmp = (2.0 + ((math.sqrt(2.0) * (math.cos(x) + -1.0)) * (-0.0625 * math.pow(math.sin(x), 2.0)))) / t_0
	else:
		tmp = (2.0 + ((math.sqrt(2.0) * (1.0 - math.cos(y))) * (-0.0625 * math.pow(math.sin(y), 2.0)))) / t_0
	return tmp

Julia

function code(x, y)
	t_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))))
	tmp = 0.0
	if ((x <= -0.00075) || !(x <= 5.5e+19))
		tmp = Float64(Float64(2.0 + Float64(Float64(sqrt(2.0) * Float64(cos(x) + -1.0)) * Float64(-0.0625 * (sin(x) ^ 2.0)))) / t_0);
	else
		tmp = Float64(Float64(2.0 + Float64(Float64(sqrt(2.0) * Float64(1.0 - cos(y))) * Float64(-0.0625 * (sin(y) ^ 2.0)))) / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_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)));
	tmp = 0.0;
	if ((x <= -0.00075) || ~((x <= 5.5e+19)))
		tmp = (2.0 + ((sqrt(2.0) * (cos(x) + -1.0)) * (-0.0625 * (sin(x) ^ 2.0)))) / t_0;
	else
		tmp = (2.0 + ((sqrt(2.0) * (1.0 - cos(y))) * (-0.0625 * (sin(y) ^ 2.0)))) / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = 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]}, If[Or[LessEqual[x, -0.00075], N[Not[LessEqual[x, 5.5e+19]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], N[(N[(2.0 + N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]]]

Derivation

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

Alternative 14: 79.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - \sqrt{5}\\ t_1 := \sqrt{5} + -1\\ \mathbf{if}\;y \leq -0.0027 \lor \neg \left(y \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right) \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_1}{2}\right) + \cos y \cdot \frac{t_0}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left({\sin x}^{2} \cdot \left(\sqrt{2} \cdot \left(\cos x + -1\right)\right)\right)}{1 + 0.5 \cdot \left(t_0 + \cos x \cdot t_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 3.0 (sqrt 5.0))) (t_1 (+ (sqrt 5.0) -1.0)))
   (if (or (<= y -0.0027) (not (<= y 5.2e-15)))
     (/
      (+ 2.0 (* (* (sqrt 2.0) (- 1.0 (cos y))) (* -0.0625 (pow (sin y) 2.0))))
      (* 3.0 (+ (+ 1.0 (* (cos x) (/ t_1 2.0))) (* (cos y) (/ t_0 2.0)))))
     (*
      0.3333333333333333
      (/
       (+
        2.0
        (* -0.0625 (* (pow (sin x) 2.0) (* (sqrt 2.0) (+ (cos x) -1.0)))))
       (+ 1.0 (* 0.5 (+ 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 <= -0.0027) || !(y <= 5.2e-15)) {
		tmp = (2.0 + ((sqrt(2.0) * (1.0 - cos(y))) * (-0.0625 * pow(sin(y), 2.0)))) / (3.0 * ((1.0 + (cos(x) * (t_1 / 2.0))) + (cos(y) * (t_0 / 2.0))));
	} else {
		tmp = 0.3333333333333333 * ((2.0 + (-0.0625 * (pow(sin(x), 2.0) * (sqrt(2.0) * (cos(x) + -1.0))))) / (1.0 + (0.5 * (t_0 + (cos(x) * 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) :: tmp
    t_0 = 3.0d0 - sqrt(5.0d0)
    t_1 = sqrt(5.0d0) + (-1.0d0)
    if ((y <= (-0.0027d0)) .or. (.not. (y <= 5.2d-15))) then
        tmp = (2.0d0 + ((sqrt(2.0d0) * (1.0d0 - cos(y))) * ((-0.0625d0) * (sin(y) ** 2.0d0)))) / (3.0d0 * ((1.0d0 + (cos(x) * (t_1 / 2.0d0))) + (cos(y) * (t_0 / 2.0d0))))
    else
        tmp = 0.3333333333333333d0 * ((2.0d0 + ((-0.0625d0) * ((sin(x) ** 2.0d0) * (sqrt(2.0d0) * (cos(x) + (-1.0d0)))))) / (1.0d0 + (0.5d0 * (t_0 + (cos(x) * t_1)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 3.0 - Math.sqrt(5.0);
	double t_1 = Math.sqrt(5.0) + -1.0;
	double tmp;
	if ((y <= -0.0027) || !(y <= 5.2e-15)) {
		tmp = (2.0 + ((Math.sqrt(2.0) * (1.0 - Math.cos(y))) * (-0.0625 * Math.pow(Math.sin(y), 2.0)))) / (3.0 * ((1.0 + (Math.cos(x) * (t_1 / 2.0))) + (Math.cos(y) * (t_0 / 2.0))));
	} else {
		tmp = 0.3333333333333333 * ((2.0 + (-0.0625 * (Math.pow(Math.sin(x), 2.0) * (Math.sqrt(2.0) * (Math.cos(x) + -1.0))))) / (1.0 + (0.5 * (t_0 + (Math.cos(x) * t_1)))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 3.0 - math.sqrt(5.0)
	t_1 = math.sqrt(5.0) + -1.0
	tmp = 0
	if (y <= -0.0027) or not (y <= 5.2e-15):
		tmp = (2.0 + ((math.sqrt(2.0) * (1.0 - math.cos(y))) * (-0.0625 * math.pow(math.sin(y), 2.0)))) / (3.0 * ((1.0 + (math.cos(x) * (t_1 / 2.0))) + (math.cos(y) * (t_0 / 2.0))))
	else:
		tmp = 0.3333333333333333 * ((2.0 + (-0.0625 * (math.pow(math.sin(x), 2.0) * (math.sqrt(2.0) * (math.cos(x) + -1.0))))) / (1.0 + (0.5 * (t_0 + (math.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 <= -0.0027) || !(y <= 5.2e-15))
		tmp = Float64(Float64(2.0 + Float64(Float64(sqrt(2.0) * Float64(1.0 - cos(y))) * Float64(-0.0625 * (sin(y) ^ 2.0)))) / Float64(3.0 * Float64(Float64(1.0 + Float64(cos(x) * Float64(t_1 / 2.0))) + Float64(cos(y) * Float64(t_0 / 2.0)))));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(2.0 + Float64(-0.0625 * Float64((sin(x) ^ 2.0) * Float64(sqrt(2.0) * Float64(cos(x) + -1.0))))) / Float64(1.0 + Float64(0.5 * Float64(t_0 + Float64(cos(x) * t_1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 3.0 - sqrt(5.0);
	t_1 = sqrt(5.0) + -1.0;
	tmp = 0.0;
	if ((y <= -0.0027) || ~((y <= 5.2e-15)))
		tmp = (2.0 + ((sqrt(2.0) * (1.0 - cos(y))) * (-0.0625 * (sin(y) ^ 2.0)))) / (3.0 * ((1.0 + (cos(x) * (t_1 / 2.0))) + (cos(y) * (t_0 / 2.0))));
	else
		tmp = 0.3333333333333333 * ((2.0 + (-0.0625 * ((sin(x) ^ 2.0) * (sqrt(2.0) * (cos(x) + -1.0))))) / (1.0 + (0.5 * (t_0 + (cos(x) * t_1)))));
	end
	tmp_2 = 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, -0.0027], N[Not[LessEqual[y, 5.2e-15]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(1.0 - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[Power[N[Sin[y], $MachinePrecision], 2.0], $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[(t$95$0 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(2.0 + N[(-0.0625 * N[(N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(0.5 * N[(t$95$0 + N[(N[Cos[x], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 15: 79.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-8} \lor \neg \left(x \leq 0.0265\right):\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\cos x + -1\right)\right) \cdot \left(-0.0625 \cdot \left(0.5 - \frac{\cos \left(2 \cdot x\right)}{2}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(\sqrt{2} \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\right)}{3 \cdot \left(1 + \left(\left(t_0 + \cos y \cdot \left(1.5 - t_0\right)\right) - 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt 5.0) 0.5)))
   (if (or (<= x -4.6e-8) (not (<= x 0.0265)))
     (/
      (+
       2.0
       (*
        (* (sqrt 2.0) (+ (cos x) -1.0))
        (* -0.0625 (- 0.5 (/ (cos (* 2.0 x)) 2.0)))))
      (*
       3.0
       (+
        (+ 1.0 (* (cos x) (/ (+ (sqrt 5.0) -1.0) 2.0)))
        (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))))
     (/
      (+
       2.0
       (* (- (cos x) (cos y)) (* (sqrt 2.0) (* -0.0625 (pow (sin y) 2.0)))))
      (* 3.0 (+ 1.0 (- (+ t_0 (* (cos y) (- 1.5 t_0))) 0.5)))))))

C

double code(double x, double y) {
	double t_0 = sqrt(5.0) * 0.5;
	double tmp;
	if ((x <= -4.6e-8) || !(x <= 0.0265)) {
		tmp = (2.0 + ((sqrt(2.0) * (cos(x) + -1.0)) * (-0.0625 * (0.5 - (cos((2.0 * x)) / 2.0))))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
	} else {
		tmp = (2.0 + ((cos(x) - cos(y)) * (sqrt(2.0) * (-0.0625 * pow(sin(y), 2.0))))) / (3.0 * (1.0 + ((t_0 + (cos(y) * (1.5 - t_0))) - 0.5)));
	}
	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) * 0.5d0
    if ((x <= (-4.6d-8)) .or. (.not. (x <= 0.0265d0))) then
        tmp = (2.0d0 + ((sqrt(2.0d0) * (cos(x) + (-1.0d0))) * ((-0.0625d0) * (0.5d0 - (cos((2.0d0 * x)) / 2.0d0))))) / (3.0d0 * ((1.0d0 + (cos(x) * ((sqrt(5.0d0) + (-1.0d0)) / 2.0d0))) + (cos(y) * ((3.0d0 - sqrt(5.0d0)) / 2.0d0))))
    else
        tmp = (2.0d0 + ((cos(x) - cos(y)) * (sqrt(2.0d0) * ((-0.0625d0) * (sin(y) ** 2.0d0))))) / (3.0d0 * (1.0d0 + ((t_0 + (cos(y) * (1.5d0 - t_0))) - 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(5.0) * 0.5;
	double tmp;
	if ((x <= -4.6e-8) || !(x <= 0.0265)) {
		tmp = (2.0 + ((Math.sqrt(2.0) * (Math.cos(x) + -1.0)) * (-0.0625 * (0.5 - (Math.cos((2.0 * x)) / 2.0))))) / (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))));
	} else {
		tmp = (2.0 + ((Math.cos(x) - Math.cos(y)) * (Math.sqrt(2.0) * (-0.0625 * Math.pow(Math.sin(y), 2.0))))) / (3.0 * (1.0 + ((t_0 + (Math.cos(y) * (1.5 - t_0))) - 0.5)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(5.0) * 0.5
	tmp = 0
	if (x <= -4.6e-8) or not (x <= 0.0265):
		tmp = (2.0 + ((math.sqrt(2.0) * (math.cos(x) + -1.0)) * (-0.0625 * (0.5 - (math.cos((2.0 * x)) / 2.0))))) / (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))))
	else:
		tmp = (2.0 + ((math.cos(x) - math.cos(y)) * (math.sqrt(2.0) * (-0.0625 * math.pow(math.sin(y), 2.0))))) / (3.0 * (1.0 + ((t_0 + (math.cos(y) * (1.5 - t_0))) - 0.5)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(5.0) * 0.5)
	tmp = 0.0
	if ((x <= -4.6e-8) || !(x <= 0.0265))
		tmp = Float64(Float64(2.0 + Float64(Float64(sqrt(2.0) * Float64(cos(x) + -1.0)) * Float64(-0.0625 * Float64(0.5 - Float64(cos(Float64(2.0 * x)) / 2.0))))) / 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)))));
	else
		tmp = Float64(Float64(2.0 + Float64(Float64(cos(x) - cos(y)) * Float64(sqrt(2.0) * Float64(-0.0625 * (sin(y) ^ 2.0))))) / Float64(3.0 * Float64(1.0 + Float64(Float64(t_0 + Float64(cos(y) * Float64(1.5 - t_0))) - 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(5.0) * 0.5;
	tmp = 0.0;
	if ((x <= -4.6e-8) || ~((x <= 0.0265)))
		tmp = (2.0 + ((sqrt(2.0) * (cos(x) + -1.0)) * (-0.0625 * (0.5 - (cos((2.0 * x)) / 2.0))))) / (3.0 * ((1.0 + (cos(x) * ((sqrt(5.0) + -1.0) / 2.0))) + (cos(y) * ((3.0 - sqrt(5.0)) / 2.0))));
	else
		tmp = (2.0 + ((cos(x) - cos(y)) * (sqrt(2.0) * (-0.0625 * (sin(y) ^ 2.0))))) / (3.0 * (1.0 + ((t_0 + (cos(y) * (1.5 - t_0))) - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[5.0], $MachinePrecision] * 0.5), $MachinePrecision]}, If[Or[LessEqual[x, -4.6e-8], N[Not[LessEqual[x, 0.0265]], $MachinePrecision]], N[(N[(2.0 + N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[(0.5 - N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / 2.0), $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], N[(N[(2.0 + N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(-0.0625 * N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[(t$95$0 + N[(N[Cos[y], $MachinePrecision] * N[(1.5 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 16: 62.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \frac{2 + \left(\sqrt{2} \cdot \left(\cos x + -1\right)\right) \cdot \left(-0.0625 \cdot \left(0.5 - \frac{\cos \left(2 \cdot x\right)}{2}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (+
   2.0
   (*
    (* (sqrt 2.0) (+ (cos x) -1.0))
    (* -0.0625 (- 0.5 (/ (cos (* 2.0 x)) 2.0)))))
  (*
   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 + ((sqrt(2.0) * (cos(x) + -1.0)) * (-0.0625 * (0.5 - (cos((2.0 * x)) / 2.0))))) / (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 + ((sqrt(2.0d0) * (cos(x) + (-1.0d0))) * ((-0.0625d0) * (0.5d0 - (cos((2.0d0 * x)) / 2.0d0))))) / (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.sqrt(2.0) * (Math.cos(x) + -1.0)) * (-0.0625 * (0.5 - (Math.cos((2.0 * x)) / 2.0))))) / (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.sqrt(2.0) * (math.cos(x) + -1.0)) * (-0.0625 * (0.5 - (math.cos((2.0 * x)) / 2.0))))) / (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(sqrt(2.0) * Float64(cos(x) + -1.0)) * Float64(-0.0625 * Float64(0.5 - Float64(cos(Float64(2.0 * x)) / 2.0))))) / 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 + ((sqrt(2.0) * (cos(x) + -1.0)) * (-0.0625 * (0.5 - (cos((2.0 * x)) / 2.0))))) / (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[Sqrt[2.0], $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * N[(-0.0625 * N[(0.5 - N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / 2.0), $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

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1. Add Preprocessing

Alternative 17: 59.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ 0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left({\sin x}^{2} \cdot \left(\sqrt{2} \cdot \left(\cos x + -1\right)\right)\right)}{1 + 0.5 \cdot \left(\left(3 - \sqrt{5}\right) + \cos x \cdot \left(\sqrt{5} + -1\right)\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (*
  0.3333333333333333
  (/
   (+ 2.0 (* -0.0625 (* (pow (sin x) 2.0) (* (sqrt 2.0) (+ (cos x) -1.0)))))
   (+ 1.0 (* 0.5 (+ (- 3.0 (sqrt 5.0)) (* (cos x) (+ (sqrt 5.0) -1.0))))))))

C

double code(double x, double y) {
	return 0.3333333333333333 * ((2.0 + (-0.0625 * (pow(sin(x), 2.0) * (sqrt(2.0) * (cos(x) + -1.0))))) / (1.0 + (0.5 * ((3.0 - sqrt(5.0)) + (cos(x) * (sqrt(5.0) + -1.0))))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.3333333333333333d0 * ((2.0d0 + ((-0.0625d0) * ((sin(x) ** 2.0d0) * (sqrt(2.0d0) * (cos(x) + (-1.0d0)))))) / (1.0d0 + (0.5d0 * ((3.0d0 - sqrt(5.0d0)) + (cos(x) * (sqrt(5.0d0) + (-1.0d0)))))))
end function

Java

public static double code(double x, double y) {
	return 0.3333333333333333 * ((2.0 + (-0.0625 * (Math.pow(Math.sin(x), 2.0) * (Math.sqrt(2.0) * (Math.cos(x) + -1.0))))) / (1.0 + (0.5 * ((3.0 - Math.sqrt(5.0)) + (Math.cos(x) * (Math.sqrt(5.0) + -1.0))))));
}

Python

def code(x, y):
	return 0.3333333333333333 * ((2.0 + (-0.0625 * (math.pow(math.sin(x), 2.0) * (math.sqrt(2.0) * (math.cos(x) + -1.0))))) / (1.0 + (0.5 * ((3.0 - math.sqrt(5.0)) + (math.cos(x) * (math.sqrt(5.0) + -1.0))))))

Julia

function code(x, y)
	return Float64(0.3333333333333333 * Float64(Float64(2.0 + Float64(-0.0625 * Float64((sin(x) ^ 2.0) * Float64(sqrt(2.0) * Float64(cos(x) + -1.0))))) / Float64(1.0 + Float64(0.5 * Float64(Float64(3.0 - sqrt(5.0)) + Float64(cos(x) * Float64(sqrt(5.0) + -1.0)))))))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.3333333333333333 * ((2.0 + (-0.0625 * ((sin(x) ^ 2.0) * (sqrt(2.0) * (cos(x) + -1.0))))) / (1.0 + (0.5 * ((3.0 - sqrt(5.0)) + (cos(x) * (sqrt(5.0) + -1.0))))));
end

Wolfram

code[x_, y_] := N[(0.3333333333333333 * N[(N[(2.0 + N[(-0.0625 * N[(N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(0.5 * N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] + N[(N[Cos[x], $MachinePrecision] * N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 18: 42.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \frac{0.6666666666666666}{1 + 0.5 \cdot \left(\left(\sqrt{5} + -1\right) + \cos y \cdot \left(3 - \sqrt{5}\right)\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  0.6666666666666666
  (+ 1.0 (* 0.5 (+ (+ (sqrt 5.0) -1.0) (* (cos y) (- 3.0 (sqrt 5.0))))))))

C

double code(double x, double y) {
	return 0.6666666666666666 / (1.0 + (0.5 * ((sqrt(5.0) + -1.0) + (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 = 0.6666666666666666d0 / (1.0d0 + (0.5d0 * ((sqrt(5.0d0) + (-1.0d0)) + (cos(y) * (3.0d0 - sqrt(5.0d0))))))
end function

Java

public static double code(double x, double y) {
	return 0.6666666666666666 / (1.0 + (0.5 * ((Math.sqrt(5.0) + -1.0) + (Math.cos(y) * (3.0 - Math.sqrt(5.0))))));
}

Python

def code(x, y):
	return 0.6666666666666666 / (1.0 + (0.5 * ((math.sqrt(5.0) + -1.0) + (math.cos(y) * (3.0 - math.sqrt(5.0))))))

Julia

function code(x, y)
	return Float64(0.6666666666666666 / Float64(1.0 + Float64(0.5 * Float64(Float64(sqrt(5.0) + -1.0) + Float64(cos(y) * Float64(3.0 - sqrt(5.0)))))))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.6666666666666666 / (1.0 + (0.5 * ((sqrt(5.0) + -1.0) + (cos(y) * (3.0 - sqrt(5.0))))));
end

Wolfram

code[x_, y_] := N[(0.6666666666666666 / N[(1.0 + N[(0.5 * N[(N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $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

Reproduce

herbie shell --seed 2023350 
(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))))))